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The author or concept searched is found in the following 102 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Accessibility | Bigelow | I 126 Accessibility relation: can be restricted: for example, by the requirement that a possible world w from the accessible possible world u does not contain any individuals that do not also contain u. That is, that the one world is only a re-structured one of the other. This would e.g. contradict Lewis counterpart theory. >Possible worlds, >Possible worlds/Lewis, >Counterpart theory/Lewis. I 136 Definition weak centering/accessibility/Lewis/Bigelow/Pargetter: we will say that degrees of accessibility are weakly centered if no possible world is more accessible from a given possible world than this possible world itself. This is best satisfied with: d(w, w) = 0. N.b.: this ensures that some additional sentences will be true in all possible worlds, in addition to those guaranteed by the above axioms. These are derivable as theorems if we take the following axioms: A9 (reflexivity) and A16. (B would > would g)> (b> g) Everyday translation: no world can be more accessible to a world than this world is accessible to itself. This leaves open the possibility that some possible worlds have the accessibility "zero-distance" from the world w. Definition strong centering/Lewis/Bigelow/Pargetter: (in the semantics for counterfactual conditionals): no possible world can be accessible from a given world as this world is accessible from itself. This is best satisfied: If w is not equal to u, then either d(w, u) is undefined or d (w, u) > 0. This semantic condition allows a completeness proof for the axiom system which we obtain by adding the axiom of the strong centering to the above axioms: (a ∧ b)> (a would > would b) >Completeness. Counterfactual logic/Lewis/Bigelow/Pargetter: with these axioms, we get Lewis' favored counterfactual logic. BigelowVsStrong centering. Modal logic/Axiom system/Bigelow/Pargetter: our system will be the one Lewis calls VW: V ": "variably strict", "W". "Weakly centered". 139 Accessibility Relation/Bigelow/Pargetter: Problem: we must restrict it, and for a proof of completeness for S5, we must show that it is reflexive, transitive, and symmetric. >Systems S4/S5. S5/Canonical Model/Bigelow/Pargetter: does not only contain the Leibnizian necessity (truth in all worlds). S5: is interesting because it allows a reductionist access to possible worlds. >Reduction. Necessity: in the canonical model a proposition is necessarily true if it is true in all accessible possible worlds. >Necessity. Possible worlds: when they are designed as the maximum consistent extensions of S5, they disintegrate into different equivalence classes. ((s) i.e. for each world there is an additional sentence describing an individual with possibly different descriptions which do not contradict the other sentences). >Possible worlds, >Equivalence classes. Equivalence classes/accessibility/Bigelow/Pargetter: within an equivalence class, all worlds are accessible to one another. But between equivalence classes there is no accessibility from one possible world to the other. ((s), then the maximum consistent extensions must be something other than I suspected, then an extension will modify all existing propositions and makes them incomparable with a subset of the previous consistent set). >Maximum consistent. Accessibility/canonical model/Bigelow/Pargetter: in a canonical model, not all possible worlds are accessible to one another. >Canonicalness. We show it this way: Fa: (spelling: latin a) be an atomic sentence that can be added to the axioms of S5, or its negation, whereby the result being a maximally consistent set or world. With this, we are constructing a world where Fa is true. If it were accessible from all other worlds, MFa would be true in all possible worlds. But a proposition which is true in all worlds must be a theorem. But we know that Fa is not Problem: R2 (universal substitution) would ensure that Mα would be true for every α, even if α = (b u ~ b). Interpretation/Bigelow/Pargetter: if the intended interpretation of S5 is Leibnizean, as we hope ((s) necessity = truth in all worlds) then it follows that this intended interpretation of S5 is not captured by the canonical model. Possible world/Bigelow/Pargetter: that supports what we want to show, namely that possible worlds are not sets of sentences. Accessibility/Bigelow/Pargetter: ...and it also shows that the accessibility relation... I 140 ... which is relevant to alethic modal logic, is not an equivalence relation. Logical truth/Bigelow/Pargetter: is truth in all possible worlds (pro Leibniz!) not merely truth in all accessible worlds? >Logical truth. I 242 Accessibility Relation/Accessibility/Bigelow/Pargetter: nevertheless, we do not believe that the accessibility relation supervenes to properties and relations of the first level of the possible worlds, but on higher level universes! >Universals, >Supervenience. Two worlds can be perfectly similar in terms of universals of the first level and still have different accessibility relations! Humean World/Bigelow/Pargetter: is an example for the failure of the supervenience of the 1st level of the accessibility relation. >Humean world. For example, "all Fs are Gs", whereby F and G are universals of the 1st level, and higher-level universals that supervene on them. I 243 Counterfactual conditional: then also counterfactual conditionals should be valid like: "If this thing had been an F, it would have been a G". We would never be sure if it was a law, even if there were no exceptions. This uncertainty is reflected in uncertainty as to whether the counterfactual conditional is true. >Counterfactuals, >Counterfactual conditionals. Even if we live in a world with laws, we allow the possibility that this world is a Humean world. It might be that the generalization is correct, but without necessity. The world would look the same in both cases. Humean World/Bigelow/Pargetter: is, with respect to the actual world, precisely a world, which is the same, without laws. For other worlds there would be other Humean worlds. I 245 Accessibility/Bigelow/Pargetter: nevertheless, there are strong reasons to believe in a supervenience of the accessibility relation on the contents of the world. This allows us to assume that the contents of the 1st level do not exhaust all the contents of the world. Combinatorial theories. Therefore, must accept higher-level universals, and hence the property theory of the world's properties. Universals/Natural Law/Bigelow/Pargetter: Higher-level universals are the key to laws. >Levels/order, >Description levels. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| Analyticity/Syntheticity | Schurz | I 106 Analytic/Synthetic/SchurzVsQuine: his discarding of the distinction is problematic: the relation between language and world contains a conventional element. E.g. if it is not clear what "raven" means, one cannot hypothesize. And this conventional element is supposed to capture just the analytic. Analytic/Schurz/(s): is the result of the conventional determination of meaning in a language. Quine/Schurz: Quine's problem is that this conventional moment operates predominantly in an ostensive way. >Ostension, >Conventions, >Meaning, >Sense. I 171 Analytic/Synthetic/QuineVsCarnap/Schurz: Quine's insight into local indistinguishability brought a profound upheaval. Carnap accepted it late. >Analyticity/Quine. However, he had recognized that several reduction theorems together produce empirical content. (see above). ((s) if one has observed that something dissolves in water, one has thereby "empirically inferred" that it does not dissolve in oil?). Reduction/Schurz: but with the term "reduction theorem" he just remained true to his reductionist program. Assignment law/terminology/Schurz: Carnap (1956)(1) calls it "correspondence rules" (K). I 172 Total theory/Carnap: "T u K". ("theory and assignment laws"). Assignment law/SchurzVsCarnap: this cannot be, because assignment laws are consequences of a theory T, which follow from the interaction of all theorems. ((s) circular). Analyticity/Carnap: sums up in (Carnap 1963(2), 964) that he failed to formulate an appropriate notion. Solution/Carnap: decomposition of theory into Ramsey-theorem and Carnap-theorem: Ramsey-theorem/Carnap: synthetic Carnap-theorem/Carnap: analytic. Analytic/synthetic/Ernest Nagel: (Nagel 1961)(3) the analytic content of mechanics is not localizable! 1. Carnap, R. "The Methological Character of Theoretical Concepts". In: Feigle,H./Scriven, M(eds.) Minnesota Studies in the Philosophy of Science, Vol I, Menneapolis: Univ. of Minnesota Press, pp. 38-76. 2. Carnap, R. (1963) "Carl G. Hempel on Scientific Theories". In: Schilpp, P. A. (ed.) The Philosophy of Rudolf Carnap, La Salle, pp. 958-965. 3. Nagel, E. (1961). The Structure of Science, London: Routledge and Kegan Paul. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Arrow’s Theorem | Public Choice Theory | Parisi I 186 Arrow’s theorem/Public choice theory/Farber: Arrow's Theorem provides a (…) rigorous proof that cycling is impossible to avoid in an even wider set of decision methods.* Cf. >Jury theorem/Public choice theory. Arrow's Theorem and its progeny identify intrinsic limitations on group decision-making that stem from the existence of diverse preferences rather than from any human failing. Thus, the paradox of majority rule, where shifting majorities can produce cycles, is not merely a defect of one particular voting method but is a general characteristic of group decisions. But there are exceptions where the premises of these theorems do not hold, and these exceptions are of critical importance in designing political institutions. Symmetry/asymmetry: We can see that escaping from cycling requires somehow either breaking the symmetry between the various options in our earlier example or else limiting voter preferences so that this kind of symmetrical situation is avoided. This could happen in various ways: (1) some options might get special weight when they are held by particular voters; (2) an agenda might favor one of the options even though it would lose against another option if they ever came up for a vote together; (3) we might go beyond the rankings of each voter by adding information such as the intensity of voter preference; or (4) voter preferences may be asymmetrical—for example, the same option might be everyone's second choice. Essentially, these are all the available techniques for escaping Arrow's Theorem. The first way to break the symmetry between the options is to exclude symmetrical preferences from consideration. Most notably, it is possible to have coherent decision-making when everyone agrees that the choices can be arrayed on a single metric, with each voter preferring the option that is closest to her ideal outcome over those that are further way. Then the preferences are no longer symmetrical because voters agree that some alternatives are more extreme than Parisi I 187 others.** If preferences are single-dimensional, majority voting is the solution to the problem of producing coherent, stable outcomes. >Decision-making/Public choice theory. * Arrow includes choices involving more than two options, and uses the axiom of Independence of Irrelevant Alternatives to show that avoidance of cycling not only requires a violation of anonymity but also implies that one voter must be a dictator whose preferences always control (Arrow, 1951)(1). ** This can be generalized to the "value restriction" condition that for every alternative under consideration, every member of the group can agree that a given option is not worst, not best, or not in the middle (Shepsle, 2010(2), p. 84). 1. Arrow, K. J. (1951). social Choice and Individual values. New Haven, CT: Yale University Press. 2. Shepsle, K. A. (2010). Analyzing Politics: Rationality, Behavior, and Institutions. 2nd edition. New York: W.W. Norton & co. Farber, Daniel A. “Public Choice Theory and Legal Institutions”. In: Parisi, Francesco (ed) (2017). The Oxford Handbook of Law and Economics. Vol 1: Methodology and Concepts. NY: Oxford University Press |
Parisi I Francesco Parisi (Ed) The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017 |
| Axioms | Bigelow | I 119 Axioms/Intuition/Bigelow/Pargetter: nevertheless, intuitions should not be allowed to throw over entire axiom systems. E.g. the principle of distribution of the disjunction can be explained as follows: Suppose that in natural languages a conditional "If A, then B" is equivalent to a quantification over situations: "In all situations where A applies, B also applies." Then you could read the distribution of the disjunction like this: Logical form: (x)((Ax v Bx) would > would Cx) (x) (Ax would > would Cx) u (x)(Bx would > would Cx)). This is indisputably logical! >Distribution, >Disjunction, >Counterfactual conditional. Bigelow/Pargetter: therefore the quantified form seems to capture the everyday language better than the unquantified. E.g. "In any situation where you would eat..." This is then a logical truth. I 120 This again shows the interplay of language and ontology. Axioms/Realism/Bigelow/Pargetter: our axioms are strengthened by a robust realistic correspondence theory. And this is an argument for a conservative, classic logic. >Correspondence theory. I 133 Theorems/Bigelow/Pargetter: Need a semantic justification because they are derived. This is the foundation (soundness). >Foundation. Question: Will the theorems also be provable? Then it is about completeness. >Proofs, >Provability, >Completeness. Axioms/Axiom/Axiom system/Axiomatic/Bigelow/Pargetter: can be understood as a method of presenting an interpretation of the logical symbols without using a meta-language (MS). >Metalanguage. That is, we have here implicit definitions of the logical symbols. This means that the truth of the axioms can be seen directly. And everyone who understands it can manifest it by simply repeating it without paraphrasing it. >Definition, >Definability. 134 Language/Bigelow/Pargetter: ultimately we need a language which we speak and understand without first establishing semantic rules. In this language, however, we can later formulate axioms for a theory: that is what we call Definition "extroverted axiomatics"/terminology/Bigelow/Pargetter: an axiomatics that is developed in an already existing language. Definition introverted axiomatics/terminology/Bigelow/Pargetter: an axiomatics with which the work begins. Extrovert Axiomatics/Bigelow/Pargetter: has no problems with "metatheorems" and no problems with the mathematical properties of the symbols used. We already know what they mean. Understanding and accepting the axioms is one thing here. That is, the implicit definition precedes the explicit definition. We must understand what we are working with. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| Axioms | Cresswell | Hughes I 120 Axiomatization/propositional calculus/Hughes/Cresswell: done in other way than with the propositional calculus. Instead of axioms we use axiom schemes and parallel theorem schemes, i.e. general principles which determine that any well-formed formula (wff) of a certain shape is a theorem. >Theorems, >Propositional calculus, >Predicate calculus, >Predicate logic, >Propositional logic, >Axiom systems. |
Cr I M. J. Cresswell Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988 Cr II M. J. Cresswell Structured Meanings Cambridge Mass. 1984 Hughes I G.E. Hughes Maxwell J. Cresswell Einführung in die Modallogik Berlin New York 1978 |
| Axioms | Duhem | I 352 Hypotheses/Duhem: It is wrong to believe that the introduction of certain hypotheses is justified by means of theorems that are, so to speak, evidently derived from ordinary life. Often an analogy is quite superficial: it consists only between the words, but not between the thoughts. Nothing but word games. E.g. The expression entropy has only a meaning in the language of the physicist. I 355 Euler commits a circular conclusion: Definition: A power is the force that brings a body from rest to movement ... DuhemVsEuler: Will Euler take away the very former sense of the word power, and give a simple word definition, whose arbitrariness is limited by nothing? (> Definition). Word definitions are arbitrary. Euler has force or used in the everyday sense It is much less a definition than a theorem, to which Euler ascribes obviousness, it is an axiom. |
Duh I P. Duhem La théorie physique, son objet et sa structure, Paris 1906 German Edition: Ziel und Struktur der physikalischen Theorien Hamburg 1998 |
| Axioms | Field | I 220 Axiom/Field: a required law can easily be proven by adding it as an axiom - Vs: but then you need for each pair of distinct predicates an axiom that says that the first one and the second does not, e.g. "The distance between x and y is r times that between z and w". Everything that substantivalism or heavy-duty Platonism may introduce as derived theorems, relationism must introduce as axioms ("no empty space"). >Substantivalism >Relationism That leads to no correct theory. Problem of quantities. The axioms used would precisely be connectable if also non-moderate characterizations are possible. The modal circumstances are adequate precisely then when they are not needed. I 249ff Axiom/Mathematics/Necessity/Field: axioms are not logically necessary, otherwise we would only need logic and no mathematics. I 275 Axioms/Field: we then only accept those that have disquotationally true modal translations. - Because of conservativism. >Conservativity. Conservatism: is a holistic property, not property of the individual axioms. Acceptability: of the axioms: depends on the context. Another theory (with the same Axiom) might not be conservative. Disquotational truth: can be better explained for individual axioms, though. >Disquotationalism. I 276 E.g. Set theory plus continuum hypothesis and set theory without continuum hypothesis can each be true for their representatives. - They can attribute different truth conditions. - This is only non-objective for Platonism. >Platonism. The two representatives can reinterpret the opposing view, so that it follows from their own view. >Kurt Gödel, relative consistency. II 142 Axiom/(s): not part of the object language. Scheme formula: can be part of the object language. Field: The scheme formula captures the notion of truth better. >Truth/Field. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Axioms | Waismann | I 15 ff Axioms/Euclid/Waismann: Among the axioms of Euclid, two groups can be distinguished: A) General size axioms e.g. "Two sizes equal to a third are also equal to each other. The part is smaller than the whole, equal added to equal results in equals". B) The actual geometrical axioms 1. Each point can be connected to every point by a straight line. 2. Every straight line can be extended beyond each of its endpoints. 3. A circle can be drawn around each point with any radius. 4. All right angles are equal to each other. 5. If two straight lines are intersected by a third such that the angles on the inner side of the two lines to one side of the third give a sum less than two right angles, then the two straight lines intersect, sufficiently extended, on the mentioned side. ("Parallel Axiom") I 16 Parallel axiom/Euclid: in history, the parallel axiom (5th axiom Euclid's) was always controversial, and because of the complexity one tried to derive contradictions, without success. On the contrary, it could be proved that E.g. similar figures would be impossible if it were not true, or E.g. there should be a largest triangle in the plane. E.g. Lambert: without the parallel axiom there would be a length unit distinguished by nature. As absurd as all these results sound, they are not a logical contradiction (this time in favor of the axiom). Bolanyi and Lobatschefsky then developed consequently conclusions from the omission of the 5th axiom and did not encounter contradictions but a new geometry! Non-Euclidean Geometry. New problem: how do we know that assumptions will not lead to contradictions in the future? For the first time the problem of non-contradiction in mathematics arose. A direct proof of the consistency is obviously not an option, for this, infinite conclusion chains would have to be considered. Non-Euclidean Geometry: Felix Klein found in 1870 that the whole system of non-Euclidean geometry can be mapped to the Euclidean, so that any contradiction in the new system would lead to a contradiction in the old. According to a prescription, a concept of Euclidean geometry is assigned to each concept of non-Euclidean geometry as its image, just as every sentence of one theory corresponds to a sentence of the other,... >Geometry. I 17 ...so that both theories have the same logical form. Within the Euclidean geometry a "model" has been established for the non-Euclidean geometry. E.g. We imagine in the Euclidean plane a fixed circle k. We now make a lexicon: By a point we mean a point inside k By a straight line we understand the piece of a straight line that runs within k. Additional provisions regulate the possibility that an arbitrary distance on a straight line can be copied infinitely often without leaving the circle. This distance, measured according to the Euclidean scale, is, of course, always smaller. A being that moves from the center of the circle to the periphery becomes smaller and smaller and can never reach the circle's edge (but not Zeno). >Zeno, >About Zeno. Proof: This vivid reflection has nothing to do with the power of proof. For a geometry thus defined, all Euclidean axioms apply except for the fifth. Fig. I 17 Circle, with rays from a point in the inner of the circle to the outside, somewhere secant. The rays fall into two classes that cut the secant, and those who do not. These two classes are separated by two straight lines (also rays), which we call "parallels", because they intersect the secant (with which they at first glance form a triangle) only non-euclidically at infinity. All the theorems of Euclidean geometry, with the exception of the fifth axiom, are in the circle consistent. I 18 But this is not an absolute consistency-proof. If there was a contradiction in the Euclidean geometry, the latter would also have to be applied in the theory of the real numbers. >Proofs, >Provability. >Real numbers. |
Waismann I F. Waismann Einführung in das mathematische Denken Darmstadt 1996 Waismann II F. Waismann Logik, Sprache, Philosophie Stuttgart 1976 |
| Bayesianism | Putnam | V 252f Bayes-Theorem/Putnam: the Bayes-Theorem implies the acceptance of a certain number of reliable observation records in an observation language. >Observation, >Observation language, >Observation sentence, >Conditional probability, >Probability. MethodsVsFetishism: the Bayes-Theorem suggests that division into formal and non-formal part is possible. PutnamVsBayes: differences in the functions of the output probability lead to irrational large differences in the actual confirmation degrees of theorems. PutnamVsSeparation: the definition of the formal part of the scientific method guarantees no rationality. |
Putnam I Hilary Putnam Von einem Realistischen Standpunkt In Von einem realistischen Standpunkt, Vincent C. Müller Frankfurt 1993 Putnam I (a) Hilary Putnam Explanation and Reference, In: Glenn Pearce & Patrick Maynard (eds.), Conceptual Change. D. Reidel. pp. 196--214 (1973) In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (b) Hilary Putnam Language and Reality, in: Mind, Language and Reality: Philosophical Papers, Volume 2. Cambridge University Press. pp. 272-90 (1995 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (c) Hilary Putnam What is Realism? in: Proceedings of the Aristotelian Society 76 (1975):pp. 177 - 194. In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (d) Hilary Putnam Models and Reality, Journal of Symbolic Logic 45 (3), 1980:pp. 464-482. In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (e) Hilary Putnam Reference and Truth In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (f) Hilary Putnam How to Be an Internal Realist and a Transcendental Idealist (at the Same Time) in: R. Haller/W. Grassl (eds): Sprache, Logik und Philosophie, Akten des 4. Internationalen Wittgenstein-Symposiums, 1979 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (g) Hilary Putnam Why there isn’t a ready-made world, Synthese 51 (2):205--228 (1982) In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (h) Hilary Putnam Pourqui les Philosophes? in: A: Jacob (ed.) L’Encyclopédie PHilosophieque Universelle, Paris 1986 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (i) Hilary Putnam Realism with a Human Face, Cambridge/MA 1990 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (k) Hilary Putnam "Irrealism and Deconstruction", 6. Giford Lecture, St. Andrews 1990, in: H. Putnam, Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992, pp. 108-133 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam II Hilary Putnam Representation and Reality, Cambridge/MA 1988 German Edition: Repräsentation und Realität Frankfurt 1999 Putnam III Hilary Putnam Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992 German Edition: Für eine Erneuerung der Philosophie Stuttgart 1997 Putnam IV Hilary Putnam "Minds and Machines", in: Sidney Hook (ed.) Dimensions of Mind, New York 1960, pp. 138-164 In Künstliche Intelligenz, Walther Ch. Zimmerli/Stefan Wolf Stuttgart 1994 Putnam V Hilary Putnam Reason, Truth and History, Cambridge/MA 1981 German Edition: Vernunft, Wahrheit und Geschichte Frankfurt 1990 Putnam VI Hilary Putnam "Realism and Reason", Proceedings of the American Philosophical Association (1976) pp. 483-98 In Truth and Meaning, Paul Horwich Aldershot 1994 Putnam VII Hilary Putnam "A Defense of Internal Realism" in: James Conant (ed.)Realism with a Human Face, Cambridge/MA 1990 pp. 30-43 In Theories of Truth, Paul Horwich Aldershot 1994 SocPut I Robert D. Putnam Bowling Alone: The Collapse and Revival of American Community New York 2000 |
| Carnap-Sentence | Schurz | I 214 Carnap-sentence/CS/C (T)/Schurz: (Carnap 1963(1), 965) had the idea to supplement the Ramsey-sentence by the following analytic theorem: ((s) elsewhere: "Carnap conditional"): C(T): R(T) > T Everyday language/(s): the Carnap-sentence states: if the Ramsey-sentence is true (i.e. if the theoretical entities exist), the theory follows from it. Carnap-sentence/(s): the meaning characterization of the theoretical terms that C(T) provides says: the n-tuple of TT (τ1,...τn) I 215 denotes an n-tuple (X1,...Xn) of entities satisfying the theoretical assertion T(X1,...Xn), provided there is such an n-tuple of entities. Theoretical Terms/meaning/Theory/Carnap/Schurz: This brings the thesis that the meaning of theoretical terms is determined by the theory itself to its logical concept. Ramsey-sentence/Carnap-sentence/Schurz: The conjunction of the two is L-equivalent with the theory itself. I.e. II- R(T) u C(T) <> T Carnap-sentence/Schurz: C(T) L-implies no non-tautological empirical theorem! I.e. E(C(T)) = E(0). Therefore the Carnap theorem is analytic. Analytic/Synthetic/Carnap/Schurz: Thus Carnap has divided global theories into a synthetic part (Ramsey-sentence) and an analytic part (Carnap-sentence). But this is still not possible with respect to the individual axioms and theorems. >Ramsey-sentence. Carnap-sentence: does not provide a meaning characterization for individual Theoretical terms, but only one for all of them together. And it provides only a partial meaning characterization of Theoretical terms. Definition/Theoretical terms/Carnap-sentence/Schurz: For a full meaning characterization in the sense of an explicit definition, the extension of the Definiendum in all Possible Worlds would have to be uniquely determined by the extension of the Definiens Terms. However, the Carnap Theorem fixes the extension only in those Possible Worlds in which there is exactly one n-tuple of entities (X1,...Xn) satisfying T(X1,...Xn). If there are more than one, the reference is ambiguous, if there is no such n-tuple at all, the Theoretical terms are denotational. Then the theory is wrong. >Theoretical terms. 1. Carnap, R. (1963) "Carl G. Hempel on Scientific Theories". In: Schilpp, P. A. (ed.) The Philosophy of Rudolf Carnap, La Salle, pp. 958-965. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Communication Models | Economic Theories | Kranton I 423 Communication Models/Bloch/Demange/Kranton/Economic Theories: (…) the model [by Bloch, Demange and Kranton] combines two classic elements of information games: “cheap talk” (Crawford and Sobel, 1982)(1) in the decision of the initial receiver of the signal as to whether or not to create a truthful message, and “persuasion” (Milgrom, 1981(2); Milgrom and Roberts, 1986(3)) in the decision of agents who subsequently choose whether to transmit the message, which they cannot transform. In our model, there are multiple equilibria, along the lines of cheap talk games. However, as in persuasion games, at the transmission stage agents have an incentive to pass on credible information to other agents. In our model (Bloch/Demange/Kranton), there is a single unknown source of information and agents are Bayesian, but due to differences in their preferences and the possibility of falsification and blocking, they may end up with different beliefs and choose different actions. >Misinformation/Economic Theories, >Communication Models/Kranton. 1. CRAWFORD, V. P., AND J. SOBEL, “Strategic Information Transmission,” Econometrica 50 (6) (1982), 1431–51. 2. MILGROM, P. R., “Good News and Bad News: Representation Theorems and Applications,” Bell Journal of Economics 12 (2), (1981), 380–91. 3. MILGROM, P., AND J. ROBERTS, “Relying on the Information of Interested Parties,” Rand Journal of Economics 17 (1986), 18–32. Francis Bloch, Gabrielle Demange & Rachel Kranton, 2018. "Rumors And Social Networks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(2), pages 421-448. |
Kranton I Rachel E. Kranton Francis Bloch Gabrielle Demange, Rumors And Social Networks 2018 Kranton II Rachel E. Kranton George A. Akerlof Identity Economics: How Our Identities Shape Our Work, Wages, and Well-Being Princeton 2011 |
| Completeness | Bigelow | I 134 Completeness/Bigelow/Pargetter: completeness occurs when our explicit semantics guarantees all and only the extroverted asserted theorems. That is, our semantics does not read anything into our language, which is not already there. >Semantics/Bigelow. Def "extroverted axiomatics"/Terminology/Bigelow/Pargetter: an axiomatics that is developed in an already existing language. >Axioms, >Axiom systems. I 135 Completeness/correspondence theory/Bigelow/Pargetter: the existence of completeness proofs provides a kind of correspondence theory. >Correspondence theory, >Proofs, >Provability. Completeness: for us, we can show that all the propositions that are true to our semantics in all possible worlds can be derived. >Derivation, >Derivability, >Possible worlds. I 137 Def completeness theorem/Bigelow/Pargetter: is a theorem that proves that if a proposition in a certain semantics is assuredly true, this proposition can be proved as a theorem. How can we prove this? How can we prove that each such proposition is a theorem? Solution: we prove the contraposition of the theorem: Instead: If a is assuredly true in semantics, a is a theorem. We prove: If a is not a theorem, it is not assuredly true in semantics. We prove this by finding an interpretation according to which it is false. >Falsification, >Verification, >Verifiability. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| Conceptualism | Quine | XI 136 Intuitionism/Quine/Lauener: he compares it with ancient conceptualism: universals are created by the mind. VII (f) 125 ConceptualismVsPlatonism/Quine: treats classes as constructions, not as discoveries - Problem: Poincaré's "impredicative" definition: Def impredicative/Def Poincaré: "impredicative" means the specification of a class through a realm of objects, within which that class is located. VII (f) 126 Classes/Conceptualism/Quine: for him, classes only exist if they originate from an ordered origin. Classes/Conceptualism/Quine: conceptualism does not require classes to exist beyond conditions of belonging to elements that can be expressed. Cantor's proof: would entail something else: It appeals to a class h of those elements of class k which are not elements of the subclasses of k to which they refer. VII (f) 127 But this is how the class h is specified impredicatively! h is itself one of the partial classes of k. >Classes/Quine. Thus a theorem of classical mathematics goes overboard in conceptualism. The same fate strikes Cantor's proof of the existence of supernumerary infinity. QuineVsConceptualism: this is a welcome relief, but there are problems with much more fundamental and desirable theorems of mathematics: e.g. the proof that every limited sequence of numbers has an upper limit. VII (a) 14 Universals Dispute/Middle Ages/Quine: the old groups reappear in modern mathematics: Realism: Logicism Conceptualism: Intuitionism Nominalism: Formalism. Conceptualism/Middle Ages/Quine: holds on to universals, but as mind-dependent. ConceptualismVsReduceability Axiom: because the reduceability axiom reintroduces the whole platonistic class logic. >Universals/Quine. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Condorcet Jury Theorem | Condorcet | Parisi I 494 Condorcet Jury Theorem/Condorcet/Nitzan/Paroush: Condorcet (1785)(1) makes the following three-part statement: 1) The probability that a team of decision-makers would collectively make the correct decision is higher than the probability that any single member of the team makes such a decision. 2) This advantage of the team over the individual performance monotonically increases with the size of the team. Parisi I 495 3) There is a complete certainty that the team’s decision is right if the size of the team tends to infinity, that is, the probability of this event tends to one with the team’s size. A “Condorcet Jury Theorem” (henceforth, CJT) is a formulation of sufficient conditions that validate the above statements. There are many CJTs, but Laplace (1815)(2) was the first to propose such a theorem. >Condorcet Jury Theorem/Laplace. Parisi I 496 VsCondorcet: In contrast to the first two parts of Condorcet’s statement, the survival of the third part is somehow surprising. Many attempts have been made to prove the validity of the third part in case of heterogeneous teams (see Boland, 1989(3); Fey, 2003(4); Kanazawa, 1998(5); and Owen, Grofman, and Feld, 1989(6)). 1. De Condorcet, N. C. (1785). Essai sur l’application de l’analyse a la probabilite des decisions rendues a la pluralite des voix. Paris: De l’imprimerie royale. 2. Laplace, P. S. de (1815). Theorie analytique des probabilities. Paris: n.p. 3. Boland, P. J. (1989). “Majority systems and the Condorcet jury theorem.” The Statistician 38(3): 181–189. 4. Fey, M. (2003). “A note on the Condorcet jury theorem with supermajority rules.” Social Choice and Welfare 20(1): 27-32. 5. Kanazawa, S. (1998). “A brief note on a further refinement of Condorcet Jury Theorem for heterogenous groups.” Mathematical Social Sciences 35(1): 69-73. 6. Owen, G., B. Grofman, and S. Feld (1989). “Proving a distribution free generalization of the Condorcet jury theorem.” Mathematical Social Sciences 17(1): 1-16. Shmuel Nitzan and Jacob Paroush. “Collective Decision-making and the Jury Theorems”. In: Parisi, Francesco (ed) (2017). The Oxford Handbook of Law and Economics. Vol 1: Methodology and Concepts. NY: Oxford University. |
Condo I N. de Condorcet Tableau historique des progrès de l’ esprit humain Paris 2004 Parisi I Francesco Parisi (Ed) The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017 |
| Condorcet Jury Theorem | Economic Theories | Parisi I 494 Condorcet Jury Theorem/Economic theories/Nitzan/Paroush: Condorcet (1785)(1) makes the following three-part statement: 1) The probability that a team of decision-makers would collectively make the correct decision is higher than the probability that any single member of the team makes such a decision. 2) This advantage of the team over the individual performance monotonically increases with the size of the team. Parisi I 495 3) There is a complete certainty that the team’s decision is right if the size of the team tends to infinity, that is, the probability of this event tends to one with the team’s size. A “Condorcet Jury Theorem” (henceforth, CJT) is a formulation of sufficient conditions that validate the above statements. There are many CJTs, but Laplace (1815)(2) was the first to propose such a theorem. >Condorcet Jury Theorem/Laplace. Parisi I 496 VsCondorcet: In contrast to the first two parts of Condorcet’s statement, the survival of the third part is somehow surprising. Many attempts have been made to prove the validity of the third part in case of heterogeneous teams (see Boland, 1989(3); Fey, 2003(4); Kanazawa, 1998(5); and Owen, Grofman, and Feld, 1989(6)). In fact, the following is a well-known version of CJT: “If a team of decision-makers utilizes a simple majority rule, the decision would be perfectly correct in the limit given that the size of Parisi I 497 the team tends to infinity, even if the individual competencies, the pis, are different, provided that pi ≥ 1∕2+ε, where the value of ε is a positive constant regardless of how small it is.” The proof of the theorem relies on the proof of Laplace where P = 1∕2+ε combined with the fact that Π is an increasing function of the team members’ competencies. >Decision theory, >Decision-making processes. 1. De Condorcet, N. C. (1785). Essai sur l’application de l’analyse a la probabilite des decisions rendues a la pluralite des voix. Paris: De l’imprimerie royale. 2. Laplace, P. S. de (1815). Theorie analytique des probabilities. Paris: n.p. 3. Boland, P. J. (1989). “Majority systems and the Condorcet jury theorem.” The Statistician 38(3): 181–189. 4. Fey, M. (2003). “A note on the Condorcet jury theorem with supermajority rules.” Social Choice and Welfare 20(1): 27-32. 5. Kanazawa, S. (1998). “A brief note on a further refinement of Condorcet Jury Theorem for heterogenous groups.” Mathematical Social Sciences 35(1): 69-73. 6. Owen, G., B. Grofman, and S. Feld (1989). “Proving a distribution free generalization of the Condorcet jury theorem.” Mathematical Social Sciences 17(1): 1-16. Shmuel Nitzan and Jacob Paroush. “Collective Decision-making and the Jury Theorems”. In: Parisi, Francesco (ed) (2017). The Oxford Handbook of Law and Economics. Vol 1: Methodology and Concepts. NY: Oxford University. |
Parisi I Francesco Parisi (Ed) The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017 |
| Condorcet Jury Theorem | Laplace | Parisi I 495 Condorcet Jury Theorem/Laplace/Nitzan/Paroush: (Laplace, 1815(1)) Specification of the problem faced by the jury: 1) There are two alternatives. 2) The alternatives are symmetric. Specification of the decision rule applied by the team: 3) The team applies the simple majority rule. Specification of the properties of the jury members: 4) All members possess identical competencies. 5) The decisional competencies are fixed. 6) All members share identical preferences. Specification of the behavior of the jury members: 7) Voting is independent. 8) Voting is sincere. Parisi I 496 The core of Laplace’s proof is the calculation of the probability of making the right collective decision (to be denoted by Π), where Π is calculated by using Bernoulli’s theorem (1713). Laplace shows, first, that Π is larger than the probability of making the right decision P by any single member of the team; second, that Π is a monotone increasing function of the size of the team; and third, that Π tends to unity with the size of the team. Of course, besides the above conditions there is an additional trivial condition that the decisional capabilities of decision-makers are not worse than that of tossing a fair coin. Namely, the probability P of making the correct decision is not less than one-half. Other properties of Π are that it is monotone increasing and concave in the size of the team, n, and in the competence of the individuals, P. Thus, given the costs and benefits of the team members’ identical competence, one can find the optimal size of a team and the optimal individual’s competence by comparing marginal costs to marginal benefits. >Jury theorem, >Marginal costs, >Decision theory, >Decision-making processes. 1. Laplace, P. S. de (1815). Theorie analytique des probabilities. Paris: n.p. Shmuel Nitzan and Jacob Paroush. “Collective Decision-making and the Jury Theorems”. In: Parisi, Francesco (ed) (2017). The Oxford Handbook of Law and Economics. Vol 1: Methodology and Concepts. NY: Oxford University. |
Parisi I Francesco Parisi (Ed) The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017 |
| Connectives | Putnam | I (c) 87 Interpretation/Putnam: interpretation is not a representation, but production. >Logical constants. E.g. classical connectives are not represented using the intuitionistic connectives, but the classical theorems are produced. >Intuitionism. Putnam: the meaning of the connectives is still not classic, because these meanings are explained by means of provability and not by truth. Change of meaning: e.g. assuming we wanted to formulate Newton's laws in intuitionistic mathematics, then we would have to limit the real numbers (for example, on the 30th decimal). I (c) 88 Then, in the classical theory, the connectives would refer to "provability in B1" and in the other to "provability in B2". Then the connectives would change their meaning when knowledge changes. I (c) 95 Realism/Putnam: the realistic conception of connectives ensures that a statement is not solely true because it follows a (any) theory. I (c) 96 Ideal Assertibility/PutnamVsPeirce: no "ideal limit" can be specified reasonably. It is not used to specify any conditions for science. >>Peirce. PutnamVsKuhn: if you do not believe in convergence but in revolutions, you should interpret the connectives intuitionistically and apprehend truth intra-theoretically. >Kuhn. I (c) 97 Truth/logic/Putnam: the meaning of "true" and the connectives are not determined by their formal logic -> Holism/Quine: the distinction between the entire theory and individual statement meanings is useless. |
Putnam I Hilary Putnam Von einem Realistischen Standpunkt In Von einem realistischen Standpunkt, Vincent C. Müller Frankfurt 1993 Putnam I (a) Hilary Putnam Explanation and Reference, In: Glenn Pearce & Patrick Maynard (eds.), Conceptual Change. D. Reidel. pp. 196--214 (1973) In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (b) Hilary Putnam Language and Reality, in: Mind, Language and Reality: Philosophical Papers, Volume 2. Cambridge University Press. pp. 272-90 (1995 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (c) Hilary Putnam What is Realism? in: Proceedings of the Aristotelian Society 76 (1975):pp. 177 - 194. In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (d) Hilary Putnam Models and Reality, Journal of Symbolic Logic 45 (3), 1980:pp. 464-482. In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (e) Hilary Putnam Reference and Truth In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (f) Hilary Putnam How to Be an Internal Realist and a Transcendental Idealist (at the Same Time) in: R. Haller/W. Grassl (eds): Sprache, Logik und Philosophie, Akten des 4. Internationalen Wittgenstein-Symposiums, 1979 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (g) Hilary Putnam Why there isn’t a ready-made world, Synthese 51 (2):205--228 (1982) In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (h) Hilary Putnam Pourqui les Philosophes? in: A: Jacob (ed.) L’Encyclopédie PHilosophieque Universelle, Paris 1986 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (i) Hilary Putnam Realism with a Human Face, Cambridge/MA 1990 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (k) Hilary Putnam "Irrealism and Deconstruction", 6. Giford Lecture, St. Andrews 1990, in: H. Putnam, Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992, pp. 108-133 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam II Hilary Putnam Representation and Reality, Cambridge/MA 1988 German Edition: Repräsentation und Realität Frankfurt 1999 Putnam III Hilary Putnam Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992 German Edition: Für eine Erneuerung der Philosophie Stuttgart 1997 Putnam IV Hilary Putnam "Minds and Machines", in: Sidney Hook (ed.) Dimensions of Mind, New York 1960, pp. 138-164 In Künstliche Intelligenz, Walther Ch. Zimmerli/Stefan Wolf Stuttgart 1994 Putnam V Hilary Putnam Reason, Truth and History, Cambridge/MA 1981 German Edition: Vernunft, Wahrheit und Geschichte Frankfurt 1990 Putnam VI Hilary Putnam "Realism and Reason", Proceedings of the American Philosophical Association (1976) pp. 483-98 In Truth and Meaning, Paul Horwich Aldershot 1994 Putnam VII Hilary Putnam "A Defense of Internal Realism" in: James Conant (ed.)Realism with a Human Face, Cambridge/MA 1990 pp. 30-43 In Theories of Truth, Paul Horwich Aldershot 1994 SocPut I Robert D. Putnam Bowling Alone: The Collapse and Revival of American Community New York 2000 |
| Consistency | Henkin | Quine IX 224 Henkin: shows the consistency of a ω-contradictory (omega-contradictory) system. (Also Goedel and Tarski). Just interpret "F" as true for all but those objects x that fulfill (7). (7) x ε N, x ≠ 0, x ≠ 1, x ≠ 2... ad infinitum >Sets/Henkin. A theory that is ω-contradictory seems unacceptable even if it is consistent. But according to Henkin, it is easy to see that the term and its definition are misleading. If a system is consistent and yet allows "Ex(x e N u ~Fx)" and "F0", "F1"...all as theorems, and if we guarantee the interpretation of "0" , "1" etc. as names of numbers, then the problem seems to be to interpret "N" as "number" and not more comprehensive. Henkin: shows that "N" can be interpreted as N containing extras even under the most favorable circumstances. (See Sets/Henkin) If the system is ω-contradictory, N must even be interpreted that way. ((s) "Extras": e.g. "...and their successors"). Sometimes it is then possible to limit "N" so that it avoids the extras, and sometimes this is not possible. For example, for every formifiable condition that is verifiably met by 0,1,2... ad infinitum, there is another condition that we can prove is also met by 0,1,2... and yet not by all things that meet the first condition. This is the chronic form of ω-contradictoriness that cannot be cured by an improved version of "N". (Quine: "numerically insegregative"). >Löwenheim. Def Omega-contradictory/(w)/Goedel: (Goedel 1931) is a system when there is a formula "Fx" such that any one of the statements "F0", "F1", "F2",... can be proved ad infinitum in the system, but also "Ex(x ε N and ~Fx)". >Contradictions, >Proofs, >Provability. |
Henkin I Leon Henkin Retracing elementary mathematics New York 1962 Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Constructivism | Quine | XIII 33 Constructivism/Mathematics/Quine: (VsUniversals). Thesis: theorems that can be shown constructively should be preferred. Def Constructivism/Mathematics/Quine: Thesis: any abstract object is specifiable. Against: Predicative Set Theory: is too weak to prove that there must be unspecifiable classes and unspecifiable real numbers. Quantification/Variables/Quine: the quantification is different if it is certain that every object in the domain is specifiable. For example, the natural numbers are such a domain. This is because there is an Arabic number for each of them. Def Substitutional Quantification/sQ/Quine: (Universal Quantification (x)): the formula preceding the quantifier becomes true under any grammatically permissible substitution for the letter "x". Referential Quantification/refQ/Substitutional Quantification: For example, natural numbers: here both are the same. >Substitutional Quantification/Quine. On the other hand: If not all objects can be specified: If not all objects in a domain can be specified by singular terms of the language used, then the two types of quantification diverge. For example, if the universal quantifier is fulfilled by all specifiable objects, but not by the non-specifiable ones, then the substitutional quantification is true and the referential quantification is false. Existential Quantification/EQu/Substitutional Quantification/refQ/Quine: behaves accordingly. XIII 35 Substitutional Quantification/Referential Quantification: diverge in the case of existential quantification if the formula is satisfied by some unspecifiable, but not by any specifiable one. Substitutional Quantification/Quine: is unrealistic for concrete objects. Specifiability/Name/Namability/namable/Quine: Question: is each concrete object individually specifiable? For example every past or future bee, every atom and every electron? Yes, by numerical coordinates with rational numbers. But unlimited referential quantification is simply more natural here. Predicative set theory: here substitutional quantification is more attractive and manageable because abstract objects are parasitic in relation to language, in a way that concrete objects are not. Abstract/Charles Parsons/Quine: abstract objects are parasitic in relation to language, concrete objects are less parasitic. Substitutional Quantification/Quine: does not simply eliminate abstract objects from ontology, but grants them a "thinner" kind of existence. Abstract/Quine: expressions themselves are abstract, but not as wild as the inhabitants of higher set theory. Substitutional Quantification/Quine: is a compromise with militant nominalism. Abstract Objects/Quine: are then classes, like those of predicative set theory (RussellVs). >Abstractness/Quine. Substitutional Quantification/Referential Quantification/Parsons: has shown how both go together (Lit). By using two kinds of variables. Then you can also link them together (intertwine). Problem/Russell: predicative set theory is inadequate for the classical mathematics of real numbers. XIII 36 Real Numbers/Russell/Quine: their theory leads to unspecifiable real numbers and other unspecifiable classes. Substitutional Quantification/Quine: this problem did not lead to the substitutional quantification by itself. Constructive Mathematics/Constructivism/QuineVsBrouwer: heated minds developed and still develop constructive mathematics that are suitable for all sciences. Problem: this leads to unattractive deviations from standard logic. Standard Logic/Constructivism/Quine: Experiments with standard logic: Weyl, Paul Lorenzen, Erret Bishop. Hao Wang, Sol Feferman. These are solutions with predicative set theory together with artistic circles. Problem: you do not know exactly how much mathematics scientists need. Nominalism/Quine: we probably do not need nominalism through and through, but an attractive approach to it. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Continuum | Quine | XIII 45 Def Discrete/Discreteness/Quine: an order of numbers or other objects is discrete if each object has an immediate predecessor or successor or both. For example, the integers are discrete. One the other hand: Def dense: fractions are dense and not discrete. Real numbers: are more than dense: they are continuous. Discrete/continuous: here we compare them as opposites. Discreteness: we need it to learn to count by distinguishing the objects. Irrational Numbers/Cantor: Theorem: most will always escape us. Number Theory: deals with integers. Real numbers: are used by the sciences. The contrast of both is illuminated by a pair of theorems: Goedel's Theorem: no proof procedure can encompass all truths of elementary number theory. Tarski's theorem: truth in the parallel theory of real numbers can be checked routinely, e.g. by a computer. N.B.: both systems are identical in their notation! The difference lies in the different interpretation of the variables (or their domains, one time the positive integers with the 0, the other time the positive real numbers with the 0). XIII 47 This leads to a difference in the truth of the formulas! a) real numbers: here the true formulas are a set that can be handled b) elementary number theory: not here. Continuity/Discreteness/Language/Quine: the interaction of the two terms is not limited to mathematics, it also exists in language: phonemes impose discreteness on the phonetic continuum. Discreteness/Quine: also allows yellowed or damaged manuscripts to be returned to a fresh state. The discreteness of the alphabet helps that the small deviations (e.g. yellowing) add up to larger ones. Continuum/Continuity: images, on the other hand, are a continuous medium: i.e. there are no standards for repairing a damaged copy or correcting a poor copy. Technology: here discreteness is often combined with continuity. Example clock: it should give the impression of moving continuously. XIII 48 Film/Quine: Continuity here is due to the weakness of our perception. Similar to the clock or our thinking about atoms over the millennia. Planck time/Quine: here we have the next approach of nature to continuity. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Decidability | Hilbert | Berka I 331 Undecidability/Predicate calculus 1st level/Goedel(1931)(1): Goedel shows with the "Arithmetication" ("Goedelisation") that the predicate calculus of the 1st level is undecidable. >Undecidability, >Gödel numbers. This was a shocking fact for the Hilbert program. Tarski (1939)(2): Tarski proved the undecidability of "Principia Mathematica" and related systems. He showed that it is fundamental, i.e. that it cannot be abolished. Rosser(3): Rosser generalized Goedel's proof by replacing the condition of the ω-consistency by that of simple consistency. >Consistency. 1. K. Goedel: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I., Mh. Math. Phys. 38, pp. 175-198. 2. A. Tarski: On undecidable statements in enlarged systems of logic and the concept of truth, JSL 4, pp. 105-112. 3. J. B. Rosser: Extensions of some theorems of Goedel and Church, JSL 1, pp. 87-91. |
Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Decision Rules | Democratic Theory | Parisi I 497 Decision Rules/democratic theory/decision-making processes/democracy/Nitzan/Paroush: Allowing heterogeneous decisional capabilities, Shapley and Grofman (1981, 1984)(1) and Nitzan and Paroush (1982(2), 1984b(3)) find that the optimal decision rule is a weighted majority rule (WMR) rather than a simple majority rule (SMR). By maximization of the likelihood that the team makes the better of the two choices it confronts, they also establish that the optimal weights are proportional to the log of the odds of the individuals’ competencies, that is, the weights, wi, are proportional to log[pi ∕(1-pi)]. Parisi I 498 For instance, in a five-member team there exist seven different efficient potentially optimal rules. These rules include the “almost expert rule,” the “almost majority rule,” and the “tie-breaking chairman rule.” The number of efficient rules increases very rapidly with the team size. For instance, in a team of nine members the number of efficient rules is already 172,958 (see Isbell, 1959)(4). Now the following question is raised: Is there a mathematical relation between the size of the team and the exact number of efficient rules? This simple question is still an open one. The existence of order relations among decision rules is first noted in Nitzan and Paroush (1985(5), p. 35). The existence of such an order means, Parisi I 499 first, that the number of rankings of m efficient rules is significantly smaller than the theoretical number m! of all possible rankings of these rules and, second, that its existence is independent of the team’s competence. Beyond the theoretical interest in studying order among efficient decision rules, the information about the order has useful applications. Since the order relations are independent of the specific competencies of the decision-makers, the knowledge about the order of the rules is important in cases where the competencies are unknown or only partially known. For instance, if for some reason (e.g. excessive costs) the optimal rule cannot be used, then even in the absence of knowledge about the decisional competencies, the team can identify by the known order of the decision rules the second-best rule, the third-best, and so on. Parisi I 501 In the context of Condorcet’s setting, given the individuals’ common objective and diverse information which yields their decisions, the optimal collective decision rule can be identified (…). >Condorcet Jury Theorem. However, in a binary setting and diverse preferences, one can reach these same optimal collective decision rules by their unique axiomatic characterization. In a more general multi-alternative setting, however, the potential success of the axiomatic approach is clouded by the classical Impossibility Theorems of Arrow (1951)(6) and his followers. As is well known, if few reasonable axioms have to be satisfied by the aggregation rule, a social welfare function does not exist. 1. Shapley, L. and B. Grofman (1984). “Optimizing group judgmental accuracy in the presence of interdependence.” Public Choice 43(3): 329-343. 2. Nitzan, S. and J. Paroush (1981). “The characterization of decisive weighted majority rules.” Economics Letters 7(2): 119-123. 3. Nitzan, S. and J. Paroush (1984b). “A general theorem and eight corollaries in search of a correct decision.” Theory and Decision 17(3): 211-220. 4. Isbell, J. R. (1959). “On the enumeration of majority games.” Mathematical Tables and Other Aids of Computation 13(65): 21-28. 5. Nitzan, S. and J. Paroush (1985). Collective Decision Making: An Economic Outlook. Cambridge: Cambridge University Press. 6. Arrow, K. J. (1951). Social Choice and Individual Values (New York: John Wiley & Sons). Shmuel Nitzan and Jacob Paroush. “Collective Decision-making and the Jury Theorems”. In: Parisi, Francesco (ed) (2017). The Oxford Handbook of Law and Economics. Vol 1: Methodology and Concepts. NY: Oxford University. |
Parisi I Francesco Parisi (Ed) The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017 |
| Decision-making Processes | Economic Theories | Parisi I 502 Decision-making processes/Economic theories/Nitzan/Paroush: Suppose (…) that asymmetry exists between the two alternatives. Asymmetry may stem from three different sources. First, the priors of the two states of nature (the defendant being innocent and the defendant being guilty) may be different. For example, assume that most people are not criminals, so in order to convict a defendant the state “innocent” is considered as a status quo that has to be refuted and the state “guilty” is deemed as the alternative that has to be proved. Thus, a collective decision to convict is expected to be “beyond any doubt,” whereas collective acquittal may remain doubtful. Second, the net benefits of a correct decision under the two states of nature can be different. The two types of errors, acquittal of a guilty defendant and conviction of an innocent defendant, may have different costs. Third, an individual’s decisional competency may depend on the state of nature. In particular, the probability to decide correctly if the state is “innocent” can be different from the probability to decide correctly if the state is “guilty.” >Decision Rules. In any case, the decisional competency of an individual is not parameterized by a single probability of making a correct choice, but by two probabilities of deciding correctly in the two states of nature. Under asymmetry it is required that one of the two alternatives, say conviction, will be the collective choice only when it receives the support of a special majority with a quota larger than one-half. Thus, under asymmetry the decision rule should be a qualified majority rule (QMR). QMRs are discussed in several works in the political context of constitutions and fundamental laws as well as in relation to juries (see, e.g., Parisi I 503 Buchanan and Tullock, 1962(1); Rae, 1969)(2). Nitzan and Paroush (1984d)(3) were the first to derive the exact quota necessary for the optimal QMR. However, their quota is derived under the restrictive conditions of identical competencies that are invariant to the state of nature. The special case of identical competencies that depend on the state of nature was extensively analyzed by Sah and Stiglitz (1988)(4) and Sah (1990(5), 1991(6)). Allowing heterogeneous and state-dependent competencies, Ben-Yashar and Nitzan (1997)(7) specify the expression for both the weight that has to be assigned to each member of the team under the optimal rule as well as the desirable quota of votes necessary for the rejection of the status quo. The optimal rule in this more general case therefore becomes a weighted qualified majority rule, WQMR. The optimal weight is now proportional to the average of the logs of the odds of the two probabilities of making a correct choice and the optimal quota is a function of four parameters: the log of the two probabilities of making a correct decision, the log of the odd of the prior probability, and the log of the ratio of the two net benefits. >Condorcet Jury Theorem, >Jury Theorem, >Arrow’s Theorem. 1. Buchanan, J. M. and G. Tullock (1962). The Calculus of Consent: Logical Foundations of Constitutional Democracy. Ann Arbor, MI: University of Michigan Press. 2. Rae, D. W. (1969). “Decision-rules and individual values in constitutional choice.” American Political Science Review 63(1): 40–56. 3. Nitzan, S. and J. Paroush (1984d). “Are qualified majority rules special?” Public Choice 42(3): 257-272. 4. Sah, R. K. and J. Stiglitz (1988). “Committees, hierarchies and polyarchies.” Economic Journal 98(391): 451-470. 5. Sah, R. K. (1990). “An explicit closed-form formula for profit-maximizing k-out-of-n systems subject to two kinds of failures.” Microelectronics and Reliability 30(6): 1123-1130. 6. Sah, R. K. (1991). “Fallibility in human organizations and political systems.” Journal of Economic Perspectives 5(2): 67-88. Sah, R. K. and J. Stiglitz (1985). 7. Ben-Yashar, R. and S. Nitzan (1997). “The optimal decision rule for fixed size committees in dichotomous choice situations - The general result.” International Economic Review 38(1): 175-187. Shmuel Nitzan and Jacob Paroush. “Collective Decision-making and the Jury Theorems”. In: Parisi, Francesco (ed) (2017). The Oxford Handbook of Law and Economics. Vol 1: Methodology and Concepts. NY: Oxford University. |
Parisi I Francesco Parisi (Ed) The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017 |
| Deduction Theorem | Wessel | We I 109 Def Deduction Theorem/calculus NS/Wessel: MT 1. If A1 ... An l B, so A1..An 1 l An> B. ((S) If the conclusion follows from the totality of the premises, so the last premise follows from the totality of the previous premises and from the last premise follows then the conclusion...) I 110 Induction proof/calculus NS/Wessel: in the conclusion B1 can stand an assumption formula (a.f.) or an axiom variant (a.v.). Is it an assumption formula, there are again two possible cases: it may be the assumption formula An or an assumption formula different from An. Deduction theorem/proof/Wessel: .. ++ .. I 111 in this proof, only the following three theorems were used: p > (q > p), p > (q > r)> (p > q> (P > r)) and p > p. Deduction theorem/Wessel: as a conclusion we get: MT 2. If A1 ... An l B, so l A1 > (A2> ..> (An> B) ...). The deduction theorem states an essential relationship between proofs and derivations. >Proofs, >Provability, >Derivation, >Derivability. In the future, it is sufficient, when proving a theorem, to prove a derivational relationship and to apply to it the deduction theorem. E.g. from the derivational relationship p > q, q > r, p l r we get by three-time application of MT 1: T3. l p > q> (q > r> (p > r)). |
Wessel I H. Wessel Logik Berlin 1999 |
| Definitions | Mates | I 248 Definitions/Mates: we need them to represent formalized theories. - They introduce designations that do not belong to the vocabulary of the language, but make them more readable. >Theories, >Formulas, >Logical formulas, >Theoretical language, >Theoretical terms, >Theoretical entities, >Definitions, >Definability. I 250 Def Creative Definition/Mates: leads to new theorems in which the defined symbol does not occur. >Symbols. Requirement: a satisfactory definition should be non-creative. >Vocabulary/Mates. I 248 Metalinguistic definitions/Mates: Metalinguistic definitions bring a name of the defined symbol in object language: the symbol itself - e.g. a) metalinguistically: if a and b are terms so is a = b for I21ab b) object-language: (x) (y) (x = y I21xy). >Metalanguage, >Object language, >Identity, >Definition/Frege, >Symbolic use. |
Mate I B. Mates Elementare Logik Göttingen 1969 Mate II B. Mates Skeptical Essays Chicago 1981 |
| Derivability | Bolzano | Berka I 18/19 Derivability/Bolzano: exists, if certain ideas i, j, which make the premises A, B, C, true, also make the conclusions M, N, O... true. Namely the epitome (the totality) of the ideas is intended to make the entire conclusions and the whole premises true. ((s) >truthmaker). Comprise/include/Bolzano: Premises: are here the included, Conclusions: the comprehensive/including sentences. I 20 Derivability/Bolzano: Problem: sentences obtained through an arbitrary exchange of ideas from given true must not always be true. (s) Exchange of ideas: insert for variables. Bolzano: thus the relationship of derivability can also exist under false theorems. E.g. Follow-up relationship/Bolzano/(s): (content-related): if it is warmer in one place, a higher temperature is displayed in this place. In reality, higher temperature is displayed because it is warmer. The thermometer does not generate the temperature. That is, the follow-up relationship consists only in one direction: Heat > Temperature. Different in the derivability: E.g. derivability/Bolzano/(s): if the sentence "... higher temperature" is true, the sentence "it is warmer" is also true and vice versa. Reversible ratio of two true sentences. Content is not decisive. I 21 Follow-up relationshiop/Bolzano: is not already present when the corresponding sentences are all true. (1) 1. B. Bolzano, Wissenschaftslehre, Sulzbach 1837 (gekürzter Nachdruck aus Bd. II S. 113-115, S. 191 – 193; § 155; §162) |
Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Discoveries | Genz | II 11 Discovery/Genz: an invented theory that proves itself becomes a discovery. II 183 Invention/discovery/Genz: question: whether the theorems of mathematics are inventions (constructivism) or discoveries (platonic): Genz: it is not clear to anyone what verifiable statements could serve to distinguish these two opinions. That is what makes the argument so attractive. >Criteria, >Constructivism, >Platonism, >Mathematics. |
Gz I H. Genz Gedankenexperimente Weinheim 1999 Gz II Henning Genz Wie die Naturgesetze Wirklichkeit schaffen. Über Physik und Realität München 2002 |
| Equal Sign | Quine | IX 9 Equal Sign/Quine: "=" is a two-digit predicate. >Predicates/Quine. IX 10 Sign/Sign Set/Quine: each theory has introduced a basic vocabulary of primitive predicates, perhaps by definition. Mostly there are only finally many, then we do not need to add the equal sign "=". Because we can then define it with the help of the others. ((s) "primitive" does not mean "one-digit"). Equal Sign/Quine: suppose the only basic predicate of a theory is "φ". Then we can define "=" by the following explanation of "x = y": (1) ∀z[(φxz ‹› φyz) u (φzx ‹› φzy)]. For obviously "x= x" proves to be a simple example of a valid formula schema of quantifier logic. The same applies to all special cases of "(x = y u F) > Fy", as far as they are statements which contain no further predicate except "φ". This is seen in the following way: first, look at all results in which the statements made by "Fx" and "Fy" differ only in one place. The immediate context of this single occurrence must then be either "φxv" and "φyv" or "φvx" and "φvy", where "v" denotes any variable, (perhaps either x or y). IX 23 Individuals/Elemental Relation/Extensionality Axiom/Quine: Suggestion: "x ε y", if x is an individual, be true or false, depending on, b x = y or x unequal to y. Thus, the problem of applying the extensionality axiom to individuals disappears. "ε" of individuals has the property of "=". (Elemental relationship of individuals: equality! ("is element of", "is contained": becomes the equal sign before individuals). IX 26 Until then, the equal sign is only defined between class abstraction terms. Between variables we need further tools ...+.... X 88 Logical Truth/Structure/Definition/Quine: our definition of logical truth inevitably referred to the grammatical structure. Problem: this view is called into question when we introduce identity (identity predicate "=", equal sign). Identity/logical truth/Quine: the traceability of logical truth to grammatical structure is questioned when identity is introduced, because e.g. "x = x" or "x = y" may not be a logical truth, because not everything can be used. ((s) >Intension: because of it, not all theorems of identity are logical truths. Quine: it is about the fact that in one logical truth one predicate must be replaced by another, but the equal sign as a predicate cannot be replaced by another predicate. Identity/Logic/Quine: Truths of Identity Theory Example "x = x", "Ey((x = y)" or "~(x = y . ~(y = x))" ((s) symmetry of identity) are not suitable as logical truths according to our definitions of logical truth. >Logical Truth/Quine. Reason: they can be wrong if "=" is replaced by other predicates. Consequence: So should we not count identity to logic, but to mathematics? Together with ">" and "ε"? >Semantic Ascent. III 268 Two different names can stand for the same object, if the equal sign is inbetween, the equation is true. It is not claimed that the names are the same! III 271 Equal Sign/Quine: "=" is a common relative term. The equal sign is necessary because two variables can refer to the same or to different objects. From a logical point of view, the use of the equal sign between variables is fundamental, not that between singular terms. III 293 Equality Sign/expressiveness/stronger/weaker/Quine: we also gain expressiveness by making the equality sign obsolete ((s) when we introduce classes). Instead of "x = y" we say that x and y belong to exactly the same classes. I.e. (a)(x ε a. bik. y ε a) Identity/Quantities/Quine: the identity of classes can be explained in a way in reverse: "a = b" means that a and b have exactly the same elements. Then the equal sign is simply a convenient shortcut. Description/Equal Sign/Quine: if we have the equal sign, we can afford the luxury of introducing descriptions without having to calculate them as primitive basic concepts. Because with the equal sign we can eliminate a description from every sentence. >Descriptions/Quine. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Equilibrium | Walras | Mause I 54 Equilibrium/Neoclassical Theory: The demand for and supply of various goods and the corresponding market equilibrium with equilibrium price and equilibrium quantity can be derived from the behaviour of individual households and companies. However, it is not this partial analysis of individual markets that is of central importance for the evaluation of markets and market equilibria, but rather the total analysis, i.e. the simultaneous consideration of all markets in an economy and the interdependencies between them (general equilibrium theory). The pioneer of total analysis was Léon Walras.(1) In its modern form it was coined by Kenneth J. Arrow and Gerard Debreu (Arrow 1951(2); Arrow and Debreu 1954(3)). In a first step, the existence of a general market equilibrium can be proven. The relative prices of all goods are determined exclusively by real economic conditions (e.g. the production technology, resources euipment or demand structure); money only plays a role insofar as the price level (in accordance with quantity theory) depends on the money supply; moreover, it is neutral. Problem: the conditions necessary for the equilibrium are never fulfilled in reality. Solution: in theory, the existence of the equilibrium is proven, but not its stability. >Neoclassical economics, >K. Arrow. 1. L. Walras, Eléments d’Economie Politique Pure. Teile I– III (1874), Teile IV– VI (1877). Lausanne 1874/ 1877. 2. K.J. Arrow, An extension of the basic theorems of classical welfare economics. In Proceedings of the second Berkeley symposium on mathematical statistics and probability, Hrsg. J. Neyman, Berkeley 1951 3. K. J. Arrow, G. Debreu Existence of equilibrium for a competitive economy. Econometrica 22: 82– 109. |
EconWalras I Léon Walras Eléments d’Economie Politique Pure Lausanne 1874 Mause I Karsten Mause Christian Müller Klaus Schubert, Politik und Wirtschaft: Ein integratives Kompendium Wiesbaden 2018 |
| Equilibrium Theory | Neoclassical Economics | Mause I 54 Equilibrium/Neoclassical Theory: The demand for and supply of various goods and the corresponding market equilibrium with equilibrium price and equilibrium quantity can be derived from the behaviour of individual households and companies. However, it is not this partial analysis of individual markets that is of central importance for the evaluation of markets and market equilibria, but rather the total analysis, i.e. the simultaneous consideration of all markets in an economy and the interdependencies between them (general equilibrium theory). The pioneer of total analysis was Léon Walras.(1) In its modern form it was coined by Kenneth J. Arrow and Gerard Debreu (Arrow 1951 (2); Arrow and Debreu 1954 (3)). In a first step, the existence of a general market equilibrium can be proven. The relative prices of all goods are determined exclusively by real economic conditions (e.g. the production technology, resources euipment or demand structure); money only plays a role insofar as the price level (in accordance with quantity theory) depends on the money supply; moreover, it is neutral. Problem: the conditions necessary for the equilibrium are never fulfilled in reality. Solution: in theory, the existence of the equilibrium is proven, but not its stability. >K. Arrow. 1. L. Walras, Eléments d’Economie Politique Pure. Teile I–III (1874), Teile IV– VI (1877). Lausanne 1874/ 1877. 2. K.J. Arrow, An extension of the basic theorems of classical welfare economics. In Proceedings of the second Berkeley symposium on mathematical statistics and probability, Hrsg. J. Neyman, Berkeley 1951. 3. K. J. Arrow, G. Debreu Existence of equilibrium for a competitive economy. Econometrica 22: 82–109. |
Mause I Karsten Mause Christian Müller Klaus Schubert, Politik und Wirtschaft: Ein integratives Kompendium Wiesbaden 2018 |
| Essentialism | Peacocke | II 322 Essentialism/Wiggins/Peacocke: if we want to read Wiggins [neclx1[Human(x1)]](Socrates) as an essentialist sentence, that Socrates is necessarily a human being, then nothing can be a human being without existing. >Necessity/Wiggins, >de re necessity, >D. Wiggins, >de re, >de dicto, cf. >Barcan formula. The translation into semantics of possible worlds would then be: "In every world in which Socrates exists, he is a human being. In general: [neclx1...lxn [A(x1...xn)]](t1...tn) - i.e. "In every world w in which all of t1...tn exist, t1...tn have the relation A in w" - if we wanted to make similar existential assumptions in the antecedence for expressions occurring in A(x1...xn) here, there would be no hope of finding a difference in the truth conditions between these forms: neclx1lx2[Rx1x2](a,b), neclx1[Rax1](b) and neclx1[Rx1b](a) - this shows that T1 contains false theorems. >Semantics of Possible Worlds, >Possible Worlds. |
Peacocke I Chr. R. Peacocke Sense and Content Oxford 1983 Peacocke II Christopher Peacocke "Truth Definitions and Actual Languges" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 |
| Euclid | Kant | Bertrand Russell Die Mathematik und die Metaphysiker 1901 in: Kursbuch 8 Mathematik 1967 25 Euclid/Kant/Russell: Kant rightly remarked that the Euclidean theorems cannot be deduced from the Euclidean axioms without the aid of numerals. a priori/RussellVsKant: Kant's doctrine of the a priori intuitions, by which he explained the possibility of pure mathematics, is completely useless for mathematics. >a priori, >Numerals, >Deduction. |
I. Kant I Günter Schulte Kant Einführung (Campus) Frankfurt 1994 Externe Quellen. ZEIT-Artikel 11/02 (Ludger Heidbrink über Rawls) Volker Gerhard "Die Frucht der Freiheit" Plädoyer für die Stammzellforschung ZEIT 27.11.03 |
| Existence | d’Abro | A. d'Abro Die Kontroversen über das Wesen der Mathematik 1939 in Kursbuch 8 Mathematik 1967 42 Existence/d'Abro: Boundaries of the Axiomatic Method: one of the goals of mathematicians is to establish so-called existence theorems that are to prove that the solution we are looking for actually exists. >Proofs, >Provability, >Theorems. Non-existence/Meinong/d'Abro: since we can truthfully say "something like a round square does not exist," there must be something like a round square, albeit as a non-existent object. At first Russell had not been able to escape this, but in 1905 he discovered a theory of representation, according to which the round square seems to be mentioned when one says: "A round square does not exist." (Principia Mathematica)(1). >Non-existence, >Round square. 43 Existence/d'Abro: in Meinong "exist" and "there is" are used synonymously, but they are not synonyms: exist in the mathematical sense means to contain no contradiction. If one takes Meinong seriously, this is evidence of the inability to think clearly, as in the joke: "Where does the light go when it goes out?". >"There is". Thus, a proof of existence for a solution is the finding that no contradiction arises from the assumption of a solution, even if the solution is not yet known. Cf. >Assertion of existence, >Contradictions, >Consistency. 43/44 The famous Dirichlet problem is an existence theorem. The question is whether or not there is always a solution for the Laplace equation satisfying certain boundary conditions. An inconsistent model has just as little claim to mathematical existence as a round square. ((s) It does not solve the problem for non-mathematical objects.) The compatibility of a postulate system can only be checked if it has only a finite number of consequences. Hilbert's postulates, however, allow infinitely many conclusions. --- 44/45 Hilbert avoids this difficulty by saying that the system is proved to be consistent when it is possible to prove the existence of a model which confirms the system. So existence equals lack of an internal inconsistency. Hilbert then asserts that the numerical model satisfies this requirement. He thus accepts the consistency of the arithmetic continuum. The only problem is that we are not sure about it. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
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| Existence Statements | Quine | VIII 24ff Existence Statement/Quine: special: "There is one thing that is so and so" (mentions the name) - general: "There is a thing that is so" (specifies a variable instead of names) - E.g. Pegasus: is a sense equivalent to description. >Descriptions, >Pegasus example, >Non-existence, >Unicorn example. XII 27 Object/Translation/Indefiniteness/Expression Conditions/Language Learning/Radical Interpretation/Quine: the expression conditions are not sufficient to be able to say with certainty what a speaker of a foreign language regards as objects. Problem: how can assertions of existence (theorems of existence) ever be empirically invalidated? Solution: the knowledge of the conditions of utterance does not ensure the reference to the subject, but it does help to clarify what serves as empirical confirmation of the truth of the whole sentence. XII 28 We then project our own acceptance of objects onto the indigenous language. We can be sure that the assumed object is an observed object in the sense that the amplified stimuli emanate quite directly from it. XII 33 Abstract/abstract object/existence/coherence/Quine: Existence assertions about abstract objects can only be judged by their coherence or by simplicity considerations. Example: to avoid paradoxes with classes. Property/Quine: the law of education for properties states that every statement that speaks about a thing ascribes a property to it (predication). This is a cultural heritage. VII (i) 167 Existence/Logic/Quine: we can dispense with such confusing notations as "a exists" because we know how to translate singular sentences of existence into more basic expressions if the singular term is contained in a description. Observation sentence: is meaningless in the past, since it is assumed that it was learned by direct conditioning. Theorem of Existence/Russell: For this reason, Russell declares singular theorems of existence pointless if their subject is a real proper name. ((s) Real proper name: "this". No, not only!"Nine" too: are names whose reference is saved. So from acquaintance, which corresponds to a descriptions. For fake names, the description corresponds to what a fiction says about it: e.g. Pegasus. "winged horse". Name/identification(s): each name corresponds to a description because no thing in the world can only be referenced by a name and for each description a name can be invented but not every description is fulfilled by an object. ((s) Precisely because of the necessary acquaintance the question whether the theorem of existence is true is pointless.) Quine: the reason is the same here. ((s) Theorem of existence (s): Example "There is Napoleon": can only refer to one learning situation. Circular, so to speak, from the very beginning. Exactly the same: e.g. "There are daisies". Davidson/(s): One could also not say meaningfully: Example: "It has turned out that this and that does not exist": because then one says only that one has learned a word wrongly. >Reference, >Learning. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Experiments | Duhem | I XIII Experiment/Duhem: The experimenter does not merely read the instruments, he uses the instruments. The following are required: 1.Theory about the domain in which measurements are made. 2.Theory of used measuring instruments. In every device there are systematic errors, the experimenter knows that. Duhem: the Ex works constantly with two devices: the concrete measuring device and an ideal structure for which the physical laws "exactly" apply. Between the phenomena ascertained in the experiment and the result of the experiment formulated by the physicist is a complex translation process. The facts which the experimenter determines are already "theoretical facts". The experimenter must always use theories for his work. The results are only useful for other physicists, if it is know which theories he has used. And whether corrections were already made. >Method. I XII An experimentum crucis (whose failure would disprove the whole theory) is rejected. (> Holism). I XXVI VsExperimentum crucis: (for example, by Quine, 1951, as the main attack against logical empiricism: Holistic view of science.) No experiment can show where the fault is located in the system. The examination of a particular hypothesis is only possible by using a whole group of further laws, ultimately the whole theory. Since Bacon, hope was linked to an experimentum crucis: a decision-making experiment between competing theories. E.g. Foucault's attempt to decide between Newton's theory of emission of light and Huygens' undulation theory sees Duhem as an experiment of the experimentum crucis. Foucault was able to show that light actually spreads slower in water, which made Newton look refuted. Duhem shows that this conclusion is not valid. The error could be in a secondary hypothesis. I 189 Experiment/Duhem: disintegrates into two parts. I 190 1. Observation of certain facts. For this, the knowledge of physics is not necessary at all. 2. Interpretation of the observed facts. For this you have to know the physics. The physicist does not write in his protocol that the instrument has indicated a certain stroke, he notes that the gas has reached a certain volume. What are the size of the volume, the temperature, the pressure? Three concrete objects? No, there are three abstract symbols that connect physical theory with facts. I 192 Definition experiment: accurate observation of a group of phenomena, plus interpretation of them. This interpretation replaces the concrete given with the help of the observation of actual ones obtained by abstract and symbolic representations which agree with them on the basis of the theories which the observer accepts as permissible. I 193 Experiment: The result is the establishment of a relationship between different concrete facts. A certain fact was artificially produced, another stems from it. I 210 Experiment/Duhem: We must know the theories that the physicist considers valid. During the experiment, the physicist continued to operate two apparatuses side by side: the actual measuring apparatus and the ideal one defined by mathematical formulas and symbols. I 215 The result of a physical experiment has not a security of the same level as a fact, established by non-scientific methods, from a healthy person by simple observation. The experiment is less direct and more dependent on a whole group of theories. I 273 Experiment/Duhem: The experiment is not the basis of theory, but the highlight. The totality of the theorems gives an ever more similar picture of the totality of the experimental facts. >Theories, >Facts. |
Duh I P. Duhem La théorie physique, son objet et sa structure, Paris 1906 German Edition: Ziel und Struktur der physikalischen Theorien Hamburg 1998 |
| Falsification | Duhem | I 245 Verification/Confirmation/Examination/Duhem: If the announced fact does not arise, the theorem is falsified. In the examination one applies a whole group of theories (according to which the instruments are built and without which they cannot be read). The occurrence or non-occurrence of the phenomenon does not result from the contentious theorem alone, but from the connection with the whole group. The failing experiment merely teaches that among all the theorems which have served to predict or to state the phenomenon, at least one must be false. If the experimenter declares that the error lies precisely in the proposition to be tested, he presupposes that all others are true. Confidence in the other sentences (for example, according to which the instruments are constructed and according to which they are read) does not occur with logical necessity. >Verification, >Confirmation. I 249 Physics is not a machine that can be dismantled. It is a system when a disturbance occurs, it has indeed been evoked by the whole system. (> System). The physicist must find the organ without being able to isolate it, because then the system does no longer work. >Physics. |
Duh I P. Duhem La théorie physique, son objet et sa structure, Paris 1906 German Edition: Ziel und Struktur der physikalischen Theorien Hamburg 1998 |
| Falsification | Schurz | I 92 Notation: II- : "follows logically". Explanation scheme/logical form/explanation/Schurz: strict all proposition & singular proposition II- singular proposition. All A are K and a is A II- a is K. Falsification scheme/falsification/logical form/Schurz: FS I: singular proposition falsifies strict universal sentence. singular sentence II- negation of strict universal sentence a is A and not K II- not all A are K FS II: existence sentence falsifies strict all proposition There is an A that is not a K II- not all A are K. >Universal sentence. I 98 Def Verifiability/Schurz: A hypothesis H is verifiable iff there is a finite and consistent set B of observation propositions from which H follows logically. This means only possible (actual) verifiability. >Verification, >Actuality, >Hypotheses, >Confirmation. Def Falsifiability/Schurz: H is falsifiable iff there is a finite consistent set B of observation propositions, from which the negation of H follows logically. This means only possible falsifiability (actual). Def Confirmability/Schurz: (resp. weakenable) is hypothesis H if there is a finitely consistent set B of observation propositions, which hears resp. degrades the validity resp. plausibility of H. Falsification/Asymmetry/Popper: Falsification is restricted to strict spatiotemporally unrestricted empirical all-hypotheses. Dual to this, unrestricted existence propositions Ex "There is a white raven" are verifiable, but not falsifiable. I 99 Spatiotemporally restricted hypotheses: are in principle verifiable and falsifiable by observing the finitely many individuals of a domain. Verifiability: no unrestricted generalization and no theoretical theorem is verifiable. Allexistence theorem/statistical generalization: not verifiable also not falsifiable because they do not imply observation theorems. Theories/falsification: neither whole theories nor single theoretical hypotheses are falsifiable. Even if they are strictly general. And this is because of holism. >Holism. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Formal Language | Tarski | Berka I 458 Formal language/Tarski: in a formal language the meaning of each term is uniquely determined by its shape. I 459 Variables: variables have no independent meaning. - Statements remain statements after translation into everyday language. Variable/Tarski: variables represent for us always names of classes of individuals. >Class name. Berka I 461 Formal language/terminology/abbreviations/spelling/Tarski: here: the studied language (object language). Symbols: N, A, I, P: negation, alternation, inclusion, quantifier - metalanguage: Symbols ng (negation), sm (sum = alternation), in (inclusion) - this is the language in which the examination is performed. ng, sm, etc. correspond to the colloquial expressions ((s) the formal symbols N, A, etc. do not). I 464 E.g. object language: Example expression: Nixi, xll: - meta language: translation of this expression: (structural-descriptive name, symbolic expression): name: "((ng ^ in) ^ v1) ^ v2" - but: see below: difference name/translation.(1) >Structural-descriptive name, >Quotation name, >Metalanguage. 1. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol 1, Lemberg 1935 --- Horwich I 112 Formal language/Tarski: in it all assertible sentences are theorems. - There may be a language with exactly specified structure, which is not formalized. - Then the assertibility may depend on extra-linguistic factors.(2) >Assertibility. 2. A. Tarski, The semantic Conceptions of Truth, Philosophy and Phenomenological Research 4, pp. 341-75 |
Tarski I A. Tarski Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 Horwich I P. Horwich (Ed.) Theories of Truth Aldershot 1994 |
| Formalism | Quine | XIII 63 Formalism/Quine: deduction is useful if you have previously doubted the truth of the result. XIII 64 For example, you can test a hypothesis by looking at the consequences of it. Euclid: had difficulties to prove theorems, the truth of which nobody doubted anymore. Elegance/Science/Euclid: he already tried, for reasons of simplicity, to limit his postulates. Deduction/Problem/Quine: how can we prevent our already existing knowledge (about the objects ("what is true")) from creeping into the evidence? One tries to simulate ignorance, but what is the point? Knowledge/Truth/Quine/(s): To "know what is true" is more a knowledge of objects than of logic (see below). Disinterpretation/Reinterpretation/Interpretation/Tradition/Quine: one possibility was reinterpretation: in which it was assumed that the logical constants retained their meaning, but the other terms were merely regarded as provisional. And that in the theorem to be proved as well as in its consequences ((s) thus practically then in everyday use, everyday language). Pure Mathematics/Quine: this led many authors to regard their object as intrinsically uninterpreted. Pure Mathematics/Formalism/Russell: here we never know what we are talking about or if what we are saying is true. QuineVsFormalism/QuineVsRussell: in his favour, he has quickly forgotten that again. XIII 65 Pure Mathematics/Science/Quine: seems to be on a par with the other sciences. Pure arithmetic, for example, has to do with pure numbers that count objects, but also electrons in the economy. Variables: go over numbers as well as over objects. Example: speed of light: here a relation is determined between a pure number (300,000) and light waves. Thereby not the number is emphasized as special, but the relation. Example: price: here the number is formed neither by the object, nor by the currency. ((s) Solution/((s): Relation instead of predicate.) Quine: relation instead of pure numbers and "pure object". QuineVsDisinterpretation/Disinterpretation/Quine: the purity of pure mathematics is not based on reinterpretation! Arithmetic/Quine: is simply concerned with numbers, not with objects of daily life. Abstract Algebra/Quine: if it exists, it is simply the theory of classes and relations. But classes and relations of all possible things, not only abstract ones. XIII 66 Logic/Quine: there was a similar problem as before with deduction, where we had to suspend our previous knowledge about objects: how can we suspend our previous knowledge about conclusions? Solution/Frege/Tradition: again through disinterpretation, but this time of the particle. (>Formalism). Formalism/Quine: ironically, it spares us from ultimate disinterpretation. We can extend the conclusions allowed by our signs. We can be sure that they are not altered by the meanings of the signs. Frege/Russell/Principia Mathematica/Quine: the Principia Mathematica(1) was a step backwards from Frege's conceptual writing in terms of formalistic rigor. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Generalization | Mates | I 173 Generalization/theorems/spelling/terminology/logic/Mates: E.g. (x) (y) Fxy <> (y) (x) Fx: generalized: II- ∧α∧α "j <> La"∧αj E.g. (Ex) (Ey) fxy <> (Ey) (Ex) fxy: II- VaVa "φ <> VaVa"φ E.g. (x) (P u Fx) <> (P u (x) Fx): II- ∧α (φ u ψ) <> (φ u Laψ) if a in φ does not occur freely E.g. (x) (Ey) (Fx u Gy) <> ((x) Fx u (Ey) Gy): II- ∧αVa "(φ u ψ) <> (∧αφ u Va" ψ) and when a does not occur freely in ψ and when a" does not occur freely in φ. >Variables/Mates, >Free variables, >Bound variables. |
Mate I B. Mates Elementare Logik Göttingen 1969 Mate II B. Mates Skeptical Essays Chicago 1981 |
| Idealization | Economic Theories | Harcourt I 66 Idealization/Method/Kaldor/Economic theories/Harcourt: Terminology/Harcourt: (…) [we distinguish between] the malleable capital world in which technical progress is disembodied and the vintage world where it is embodied (…). Harcourt I 80 VsIdealizations: [a] strand of criticism is especially associated with the works of Kaldor [1955-6(1), 1957(2), 1959a(3), 1959b(4), 1962(5), 1966(6)]. It relates to a denial of the usefulness and the relevance of the assumptions of perfect (as opposed to some) competition, constant returns to scale, static expectations and perfect foresight, and marginalist and maximizing explanations of the choice of technique and factor rewards. Kaldor/Harcourt: For Kaldor, even the notion of a cost-minimizing choice of technique in a vintage model* will not hold (see Kaldor and Mirrlees [1962](5)) and he substitutes, instead, a pay-off period criterion. Kaldor is, of course, an enthusiastic proponent of the embodied view of technical progress. Harcourt I 81 He has himself produced technical progress functions of at least three vintages; he switched from a total one in Kaldor [1957](2) through a compromise in Kaldor [1959a](3) to a marginal one in Kaldor and Mirrlees [1962](5), following Black's impertinent reminder, Black [1962](7), that the first, when linear, implied a production function of a special form, Cobb-Douglas, no less! >Cobb-Douglas production function. Kaldor did keep one strand of the original vintage approach, namely, the scrapping rule associated with the equality of the expected price and wage costs, though this is inconsistent, as Nuti [1969](8) points out, with an assumption of an imperfectly competitive market structure,* which no matter what its nature, will always ensure that prices are greater than the wage costs of any vintage operating (but see also, Robinson [1969c](9)).** Kaldor also feels that a major contribution by Arrow [1962](10) - his work on learning by doing-puts a shaft through the pure form of neoclassical analysis, a view that reflects, presumably, Arrow's own summary of the implications of his article. Thus: Arrow: „The theorems about the economic world presented here differ from those in most standard economic theories: profits are the result of technical change; in a free-enterprise system, the rate of investment will be less than the optimum; net investment and the stock of capital become subordinate concepts, with gross investment taking a leading role.“ (p. 156.) Measurements/Harcourt: The point may perhaps be most simply put as follows. To measure the ex ante elasticity of substitution, ideally we need observations on the ex ante production function itself, or, if we may assume that the choice of technique from the function is undertaken by cost-minimizing businessmen with static expectations, data on the labour productivity of the latest vintages and the current wage levels ruling in the same industries in different countries. Harcourt I 82 In a vintage world, though, we have not observations on the labour productivity of the wage-earners on the latest machines, we only have observations on the average productivity of the total work force spread over all the vintages that are currently in use. Moreover, the ratios of the productivity on the latest vintages to overall productivity in each industry and country are statistics which reflect the economic histories, and especially movements of wages and rates of accumulation, of each industry in each country for periods for which there are vintages operating in their respective capital stocks. Moreover, subsequent investigations of the nature of the biases suggest, first, that they are substantial and, secondly, that the discrepancies between the observed and desired slopes could go either way, depending upon which a priori and equally plausible story is told, see Harcourt [1966](16). * Kaldor is in excellent company on this one, see Sargent [1968](11), Harcourt [1968a(12), 1968b(13)]. Solow et al. [1966](14) state the correct rule of zero quasi-rents, see pp. 111-12, where they tell of the price being the wage cost of the no rent vintage marked up by a profit margin. ** Kaldor [1970](15) admits the logic of Nuti's point but poses an hypothesis, as yet untested, that minimizes its importance empirically. 1. Kaldor, N. [1955-6] 'Alternative Theories of Distribution', Review of Economic Studies, xxm, pp. 83-100. 2. Kaldor, N. [1957] 'A Model of Economic Growth', Economic Journal, LXVII, pp. 591-624. 3. Kaldor, N. [1959a] 'Economic Growth and the Problem of Inflation - Part i', Economica, xxvi, pp. 212-26. 4. Kaldor, N. [1959b] 'Economic Growth and the Problem of Inflation - Part u Economica, xxvi, pp. 287-98. 5. Kaldor, N. and Mirrlees, J. A. [1962] 'A New Model of Economic Growth', Review of Economic Studies, xxix, pp. 174-92. 6. Kaldor, N. [1966] 'Marginal Productivity and the Macro-Economic Theories of Distribution', Review of Economic Studies, xxxm, pp. 309-19. 7. Black, J. [1962] 'The Technical Progress Function and the Production Function', Economica, xxix, pp. 166-70. 8. Nuti, D. M. [1969] 'The Degree of Monopoly in the Kaldor-Mirrlees Growth Model', Review of Economic Studies, xxxvi, pp. 257-60 9. Robinson, Joan [1969c] 'A Further Note', Review of Economic Studies, xxxvi, pp. 260-2. 10. Arrow, K. J. [1962] The Economic Implications of Learning by Doing', Review of Economic Studies, xxix, pp. 155-73. 11. Sargent, J. R. [1968] 'Recent Growth Experience in the Economy of the United Kingdom', Economic Journal, Lxxvin, pp. 19-42. 12. Harcourt, G. C. [1968a] 'Investment-Decision Criteria, Capital-Intensity and the Choice of Techniques', Czechoslovak Economic Papers, ix, pp. 65-91. 13. Harcourt, G. C. [1968b] 'Investment-Decision Criteria, Investment Incentives and the Choice of Technique', Economic Journal, LXXVIII, pp. 77-95. 14. Solow, R. M., Tobin, J., von Weizsacker, C. C. and Yaari, M. [1966] 'Neoclassical Growth with Fixed Factor Proportions', Review of Economic Studies, xxxm, pp. 79-115. 15. Kaldor, N. [1970] 'Some Fallacies in the Interpretation of Kaldor', Review of Economic Studies, xxxvu (1), pp. 1-7. 16. Harcourt, G. C. [1966] 'Biases in Empirical Estimates of the Elasticities of Substitution of C.E.S. Production Functions', Review of Economic Studies, xxxni, pp. 227-33. |
Harcourt I Geoffrey C. Harcourt Some Cambridge controversies in the theory of capital Cambridge 1972 |
| Identity | Bigelow | I 140 Identity/Bigelow/Pargetter: we understand this here as a 2-digit predicate, we do not need to expand the language. I 141 Axioms: A19. (x)(x = x) A20. (a u ~a (σ/λ) > σ unequal λ) Everyday language translation: if something is true of something and not true of something, then these two things cannot be identical. I 141 Contingent Identity/Bigelow/Pargetter: these two axioms have a surprising consequence: namely that all identity is necessary. Cf. >Identity/Kripke. There is then no contingent identity. Non-identity is then also necessary. So the following can be proved as theorems: NI. (x = y) > N(x = y) NNI. (x unequal y) > N(x unequal y) Semantic rule: then causes an identity statement to be true in all possible worlds or true in none. >Possible worlds, >Necessity, >Truth. Valuation rule/identity/Bigelow/Pargetter: V (=) (c, c) = W W: is the set of all possible worlds. Identity statements/Bigelow/Pargetter: are then either necessary or impossible. This is surprising and shows another illustration of the interplay between semantics and ontology. >Semantics, >Ontology. Ontology/Bigelow/Pargetter: is what is suggested to us by a streamlined and plausible semantics. Identity/Science/Bigelow/Pargetter: in the history of science there have often been discoveries that have shown us that things we thought were different are identical. Cf. >Natural kinds/Putnam, >Progress, >Science, >Knowledge. I 143 Now one should think that these are contingent identities. >Contingency. Contingent Identity/Semantics/Bigelow/Pargetter: if they like contingent identity, they would have to change the semantics. And that is not hard: Def Diversity/new: instead of saying that two things are different, if something is true of one but not true of the other, we could say that something non-modal is true of one, but not true of the other. That brings out some new systems. >Cf. >Leibniz principle, >Indistinguishability, >Distinctions. It is interesting to note that some of these systems verify NNI while they continue to falsify NI. For example, it is more difficult to allow New York and Miami to be one and the same city than to allow Miami to be two cities. Identity/BigelowVsContingent Identity/Bigelow/Pargetter: we should let the semantics decide and say that there is simply no contingent identity. Contingent Identity/Bigelow/Pargetter: instead of changing the semantics and then to allow it nevertheless, we should rather explain why they seem to exist: e.g. Theory of descriptions/Russell/Bigelow/Pargetter: provides a means to reconcile contingently with necessary identities: assertions of the form the F = the G can be analyzed as contingent by saying that the properties F and G are co-instantiated by a single thing. This is still compatible with the necessary self-identity. >Theory of descriptions/Russell, >Descriptions. Bigelow/Pargetter: through descriptions most contingent identities are explained away. I 144 Introverted Realism/Bigelow/Pargetter: (see above Chapter 1) introverted realism, as can be seen here, can reinforce the extroverted realism from which it originated. >Realism/Bigelow, >Realism. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| International Trade | Parrinello | Kurz I 304 International Trade/Parrinello/Kurz: Sergio Parrinello is to be credited with having pioneered the extension of Piero Sraffa's analysis at least in two important directionsl First, in 1970 he reformulated the pure theory of international trade within a 'classical' framework of the analysis in which capital consists of heteregeneous produced means of production (Parrinello 1970)(1). This was the starting point of a number of contributions by Steedman, Metcalfe, Mainwaring and others who showed that several of the traditional trade theorems, derived within the Heckscher-Ohlin-Samuelson trade model, do not carry over to a framework with a positive rate of profits and heterogeneous capital goods. 1. Parrinello, S. (1970). 'Introduzione ad una teoria neoricardiana del commercio internazionale', Studi Economici, 25, pp. 267-321. Kurz, Heinz D. and Salvadori, Neri. „The 'classical' approach to exhaustible resources. Parrinello and the others.“ In: Kurz, Heinz; Salvadori, Neri 2015. Revisiting Classical Economics: Studies in Long-Period Analysis (Routledge Studies in the History of Economics). London, UK: Routledge. |
Parrinello I Sergio Parrinello Exhaustible Natural Resources and the Classical Method of Long-period Equilibrium London: MacMillan 1983 Kurz I Heinz D. Kurz Neri Salvadori Revisiting Classical Economics: Studies in Long-Period Analysis (Routledge Studies in the History of Economics). Routledge. London 2015 |
| Interpretation | Davidson | Glüer II 28 Interpretation Theory/Glüer: must not assume that their theorems were derived with the help of a translation (circle). Therefore: DavidsonVsTarski: presupposing truth to explain meaning. Glüer II 29/30 Def interpretative/Glüer: a theory is interpretative if all theory equivalences are to be obtained from the schema T are true. Because truth conditions are given in the recursion to the structure of the sentences. Meaning holism: a sentence only has meaning in the context of the language. >Meaning holism. Thus the problem is "Snow is white iff grass is green is excluded, because such a theory could not imply at the same time a true T-equivalence for the sentences "This is white" or "That is snow". >Meaning Holism. Glüer II 117/8 Interpretation/action/explanation/Davidson/Glüer: an action is only interpretable if it can be described as part of a rational structure - this also applies to speech action - therefore, actions are linked to propositional attitudes - each action is an interpreted action. N.B.: therefore it is no empirical question whether an acting person is rational. - ((s) Because it is presupposed). An event that cannot be described in the language of the propositional attitudes is not an action - (because it is not interpretable). Frank I 645 Mental states/proposition/self-attribution/external-ascription/Davidson: we have to start from sentences or utterances instead of propositions or meanings - otherwise, different types of sources are suggested. Instead: relationships between actors and utterances. There is no different knowledge and no different criteria. Solution : If someone knows that I think of a sentence as correct, he knows what I believe - it would be circular to explain the basic asymmetry by an asymmetry of certainty. >Interpretation. I 648 Interpretation/mental states/external-ascription/Davidson: also the speaker can problematize his sentences. - He can also be wrong about the meaning of his words. - He also needs the Tarski-theory. Asymmetry: the listener/interpreter cannot be sure that the Tarski-theory is the best method for external attribution. The best thing the speaker can do is to be interpretable. Donald Davidson (1984a): First Person Authority, in: Dialectica38 (1984), 101-111 - - - Graeser I 167 Interpretation/Davidson: utterances are verifiable, without the individual propositional attitudes of the speakers being known. Radical interpretation: equality of meaning cannot be assumed, otherwise there is circularity. >Truth conditions/Davidson. Davidson V 139 Truth/Interpretation/Davidson: the contrast between truth and falsity can only occur in the context of interpretation. |
Davidson I D. Davidson Der Mythos des Subjektiven Stuttgart 1993 Davidson I (a) Donald Davidson "Tho Conditions of Thoughts", in: Le Cahier du Collège de Philosophie, Paris 1989, pp. 163-171 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson I (b) Donald Davidson "What is Present to the Mind?" in: J. Brandl/W. Gombocz (eds) The MInd of Donald Davidson, Amsterdam 1989, pp. 3-18 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson I (c) Donald Davidson "Meaning, Truth and Evidence", in: R. Barrett/R. Gibson (eds.) Perspectives on Quine, Cambridge/MA 1990, pp. 68-79 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson I (d) Donald Davidson "Epistemology Externalized", Ms 1989 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson I (e) Donald Davidson "The Myth of the Subjective", in: M. Benedikt/R. Burger (eds.) Bewußtsein, Sprache und die Kunst, Wien 1988, pp. 45-54 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson II Donald Davidson "Reply to Foster" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 Davidson III D. Davidson Essays on Actions and Events, Oxford 1980 German Edition: Handlung und Ereignis Frankfurt 1990 Davidson IV D. Davidson Inquiries into Truth and Interpretation, Oxford 1984 German Edition: Wahrheit und Interpretation Frankfurt 1990 Davidson V Donald Davidson "Rational Animals", in: D. Davidson, Subjective, Intersubjective, Objective, Oxford 2001, pp. 95-105 In Der Geist der Tiere, D Perler/M. Wild Frankfurt/M. 2005 D II K. Glüer D. Davidson Zur Einführung Hamburg 1993 Fra I M. Frank (Hrsg.) Analytische Theorien des Selbstbewusstseins Frankfurt 1994 Grae I A. Graeser Positionen der Gegenwartsphilosophie. München 2002 |
| Isomorphism | Waismann | I 53 Isomorphism/Mathematics/general public/generalization/axioms/Hilbert/Waismann: New: in modern mathematics one came to the realization that geometrical sentences can be applied to a completely different field. For example, all the theorems that are about the straight lines of our space can be interpreted as being about all the points of a four-dimensional space. The two thought systems are completely isomorphic (built the same). The sensuous appearance thus plays no role for the validity of the sentences. One is now consciously dispensing with saying what a straight line is. >Geometry, >Space. I 54 Point, line, plane, are understood to mean any things for which the axioms set forth are true. Hilbert gives an example: the numerical distribution of deviations in the cultivation of Drosophila (flies) coincide with the linear Euclidean axioms of congruence and the geometric concept "between". So simple and so accurate as you would not have dreamed of. >Analogies, >Proofs, >Provability. I 55 The last step: also the signs of the logic calculus are content-wise undefined. (connection signs). >Logical constants, >Equal sign, Connectives, >Identity. Problem: consistency must first be defined e.g.: Def consistent: is a formula system, if, in it, 1 unequal 1 does never occur. >Consistency. Metamathematics is then content-related, with the main goal of consistency. Hilbert: The axioms and provable propositions are representations of the thoughts which constituted the usual method of the previous mathematics, but they are not themselves the truths in the absolute sense. >Truth/Waismann, >Truth/Hilbert, >Axioms/Hilbert. |
Waismann I F. Waismann Einführung in das mathematische Denken Darmstadt 1996 Waismann II F. Waismann Logik, Sprache, Philosophie Stuttgart 1976 |
| Jury Theorem | Condorcet | Gaus I 148 Jury theorem/Condorcet/Dryzek: This theorem demonstrates that if each citizen has a better than even chance of being correct in his/her judgement, then the larger the number of voters, the greater the chance of the majority choosing the correct option. The jury theorem therefore justifies the rationality of majoritarian democracy, at least in a republican context of a search for the common good, though only if each citizen reaches and exercises independent judgement. So there should be no factions (which reduce the effective number of voters) and, it might seem, no communication. These, at least, were Rousseau's own views: deliberation should only be a matter of internal reflection, not communication. However, as Robert Goodin (2002(1): 125) and others point out, discussion is fine so long as people then subsequently exercise their own independent judgements when voting. >Democracy/Dryzek, >Deliberative Democray/Dryzek. Problems with deliberation and democracy: If democracy involves aggregation (however much it is downplayed by deliberative democrats), that can be across judgements and not just across preferences as emphasized in social choice theory. Such judgements can involve disagreement over (say) what is in the common good. This epistemic way of thinking about democracy is associated with Rousseau, according to whom the general will can be ascertained by voting. Bernard Grofman and Scott Feld (1988)(2) argue that if indeed there is such a thing as the common good, though people differ in their judgements about which option will best serve it, then Condorcet's jury theorem applies. 1 Goodin, Robert E. (2002) Reflective Democracy. Oxford: Oxford University Press. 2. Grofman, Bernard and Scott Feld (1988) 'Rousseau's general will: a Condorcetian perspective'. American Political Science Review, 82: 567-76. Dryzek, John S. 2004. „Democratic Political Theory“. In: Gaus, Gerald F. & Kukathas, Chandran 2004. Handbook of Political Theory. SAGE Publications Parisi I 494 Jury theorem/Condorcet/Nitzan/Paroush: The Marquis de Condorcet (1743–1794) is considered one of the pioneers of the social sciences. In the English literature, Baker (1976)(1) and Black (1958)(2) were among the first to turn the attention of the scientific community to the importance of Condorcet’s writings (see Young, 1995)(3). In 1785 no jury existed in France. Condorcet applied probability theory to judicial questions and argued that the English demand for unanimity among jurors was unreasonable, suggesting instead a jury of twelve members that can convict with a majority of at least ten. >Condorcet Jury Theorem, >Decision-making processes. 1. Baker, M. K., ed. (1976). Condorcet: selected writings. Indianapolis, IN: Bobbs-Merrill. 2. Black, D. (1958). The Theory of Committees and Elections. Cambridge: Cambridge University Press. 3. Young, P. (1995). “Optimal Voting Rules.” Journal of Economic Perspectives 9(1): 51–64. Shmuel Nitzan and Jacob Paroush. “Collective Decision-making and the Jury Theorems”. In: Parisi, Francesco (ed) (2017). The Oxford Handbook of Law and Economics. Vol 1: Methodology and Concepts. NY: Oxford University. |
Condo I N. de Condorcet Tableau historique des progrès de l’ esprit humain Paris 2004 Gaus I Gerald F. Gaus Chandran Kukathas Handbook of Political Theory London 2004 Parisi I Francesco Parisi (Ed) The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017 |
| Jury Theorem | Economic Theories | Parisi I 494 Jury theorem/Economic theories/Nitzan/Paroush: In 1785 no jury existed in France. Condorcet applied probability theory to judicial questions and argued that the English demand for unanimity among jurors was unreasonable, suggesting instead a jury of twelve members that can convict with a majority of at least ten. In 1815 the first French juries used Condorcet’s rule but later adopted the simple majority rule. At that time the mathematician Laplace argued that simple majority is a dangerous decision rule for juries. Since 1837 juries had been established on several different plans, but the French law has never believed that one could count on twelve people agreeing (see Hacking, 1990(1), ch. 11). Since the 1970s, several works have analyzed the jury system by applying probability theory as well as statistical data. Gelfand and Solomon (1973(2), 1975(3)), Gerardi (2000)(4), Klevorick and Rothschild (1979)(5), and Lee, Broedersz, and Bialek (2013)(6) are a few such studies. >Condordet Jury Theorem, >Decision theory, >Decision-making processes. 1. Hacking, I. (1990). The Taming of Chance. Cambridge: Cambridge University Press. 2. Gelfand, A. and H. Solomon (1973). “A study of Poisson’s model for jury verdicts in criminal and civil courts.” Journal of the American Statistical Association 68(342): 271–278. 3. Gelfand, A. and H. Solomon (1975). “Analyzing the decision-making process of the American jury.” Journal of the American Statistical Association 70(350): 305–310. 4. Gerardi, D. (2000). “Jury verdicts and preference diversity.” American Political Science Review 94(2): 395–406. 5. Klevorick, A. K. and M. Rothschild (1979). “A model of the jury decision process.” Journal of Legal Studies 8(1): 141–164. 6. Lee, E. D., C. P. Broedersz, and W. Bialek (2013). “Statistical mechanics of the US Supreme Court.” arXiv preprint arXiv:1306.5004. Shmuel Nitzan and Jacob Paroush. “Collective Decision-making and the Jury Theorems”. In: Parisi, Francesco (ed) (2017). The Oxford Handbook of Law and Economics. Vol 1: Methodology and Concepts. NY: Oxford University. |
Parisi I Francesco Parisi (Ed) The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017 |
| Language | Bigelow | I 131 Language/Bigelow/Pargetter: the sentences of the language can be divided into two parts: a) Theorems (logically necessary). b) Non-theorems. (These can also be wrong). Non-theorems: even they may be necessary true. For example, that electrons have a negative charge. Metaphysically necessary/Bigelow/Pargetter: such sentences can be called "metaphysically necessary". Because its truth is not guaranteed by theorems. (Or does not follow from logic alone). >Metaphysical necessity, >Logical truth, >Truth, >Necessity. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| Laws | Duhem | I 23 Definition Experimental Law/Duhem: Summary of experimental experiences that allow for predictions. ((s) Only predictions about future experiments, not about reality). >Predictions, >Reality, >Nature. I 24 Instead of remembering the various cases of the refraction of light, we can reproduce or simulate all those occurring instances immediately. >Generalization. I 26 Experimental physics gives us the laws as a whole group, unsegmented. The theorist classifies the variation that opposes the observer. Wherever there is order, there is also beauty. >Experiments. I 187 The goal of every physical theory is the representation of experimental laws. I 189 The physical law is not only the essence of a myriad of experiments. I 217 Laws/Duhem: In the same way as the laws of ordinary understanding are based on the observation of facts by the natural resources of man, the laws of physics are based on the results of physical experiments. Almost everything we have said about the experiments can be extended to the physical laws. E.g. the law of the ordinary mind: Every man is mortal. This law certainly combines abstract expressions. But these abstractions are by no means theoretical symbols. >Symbols, >Theoretical terms, >Observation language, >Observation sentences. I 219 Abstractions/Duhem: E.g. Abstraction of the ordinary mind: Before the thunder is heard, one sees the flash. The concepts are abstract, but the sensory rumbling and twitching is recognizable. This is no longer the case with the laws of physics. E.g. at constant temperature, the volumes occupied by the same gas mass are inversely proportional to the pressures under which it is placed. The notions are not only abstract, but symbolic to boot, and the symbols get a meaning only through the physical theories. The relations are by no means immediate; they are only produced by means of instruments. Now there are theories which in a certain way exclude each other, or components, which are assigned in different ways depending on the theory. I 221 E.g. Law: All gases compress and dilate in the same way. Now we ask a physicist whether the iodine vapor follows this law or not. A physicist argues that the iodine vapor is a simple gas. The density relative to the air is constant. The experiment now shows that the density of the iodine vapor relative to air depends on the temperature and the pressure. He now concludes that iodine vapor does not correspond to the given law. According to another physicist, iodine vapor is not a simple gas, but the mixture of two gases. Then the law is no longer valid that the density is constant with respect to the air, but rather that it varies with temperature and pressure. Our second physicist now concludes that iodine vapor is no exception to the rule. I 222 Thus the two physicists have completely different opinions as to a law which they both pronounce in the same form. They utter the same word and mean different theorems. In order to compare this expression with the reality, they carry out calculations so different that the one can find that the law is confirmed by the facts while the other considers it to be disproved. Definition Physical Law/Duhem: a symbolic relationship whose application to concrete reality demands that one should know and accept a whole group of theories. I 233 ... It will be said that an original law was by no means overturned by the later attempts, but the experiments had merely shown that the new law must be added. But those who say this must recognize that the primitive law must be given with special conditions, so that it does not lead to serious errors. The old law can no longer stand alone! The physical laws are therefore all provisional, since no revisions can be ruled out for the future. I 234 E.g. the gravitational law is violated by capillary phenomena. So that it is not disproved, one must change it. One may consider that the formula according to which the attraction is inversely proportional to the square of the distance is not an exact, but only an approximate one. >Idealization. |
Duh I P. Duhem La théorie physique, son objet et sa structure, Paris 1906 German Edition: Ziel und Struktur der physikalischen Theorien Hamburg 1998 |
| Logic | Dummett | Brandom I 494 Logic/Dummett/Brandom: Dummett per wide view: the derivability relation is decisive, not theorems. >Derivability. Validity is based on antecedent sets of multi-values. >Multi-valued logic. I.e., synthetic, not analytic application of the apparatus. >Analyticity/syntheticity. Not informal assertional validity but formal inferential validity. >Validity. I 495 Brandom: per extension to material inferences. >Conditionals. |
Dummett I M. Dummett The Origins of the Analytical Philosophy, London 1988 German Edition: Ursprünge der analytischen Philosophie Frankfurt 1992 Dummett II Michael Dummett "What ist a Theory of Meaning?" (ii) In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 Dummett III M. Dummett Wahrheit Stuttgart 1982 Dummett III (a) Michael Dummett "Truth" in: Proceedings of the Aristotelian Society 59 (1959) pp.141-162 In Wahrheit, Michael Dummett Stuttgart 1982 Dummett III (b) Michael Dummett "Frege’s Distiction between Sense and Reference", in: M. Dummett, Truth and Other Enigmas, London 1978, pp. 116-144 In Wahrheit, Stuttgart 1982 Dummett III (c) Michael Dummett "What is a Theory of Meaning?" in: S. Guttenplan (ed.) Mind and Language, Oxford 1975, pp. 97-138 In Wahrheit, Michael Dummett Stuttgart 1982 Dummett III (d) Michael Dummett "Bringing About the Past" in: Philosophical Review 73 (1964) pp.338-359 In Wahrheit, Michael Dummett Stuttgart 1982 Dummett III (e) Michael Dummett "Can Analytical Philosophy be Systematic, and Ought it to be?" in: Hegel-Studien, Beiheft 17 (1977) S. 305-326 In Wahrheit, Michael Dummett Stuttgart 1982 Bra I R. Brandom Making it exlicit. Reasoning, Representing, and Discursive Commitment, Cambridge/MA 1994 German Edition: Expressive Vernunft Frankfurt 2000 Bra II R. Brandom Articulating reasons. An Introduction to Inferentialism, Cambridge/MA 2001 German Edition: Begründen und Begreifen Frankfurt 2001 |
| Logic | Logic Texts | Hoyningen-Huene II 148f Relation of logic to reality: A: No one can read this book in three days. B: A hard-working student can read this book in three days. Whether there are hard-working students is something that cannot be captured with the statement logic. The inconsistency of the example can only be detected with the predicate logic. Other inconsistencies cannot be captured by the means of logic at all: A: Hans is a giant. - B: Hans is a dwarf. --- Read III 62f Difference compact/non-compact: classical logic is a logic of the 1st level. A categorical set of axioms for arithmetic must be a second-level logic. (Quantifiers also for properties). >Second order logic. Logic first order/second order are not to be distinguished syntactically, but semantically! E.g. Napoleon has all properties of an emperor: are not syntactically to be distinguished, whether logic 1st or 2nd level. III 70ff VsClassical Logic: This reduction, of course, fails. For "nothing is round and square" is necessarily true, but its non-logical components cannot be interpreted in any way that makes this statement false. Allowing variable areas of definition for classical representation was a catastrophe. The modality has returned. We can make a substitution, but we cannot really change the range. >Range, >Modality. If an object is round, it follows that it is not square. But this conclusion is not valid thanks to the form, but thanks to the content. III 79 It was a mistake to express the truth-preservation criterion as "it is impossible that the premisses are true and the conclusion false". Because it is not so obvious that there is a need to conclude from A to B. Provided he is cowardly, it follows that he is either cowardly or - what one wants. But simply from the fact that he is cowardly does not follow that if he is not cowardly - what one wants. >EFQ/ex falso quodlibet. III 151 Logic 1st order: individuals, 2nd order: variables for predicates, distribution of the predicates by quantifiers. 1st level allows restricted vocabulary of the 2nd level: existence and universal quantifier! >Existential quantification, >Universal quantification, >Existence predicate, >Existence. III 161 Free logic: no existence assumptions - no conclusion from the absence of the truth value to falsehood - global evaluation. >Truth value, >Truth value gaps, >Truth value agglomeration, >Valuation. --- Menne I 26 Justification of Logic/Menne: the so-called logical principles of identity, of consistency, and the excluded middle are not sufficient to derive the logic. In addition, ten theorems and rules of the propositional logic are needed, just to derive the syllogistic exactly. These axioms do not represent obvious ontological principles. Kant: transcendental justification of logic. It must be valid a priori. >Logic/Kant. Menne I 28 The justification from the language: oversees that there is no explicit logic at all if the language itself already contained logic. Precisely because language does not always proceed logically, the logic is needed for the standardization of language. Menne: there must be a recursive procedure for justification. >Justification, >Recursion. |
Logic Texts Me I Albert Menne Folgerichtig Denken Darmstadt 1988 HH II Hoyningen-Huene Formale Logik, Stuttgart 1998 Re III Stephen Read Philosophie der Logik Hamburg 1997 Sal IV Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983 Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001 Re III St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 Me I A. Menne Folgerichtig Denken Darmstadt 1997 |
| Logical Truth | Bigelow | I 132 Logical Truth/Bigelow/Pargetter: Problem: Logical and non-logical truths are not easy to distinguish. For example, you could simply add a to the axioms, then Na would be a theorem! (Because of the rule of necessitating, necessitation, see above.). Problem: the truth of "a" ultimately depends on our interpretation of the predicates. >Interpretation, >Valuation, >Predicates. Theorems: on the other hand, remain true with every interpretation. For them, it only depends on the interpretation of the other symbols (not the names and predicates). >Variables, >Symbols, >Logical constants. Logical truth/Bigelow/Pargetter: can be characterized in two ways a) axiomatically (true from the list of axioms). b) semantically (true by interpreting the logical symbols). >Axioms, >Axiom Systems, >Semantics. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| Majorities | Democratic Theory | Parisi I 497 Majorities/Democratic theory/decision-making/democracy/Nitzan/Paroush: Condorcet, who was a great fan of the wisdom of the crowd, was among the first to lay down the philosophical foundations of democracy. In particular, he strongly believed in the superiority of simple majority over other decision rules (see Grofman, 1975)(1). >Jury theorem/Condorcet, >Condorcet Jury Theorem, >Collective intelligence, >Democracy. But, it is known today that if the team members’ competencies are “public knowledge,” the simple majority rule may lose its superiority. Many studies have suggested alternative criteria for the optimality of a decision rule (see, e.g., Rae, 1969(2); Straffin, 1977(3); Fishburn and Gehrlein, 1977(4)). However, in what follows, the assumption that the team’s competence, Π, is the criterion for the optimality of the decision rule is preserved. Note that given that the team members share homogenous preferences, this criterion is also consistent with (equivalent to) expected utility. Allowing heterogeneous decisional capabilities, Shapley and Grofman (1981(5), 1984(6)) and Nitzan and Paroush (1982(7), 1984b(8)) find that the optimal decision rule is a weighted majority rule (WMR) rather than a simple majority rule (SMR). By maximization of the likelihood that the team makes the better of the two choices it confronts, they also establish that the optimal weights are proportional to the log of the odds of the individuals’ competencies, that is, the weights, wi, are proportional to log[pi ∕(1-pi)]. >Decision-making processes, >Decision rules. 1. Grofman, B. (1975). “A comment on ‘Democratic Theory: A Preliminary Mathematical Model.” Public Choice 21(1): 100-103. 2. Rae, D. W. (1969). “Decision-rules and individual values in constitutional choice.” American Political Science Review 63(1): 40-56. 3. Straffin, Jr., P. D. (1977). “Majority rule and general decision rules.” Theory and Decision 8(4): 351-360. 4. Fishburn, P. C. and W. V. Gehrlein (1977). “Collective rationality versus distribution of power of binary social choice functions.” Journal of Economic Theory 15(1): 72-91. 5. Shapley, L. and B. Grofman (1984). “Optimizing group judgmental accuracy in the presence of interdependence.” Public Choice 43(3): 329-343. 6. Nitzan, S. and J. Paroush (1981). “The characterization of decisive weighted majority rules.” Economics Letters 7(2): 119-123. 7. Nitzan, S. and J. Paroush (1984b). “A general theorem and eight corollaries in search of a correct decision.” Theory and Decision 17(3): 211-220. Shmuel Nitzan and Jacob Paroush. “Collective Decision-making and the Jury Theorems”. In: Parisi, Francesco (ed) (2017). The Oxford Handbook of Law and Economics. Vol 1: Methodology and Concepts. NY: Oxford University. |
Parisi I Francesco Parisi (Ed) The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017 |
| Mathematics | Waismann | I 84 Mathematics/Waismann: in our view, mathematics is not tautological, nor is it a mere branch of logic. It rests only on its own determinations. The belief that mathematics is more securely founded by logic is a misunderstanding. 2 + 2 = 4 does not correspond to a tautology, but to an instruction. It is much closer to an empirical proposition than a tautology. It is just a rule, similar to chess, which is obeyed or transgressed. This would not be possible in the case of a tautology, for what is it to obey or transgress a tautology? The opinion that the entire mathematics is based on Peano's 5 axioms can no longer be maintained today. Mathematics is a multiplicity of systems. The theorems of arithmetic are neither true nor false, but are compatible or incompatible with certain determinations. >Theorems, >Proofs, >Provability. Thus a certain dualism is overcome: I 85 It was believed that only the natural numbers were eternal, irrefutable truths, or they expressed them, whereas the rational and real numbers were mere conventions. (Kronecker). WaismannVsKronecker: that is a half measure, and the whole development of arithmetic shows which way we have to go: the possibility of a number series 1,2,3,4,5,... - many have already been mentioned. E.g. if we think that a distance is divided into parts by points, then it makes sense to say that the distance has 2,3,4... parts, but not: "the distance has a part." One would rather like to count here: 0,2,3,4... and this corresponds to the sentence series: "The distance is undivided", "the distance is divided into two parts", ... etc. i.e. we do not count here according to the scheme we use, and yet this is an everyday case. ((s) linguistic overvaluation of "consists of." Solution: 1 = fake part.) But not only the number series, but also the operations we might think of as changed: Suppose, we should carry out additions with many millions of digits. The results of two computers will not match then. Is the concept of probability introduced into arithmetics here? Or a new calculation is introduced. The error of logic was that it thought it had firmly underpinned the arithmetic. Frege: "The foundation stones, fixed in an eternal ground, are, however, flooded by our thinking, but they are not movable." WaismannVsFrege: already the expression "justifying" the arithmetic gives us a false picture,... I 86 ...as if its building was built on ground truths, while it is a calculus, which proceeds only from certain determinations, free-floating, like the solar system, which rests on nothing. We can only describe the arithmetic, i.e. specify their rules, but not justify it. |
Waismann I F. Waismann Einführung in das mathematische Denken Darmstadt 1996 Waismann II F. Waismann Logik, Sprache, Philosophie Stuttgart 1976 |
| Meaning Change | Lyotard | Sokal I 158 Meaning Change/Lyotard/BricmontVsLyotard/SokalVsLyotard/Lyotard: Lyotard(1) speaks of a "postmodern science" which develops the theory of its own evolution as discontinuous, catastrophic. It is "not to be corrected". It suggests a legitimation model that is by no means that of the best performance, but that of difference understood as paralogy. >Postmodernism. SokalVsLyotard: The theories quoted by Lyotard naturally produce new knowledge, but they do not change the meaning of the word. (Note: with one limitation: meta theorems in mathematical logic such as Gödel's theorem or independence theorems in set theory have a logical status that is slightly different from conventional mathematical theorems.) >Meaning change, >Theory change, >Theories, >Science, >Knowledge. For the correct use of the concepts of physics and mathematics see >Sokal/Bricmont, >Feynman, or >Thorne. 1. J. F. Lyotard, Das postmoderne Wissen. Ein Bericht. Wien, 1993, p. 172f. |
Lyo I J. F. Lyotard Dérive à partir de Marx et Freud Lyotard II J.F. Lyotard Das postmoderne Wissen. Ein Bericht. Wien 1993 Sokal I Alan Sokal Jean Bricmont Fashionabel Nonsense. Postmodern Intellectuals Abuse of Science, New York 1998 German Edition: Eleganter Unsinn. Wie die Denker der Postmoderne die Wissenschaften missbrauchen München 1999 Sokal II Alan Sokal Fashionable Nonsense: Postmodern Intellectuals’ Abuse of Science New York 1999 |
| Meaning Theory | Avramides | I 7ff Theory of meaning/meaning theory/Davidson/Dummett/Avramides : Davidson and Dummett represented a "pessimistic" approach: Instead of asking directly what is meaning, we can only wonder how a theory of meaning must look. Meaning theory/Dummett: "meaning is what meaning theory explains". Avramides: Dummett stands in stark contrast to Grice. DummettVsGrice. Avramides: Dummett's approach is too pessimistic. Meaning theory/Davidson: what form must a meaning theory have? 1st Theorems must be comprehensible to speakers and hearers 2nd We will have to explain potentially infinitely many sentences 3rd We will have to explain compositionality. Solution/Davidson: a semantic notion of truth (Tarski) will have to understand the language. DummettVsDavidson: verification. Conditions of verification instead of truth conditions. >Verification conditions, >Truth conditions. I 94 Meaning theory/Grice/John Biro/Avramides: it is about the theory, not about how to find out the meaning but what it constitutes. - Not what reveals the significance, but what does it mean that an expression has a meaning. Biro: "Constitution of meaning is one thing - to tell you is another". |
Avr I A. Avramides Meaning and Mind Boston 1989 |
| Meaning Theory | Foster | I 4 Meaning Theory/m.th./Foster: the meaning theory does not say what is "meaning" but it reveals what conditions it must meet. - Analog: Science theory does not explain what is the concept of a natural law, but it covers the canon of scientific methods. I 6 Meaning Theory/Foster: the extension of "means that p" is not determined by the truth value or the extensional structure of the sentence , which is used for "p". - It is an error to presuppose an intensional idiom for "that means" (presupposes what we are looking for). - Solution: Extension instead of intension. I 7 Meaning Theory/ Foster: examined language L: is about (contingent) facts - metalanguage: uses essentially methodological vocabulary (not contingent) to establish the theorems. I 11 Meaning Theory/truth theory/FosterVsDavidson: the truth condition is determined to set out the specific truth value in all circumstances. - Problem : Tarski: the scheme would correspond to a counterfactual condition "would be true if ... " - but the schema is indicative. I 17 Meaning Theory/Foster: Problem: all T-sentences of the Tarski schema ("Snow is white" is true iff snwo is white) remain true if one uses just something that preserves the truth values and the right side is a translation of the left. - It provides no meaning, only a truth-definition. A meaning Theory can arise when one knows that the conditions are met - i.e. that the truth th. is a meaning theory. I 19 But only if the theory is formulated in the same language as the object language - Because the theory is not really interpreting. Solution/Foster: We need the facts and the knowledge that the facts are truth-theoretical. I 20 Then the meaning theory is a single sentence: q *: " a truth theory T in L represents that ... " - I 21 ... if we are aware, we can find out what determines each selected sentence. - This implies the ability to interpret each sentence due to its structure , because it implies to perceive what each element contributes. ( >Compositionality) Per: that is interpretive. Vs: Problem: "notes that" is still intensional! I 22 E.g. someone who does not know what U denotes, could know the facts that U says . - Problem: if the meaning theory is purely extensional, then it is no longer interpreting. Summary: Meaning theory/Foster: is a meaning theory for an object language L0 in the design of an appropriate range of possible worlds if it exhausts all possible facts that allows our philosophical standpoint. This together with a finite set of axioms true, which provides for each L0 - sentence S the relevant canonical reformulation of the T-conditional. This would consist of the scheme "(w) (x is true-of-w, if w, then it would be the case that p)" by inserting the structural description (sound, character) of S for "p." Instead of "part-of" relation "material-part-of" is between x and y: if y is a world and x is an ordered pair whose first element is the class of all material things, and whose second element is the class of all ordered pairs of all the tangible things that are in the part-whole relation. |
Foster I John A. Foster "Meaning and Truth Theory" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 |
| Metalanguage | Prior | I 103 Metalanguage/Prior: Problem: "I say something wrong" cannot be the only thing I say. Then a meta language is necessary, otherwise follows an absurdity: I could choose a short time interval in which I could say nothing else. Also: the language in which the theorems are expressed, can not be the same as the language used in some other opportunities to do so. >Levels/order, >Description levels. A hierarchy is possible without metalanguage : e.g. "N": "something that Prior says between t and t is not the case": then: N is a true sentence if and only if ... something is not the case. ((s) Without quotation marks). E.g. VsMetalanguage. "I’ll be damned if grass is pink." ((s) quasi-operator). >Operators. Prior: "isolation" through "I’ll be". Solution: a meta-part of the language (isolated), no complete metalanguage. Cf. >Object language. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
| Method | Duhem | I 250 Method/Duhem: The method of ad absurdum guiding can become an evidence. In order to prove that a theorem is correct, it is sufficient to drive the exactly opposite theorem into an absurd consequence. The Greek mathematicians had made extended use of this method. Those who equate the experimental contradiction with the ad absurdum guiding mean that one makes equal use in physics as in geometry. That's not right. The name experimentum Crucis refers to a crossroad of the decision. E.g. there are two hypotheses about the nature of the light. I 251 For Newton, Laplace, and Biot light consists of projectiles. For Huygens, Fresnel et al. it consists of vibrations. According to the first, light moves faster in water than in the air. Foucault's experiment with rotating mirrors proves that the greenish strip ... appears at a certain point. The dispute is decided, light is not a body, but a vibration propagating in the ether. DuhemVs: The experiment of Foucault does not decide between two hypotheses of emission and undulation, but between two theoretical groups, which must be taken as a whole, between two complete systems of Newton's optics and Huygens' optics. >Hypotheses, >Theories. I 252 But let us assume that both are correct. In addition to two theorems of geometry that contradict each other, there is no place for a third. This is different in physics. I 253 Experiment/Method/Duhem: One cannot reconstruct the form of ad absurdum guiding with the experimental method. The geometry, however, also has the direct proof, but it cannot be comprehended in the experiment either. >Experiments, >Observation. I 260 E.g. the theoretician cannot only use the Kepler laws for justification, since these are determined solely by the concrete individual objects. He must show that the observed disturbances coincide with the previously calculated ones. --- I 278 Method/Duhem: Interlocutor: The discussion that leads to a theory is a link, it is not justified to seek in it a physical sense. The demand that every mathematical operation used in the course is given a physical sense would inhibit the progress. One has also tried to ban the differential calculus for physics. >Calculus. |
Duh I P. Duhem La théorie physique, son objet et sa structure, Paris 1906 German Edition: Ziel und Struktur der physikalischen Theorien Hamburg 1998 |
| Method | Menger | Coyne I 7 Method/Menger/Coyne/Boettke: (…) Carl Menger provided a unique set of methodological principles that are at the foundation of what makes Austrian economics distinct. These principles are grounded in the core purpose of economics, which is the intelligibility of the world in which we live. Further, since their goal is to understand the human world, economists must render the events under examination intelligible in terms of purposeful human action. This leads to the recognition that only individuals face decisions and make choices, though undoubtedly conditioned by their social surroundings. >Decision, >Decision making process, >Actions. Methodological individualism: Therefore, social phenomena are only rendered intelligible if the economist traces those phenomena back to individual decisions. This is the concept of “methodological individualism,” which holds that people, with their unique purposes and plans, are the beginning of all economics analysis. Groups and organizations, which consist of people, do not engage in choice and do not have purposes and plans absent the individuals that constitute the group. This involves starting with the individual choosers and tracing out the implications of their decisions in light of their desired ends. Analysis: These core principles - methodological individualism and purposive behaviour - have important implications for the way that we engage in economic analysis. We are interested in explaining a variety of complex phenomena - for example, exchange, price formation - and to do so we appreciate that these phenomena are composed of the actions of numerous individual actors. It is only by appreciating the purposes and plans of individuals that we can hope to make sense of the world. The theorems of economics - that is, the concepts of marginal utility and opportunity cost, and the principle of demand and supply - are all derived from reflection upon purposefulness in human action. >Marginal utility, >Opportunity cost, >Demand, >Supply, >Price, >Exchange. Economic theory does not represent a set of testable hypotheses, but rather a set of conceptual tools that aid us in reading and understanding the complexities of the empirical world. This is fundamentally different from the scientific method employed in the natural sciences. >Human Action/Austrian School. |
Meng I K. Menger Selected Papers in Logic and Foundations, Didactics, Economics (Vienna Circle Collection) 1979 Coyne I Christopher J. Coyne Peter J. Boettke The Essential Austrian Economics Vancouver 2020 |
| Modalities | Field | I 185 Modality/Field: many people believe there can be a simple exchange between modality and ontology: one simply avoids an enrichment of the ontology by modal statements. >Ontology, >Modal logic. I 255 Modalization/Mathematics/Physics/Field: "Possible Mathematics": 1. Does not allow to preserve platonic physics 2. Advantage: This avoids the indispensability argument 3. False: "It is possible that mathematics is true" - but correct: Conservativity of modality. ((s) Mathematics does not change the content of physical statements). 4. For Platonic physics one still needs to use unmodalized mathematics. 5. Field: but we can formulate physics based neither on mathematics nor on modality: comparative predicates instead of numeric functors. - (257 +) >Platonism, >Mathematics, >Physics, >Conservativity. I 272f Modal translation/mathematics/Putnam/Field: the idea is that in the modal translation acceptable sentences become true modal statements and unacceptable sentences false modal statements. Field: then there are two ways of looking at the translations: 1st as true equivalences: then the modal translation shows the truth of the Platonic theorems. (Truth preservation). >Truth transfer. I 273 2nd we can regard the modal translation as true truths: then the Platonic propositions are literally false. ((s) symmetry/asymmetry). N.B.: It does not make any difference which view is accepted. They only differ verbally in the use of the word "true". >Truth. I 274 Truth/mathematical entities/mE/Field: if a modal translation is to be true, "true" must be considered non-disquotational in order to avoid mathematical entities. - True: can then only mean: it turns out to be disquotational true in the modal translation, otherwise the existence of mathematical entities would be implied. - ((s) "Non-disquotational": = "turns out as disquotational.") (No circle). |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Motion | Field | I 193 Def Problem of Quantities/S/R/Field: the representational theorems used for the generation of many numerical functors in physics (e.g. distance, relative velocity, acceleration). - They are not available for relativism because they depend on structural regularities of the space time which are lost when one discards those parts of the space time that are not completely occupied by matter as the space is. - Definition of distance without numbers by congruence and "between". >Spacetime, >Representation theorem. III 84f Law of movement/Nominalisation/Field: therefore we need the concepts trajectory and differentiation of the vector field. Cf. >Nominalism. Derivation: of scalars can be equated with differences of scalars - so also derivations of vectors with differences of vectors. Problem: differences of vectors are themselves vectors; spacetime can be assumed to be infinite, but not temperature. III 88 Law of movement/Nominalisation/Field: with the concept of the tangent on a trajectory. - The trajectory can be differentiated if the tangent is not purely spatial. - The accelerations of points (on one or more trajectories) are compared with the gradients of the gravitational potential at the points. Def Law of movement/Newtonian gravitational theory/Field: (if only gravitational forces are effective): for every such T, T',z,z',S,S', y and y': there is a positive real number k so that a) the second directional derivative of the spatial separation of S from T to z in relation to zy> is taken twice is k-times the gradient of the gravitational potential on z. b) the second directional derivative of the spatial trajectory from S' from T' to z' corresponding to the other coated symbols. Nominalistic: one only has to use the second directional derivative in (12'). |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Natural Laws | Schurz | I 93 Natural Law/Schurz: Strict spatiotemporally unrestricted all propositions are candidates for natural laws. If they were true, they would express real laws of nature. They are called law-like. I 94 Law-like/Schurz: Spatiotemporally unrestricted Ex All bodies attract each other. Bsp All living beings must die once. Spatiotemporally limited: Bsp Mammals in polar regions have a rounder shape compared to conspecifics in warmer regions (Germann's law). Scientificity/Schurz: depends here on the size of the area. Allsatz/Schurz: In order to avoid gradual differences, one spoke of fundamental and derived Allsätze Def Fundamental All Theorem/Carnap/Hempel: contains no individual constants and no spatiotemporal restrictions. >Individual constants. Def Derived All Theorem/Carnap/Hempel: a derived all theorem can be derived from background knowledge from other all theorems together with singular initial conditions. >Initial conditions. I 95 Ernest NagelVsCarnap/NagelVsHempel: According to this, also an accidental all theorem can be a derived law: Ex "All screws on Smith's car are rusty". Solution/E. Nagel: Only fundamental all propositions can be laws. Hempel: conceded that, thus law-likeness remains gradual! Law-like/statistics/Schurz: also here there is law-likeness: Ex 50 % of all caesium 137 atoms have decayed after 30 years. Example 80 % of all lung cancer patients were heavy smokers. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Nature | Aristotle | Gaus I 312 Nature/Aristotle/Keyt/Miller: Plato had already attempted to combat Protagorean relativism and conventionalism by an appeal to nature, but the nature to which he appealed was either divine reason (in the Laws) or a realm of incorporeal and changeless Forms existing beyond time and space (in the Republic). (PlatoVsRelativism, PlatoVsProtagoras: >Protagoras/Plato, >Relativism/Protagoras). AristotleVsPlato: though Aristotle too wishes to combat relativism by an appeal to nature, he wishes to do so without invoking a suprasensible standard or a supernatural being: his aim is to avoid Platonism as well as relativism. (...) Aristotle, by identifying nature with the realm of sensible objects and of change (Metaph. XII.l.1069a30-b2), brings it down to earth. Nature/Aristotle: Aristotle's concept of nature, unlike Plato's, would be recognizable to a modern physicist or biologist. Gaus I 313 Nature makes its first appearance in three basic theorems that stand as the portal to the Politics: (1) the polis exists by nature, (2) man is by nature a political animal, and (3) the polis is prior by nature to the individual (Pol. 1.2). These statements are referred to as theorems because they are not simply asserted but argued for. Problems: nothing concerning them or the arguments supporting them is uncontroversial. The very content of the theorems is contested, for it is unclear what 'nature' means in each of them. Aristotle distinguishes several senses of 'nature' (Phys. II.1; Metaph. V .4), the most important of which correspond to his four causes (final, formal, efficient, and material); but he usually relies on the context to indicate the intended sense of a particular occurrence of the term. It has even been suggested that 'nature' has an entirely different sense in the Politics than it has in the physical and metaphysical treatises. Questions: what is Aristotle tacitly assuming? Are the arguments valid or invalid? How plausible are his premises? The tenability of Aristotle's naturalism depends upon the answer to these questions. (For the controversy see Ambler, 1985(1); Keyt, 1991b(2); Depew, 1995(3); Miller, 1995(4): 27-66; and Saunders, 1995(5): 59-71.) Aristotle's analysis of nature leads to a complex treatment of the antithesis between physis and nomos. >Nomos/Aristotle. Phys.: Aristotle Physics Pol: Aristotle Politics Metaph.: Aristotle Metaphysics 1. Ambler, Wayne (1985) 'Aristotle's understanding of the naturalness of the city'. Review of Politics, 47: 163—85. 2. Keyt, David (1991b) 'Three basic theorems in Aristotle's Politics'. In David Keyt and Fred D. Miller, eds, A Companion to Aristotle's Politics. Oxford: Blackwell. 3. Depew, David J. (1995) 'Humans and other political animals in Aristotle's History of Animals'. Phronesis, 40: 159-81. 4. Miller, Fred D. (1995) Nature, Justice, and Rights in Aristotle's Politics. Oxford: Claredon. 5. Saunders, Trevor J. (1995) Aristotle Politics Books I and 11. Oxford: Clarendon. Keyt, David and Miller, Fred D. jr. 2004. „Ancient Greek Political Thought“. In: Gaus, Gerald F. & Kukathas, Chandran 2004. Handbook of Political Theory. SAGE Publications |
Gaus I Gerald F. Gaus Chandran Kukathas Handbook of Political Theory London 2004 |
| Neural Networks | Minsky | Norvig I 16 Neural Networks/Minsky: Two undergraduate students at Harvard, Marvin Minsky and Dean Edmonds, built the first neural network computer in 1950. The SNARC, as it was called, used 3000 vacuum tubes and a surplus automatic pilot mechanism from a B-24 bomber to simulate a network of 40 neurons. Later, at Princeton, Minsky studied universal computation in neural networks. Norvig I 17 Minsky was later to prove influential theorems showing the limitations of neural network research. >Artificial Neural Networks, >Networks, >Artificial Intelligence, >Artificial Consciousness. |
Minsky I Marvin Minsky The Society of Mind New York 1985 Minsky II Marvin Minsky Semantic Information Processing Cambridge, MA 2003 Norvig I Peter Norvig Stuart J. Russell Artificial Intelligence: A Modern Approach Upper Saddle River, NJ 2010 |
| Number Theory | Quine | IX 81 Elementary Number Theory/Quine: this is the theory that can only be expressed with the terms "zero, successor, sum, power, product, identity" and with the help of connections from propositional logic and quantification using natural numbers. One can omit the first four of these points or the first two and the fifth. But the more detailed list is convenient, because the classical axiom system fits directly to it. Quine: our quantifiable variables allow other objects than numbers. However, we will now tacitly introduce a limitation to "x ε N". Elementary Number Theory/Quine: less than/equal to: superfluous here. "Ez(x + z = y)" - x ε N > Λ + x = x. - x,y ε N >{x} + y = {x+y}. IX 239 Relative Strength/Proof Theory/Theory/Provability/Quine: Goedel, incompleteness theorem (1931)(1). Since number theory can be developed in set theory, this means that the class of all theorems IX 239 (in reality, all the Goedel numbers of theorems) of an existing set theory can be defined in that same set theory, and different things can be proved about it in it. >Set Theory/Quine. Incompleteness Theorem: as a consequence, however, Goedel showed that set theory (if it is free of contradiction) cannot prove one thing through the class of its own theorems, namely that it is consistent, i.e., for example, that "0 = 1" does not lie within it. If the consistency of one set theory can be proved in another, then the latter is the stronger (unless both are contradictory). Zermelo's system is stronger than type theory. >Type theory, >Strength of theories, >Set theory, >Provability. 1.Kurt Gödel: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. In: Monatshefte für Mathematik und Physik. 38, 1931, S. 173–198, doi:10.1007/BF01700692 II 178 Elementary number theory is the modest part of mathematics that deals with the addition and multiplication of integers. It does not matter if some true statements will remain unprovable. This is the core of Goedel's theorem. He has shown how one can form a sentence with any given proof procedure purely in the poor notation of elementary number theory, which can be proved then and only then if it is wrong. But wait! The sentence cannot be proved and still be wrong. So it is true, but not provable. Quine: we used to believe that mathematical truth consists in provability. Now we see that this view is untenable to mathematics as a whole. II 179 Goedel's incompleteness theorem (the techniques applied there) has proved useful in other fields: Recursive number theory, or recursion theory for short. Or hierarchy theory. >Goedel/Quine. III 311 Elementary Number Theory/Quine: does not even have a complete proof procedure. Proof: reductio ad absurdum: suppose we had it with which to prove every true sentence in the spelling of the elementary number theory, III 312 then there would also be a complete refutation procedure: to refute a sentence one would prove its negation. But then we could combine the proof and refutation procedure of page III 247 to a decision procedure. V 165 Substitutional Quantification/Referential Quantification/Numbers/Quine: Dilemma: the substitutional quantification does not help elementary number theory to any ontological thrift, for either the numbers run out or there are infinitely many number signs. If the explanatory speech of an infinite number sign itself is to be understood again in the sense of insertion, we face a problem at least as serious as that of numbers - if it is to be understood in the sense of referential quantification, then one could also be satisfied from the outset uncritically with object quantification via numbers. >Quantification/Quine. V 166 Truth conditions: if one now assumes substitutional quantification, one can actually explain the truth conditions for them by numbers by speaking only of number signs and their insertion. Problem: if numerals are to serve their purpose, they must be as abstract as numbers. Expressions, of which there should be an infinite number, could be identified by their Goedel numbers. No other approach leads to a noticeable reduction in abstraction. Substitutional quantification: forces to renounce the law that every number has a successor. A number would be the last, but the substitutional quantification theorist would not know which one. It would depend on actual inscriptions in the present and future. (Quine/Goodman 1947). This would be similar to Esenin Volpin's theory of producible numbers: one would have an unknown finite bound. V 191 QuineVsSubstitutional Quantification: the expressions to be used are abstract entities as are the numbers themselves. V 192 NominalismVsVs: one could reduce the ontology of real numbers or set theory to that of elementary number theory by establishing truth conditions for substitutional quantification on the basis of Goedel numbers. >Goedel Numbers/Quine. QuineVs: this is not nominalistic, but Pythagorean. It is not about the high estimation of the concrete and disgust for the abstract, but about the acceptance of natural numbers and the rejection of most transcendent numbers. As Kronecker says: "The natural numbers were created by God, the others are human work". QuineVs: but even that is not possible, we saw above that the subsitutional quantification over classes is basically not compatible with the object quantification over objects. V 193 VsVs: one could also understand the quantification of objects in this way. QuineVs: that wasn't possible because there aren't enough names. You could teach space-time coordination, but that doesn't explain language learning. X 79 Validity/Sentence/Quantity/Schema/Quine: if quantities and sentences fall apart in this way, there should be a difference between these two definitions of validity about schema (with sentences) and models (with sentences). But it follows from the Löwenheim theorem that the two definitions of validity (using sentences or sets) do not fall apart as long as the object language is not too weak in expression. Condition: the object language must be able to express (contain) the elementary number theory. Object Language: In such a language, a scheme that remains true in all insertions of propositions is also fulfilled by all models and vice versa. >Object Language/Quine The requirement of elementary number theory is rather weak. Def Elementary Number Theory/Quine: speaks about positive integers by means of addition, multiplication, identity, truth functions and quantification. Standard Grammar/Quine: the standard grammar would express the functors of addition, multiplication, like identity, by suitable predicates. X 83 Elementary Number Theory/Quine: is similar to the theory of finite n-tuples and effectively equivalent to a certain part of set theory, but only to the theory of finite sets. XI 94 Translation Indeterminacy/Quine/Harman/Lauener: ("Words and Objections"): e.g. translation of number theory into the language of set theory by Zermelo or von Neumann: both versions translate true or false sentences of number theory into true or false sentences of set theory. Only the truth values of sentences like e.g. "The number two has exactly one element", which had no sense before translation, differ from each other in both systems. (XI 179: it is true in von Neumann's and false in Zermelo's system, in number theory it is meaningless). XI 94 Since they both serve all purposes of number theory in the same way, it is not possible to mark one of them as a correct translation. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Omniscience | Strobach | Stro I 125 Logical omniscience/Strobach: arises because propositional logic theorems are valid in all possible worlds and all possible worlds that are compatible with a knowledge trivially are possible worlds. >Possible worlds, >Compatibility, >Propositional logic. If that were true, one needed to learn no proof techniques. - The same problem also exists with faith and belief. >Beliefs. Instead: it happens that you know something, but are not aware of its logical consequences. >Knowledge, >Logic, >Conclusions. |
Stro I N. Strobach Einführung in die Logik Darmstadt 2005 |
| Paradoxes | Prior | Cresswell II 110 Paradox/liar/Cretans/Prior/Cresswell: thesis: the Cretan must, so that he can have expressed anything , have said more than one sentence. ((s) Otherwise the sentence refutes itself and thus logically expresses nothing). Cresswell II 180ff Paradox/Cohen/Prior/Cresswell: (Cohen 1957, p. 225)(1), (Prior 1962)(2). Cohen: E.g. When the policeman testifies that everything that the prisoner says is wrong, and the prisoner explains that something that the policeman testified is true, then something that the police officer testified is wrong and something that the prisoner explains, true. Notation: d1: "the policeman testified that:" d2:" the prisoner explains". Logical form: (d1 p(d2p> ~ p) u d2Ep(d1 p up))> (Ep (d1P u ~ p) u Ep (d2p up)) Liar/Prior: d: "was told by a Cretan": dp (dp> ~ p)> (Ep (dp up) and Ep (dp u ~ p)) (ii) dp (dp> ~ p)> Ep Eq(p unequal q) u dp u dq). (ii) states that the Cretans must have said at least two things. --- Prior I 81 Prior/(s): tautology p > pq. Prior reads it like this: p E.g. Say, q: adverb. E.g. CpAKpqKpNq: if it is the case that p, then either it is the case that p-and-q or it is the case that p-but-not-q. Moore's paradox: the same device can be used for it, I believe that it is raining, but of course it does not rain. Philosophers have found it remarkably difficult to explain what is wrong with it - but that happens all the time. Prior I 2 Moore's Paradox/Prior: we only need normal truth and error (error or dishonesty as the only options). >Truth, >Truthfulness, >Error. Prior I 85 Preface paradox/Prior: thesis that something is in the book, is not the case, can only be claimed outside of the book. >Levels/order, >Description levels. Variant: book with only one sentence: something in this book is wrong: sequence of theorems: 1. then something is wrong 2. the say that something is wrong in the book is true 3. which in turn is true 4. then something is wrong in the book and something is true. ((s) But only a statement). Prior: But then at least two different things are said in the book - by contraposition: if nothing is wrong in the book, except that it is said that something is wrong in the book, then this is not said in the book. Prior I 88 Preface paradox/Prior: in the book there is something wrong just cannot be the only assertion - but self-reference is not the problem. >Self-reference. Prior I 96f Preface Paradox/Prior: Parallel/Cohen E.g. If John has a brown cow which is then and only then pregnant if any animal of John is not pregnant, then any animal of John is not pregnant - Proof: e.g. hypothesi : when an animal of John is not pregnant, the cow is pregnant so if the cow is not pregnant, the other animal is pregnant - and therefore (because the cow is only pregnant, when another animal is not, then an animal of John is not pregnant. - He must have at least two animals - Prior: oddly enough, not essential that the pregnant animal must be a brown cow, just so: for x, x means that the sky is blue and x is true, iff grass is green. Both elements are quite irrelevant for each other - Even for the preface paradox. Prior I 98 Preface paradox/PriorVsTarski: my concept of truth here non-Tarski: truth is not property of sentences, but of propositions. - That means, Quasi properties of quasi-objects. - Rather adverbs than adjectives. - E.g. truthfully and incorrectly. >Sentences, >Propositions, >Truth/Tarski, >Truth Definition/Tarski. 1. L.J. Cohen (1957). The Diversity of Meaning. London, 1962. 2. Arthur Prior (1960). On a family of paradoxes. Notre Dame Journal of Formal Logic 2 (1):16-32 |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 Cr I M. J. Cresswell Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988 Cr II M. J. Cresswell Structured Meanings Cambridge Mass. 1984 |
| Physics | Duhem | I XXI Physics/Duhem: the work of the physicist in 4 steps: 1. Definition and measurement of the physical quantities (also combined quantities) the symbols of the theory are given a physical meaning only to the extent that measurement methods for the quantities are given. 2. Formulation of hypotheses. Here, quantities are linked together. I XXII 3. The mathematical development of the theory e.g. the slowed down motion on the inclined plane is the responsibility of the logician and the mathematician alone. 4. Review by experiment. "Consistency with experience is the only criterion of truth for a physical theory." I 150 Theoretical Physics/Duhem: cannot grasp the sensually perceptible phenomena. It cannot therefore decide whether these properties are qualitative or quantitative. Theoretical physics confines itself to representing perceptible phenomena through signs, by symbols. It does not capture the reality of things. I 275 Physics/Duhem: must respect the mathematical rules strictly. The mathematical symbols have only meaning under properly determined conditions. To define these symbols is to enumerate the conditions. E.g. because of the definition, an absolute temperature can only be positive, the mass of a body invariable. Postulates: The theory has the principle of postulates, i.e. theorems which it can express as it likes, if there are no contradictions within the postulates, or between them. Only such rules weigh on the construction of the theory. The physical theory can take any path that is logical. In particular, it is free to give no account of the experimental facts. This is no longer the case when the theory is fully developed. Then it becomes necessary to compare the group of mathematical theorems with the group of experimental data. It may then turn out that it must be discarded, although it is logically correct because it is physically false because of the observation. >Theories, >Observation, >Observation language, >Theoretical terms. I 276 It is a mistake that all the conclusions made by the mathematician have a physical meaning. Similarly, (falsely) any calculation carried out during a measurement procedure would have to have a correspondence in a property of the examined body. That is not the case. Only the concluding formulas deal with the observed objects. E.g. Dissociation of a perfect gas mixture into its elements, which were regarded as perfect gases. I 277 Measuring: e.g. no thermometer can determine the highest temperature. The symbol for absolute temperature does not correspond to any of the measuring methods. What is called a perfect gas in thermodynamics is only an approximate picture of a real gas. >Experiments, >Idealization. |
Duh I P. Duhem La théorie physique, son objet et sa structure, Paris 1906 German Edition: Ziel und Struktur der physikalischen Theorien Hamburg 1998 |
| Picture Theory | Epicurus | Adorno XIII 213 Picture theory/image theory/recognize/sensations/Epicurus/Adorno: image theory is a theory that Epicurus bases on its > aporetic terms. It has been of extraordinary and disastrous effect. Thesis: according to Democritus, the matter made up of atoms fundamentally emits tiny pictures, which affect us or are even identical with our sensations. >Atoms/Democritus, >Democritus. XIII 214 Aporetic terms/Adorno: aporetic terms prepare new aporias here. AdornoVsEpicurus: Thus, to bring together his two theorems, Epicurus is compelled to a metaphysical settlement, which cannot be combined with the denial of metaphysics by his materialism. >Metaphysics/Aristotle, >Metaphysics. |
A I Th. W. Adorno Max Horkheimer Dialektik der Aufklärung Frankfurt 1978 A II Theodor W. Adorno Negative Dialektik Frankfurt/M. 2000 A III Theodor W. Adorno Ästhetische Theorie Frankfurt/M. 1973 A IV Theodor W. Adorno Minima Moralia Frankfurt/M. 2003 A V Theodor W. Adorno Philosophie der neuen Musik Frankfurt/M. 1995 A VI Theodor W. Adorno Gesammelte Schriften, Band 5: Zur Metakritik der Erkenntnistheorie. Drei Studien zu Hegel Frankfurt/M. 1071 A VII Theodor W. Adorno Noten zur Literatur (I - IV) Frankfurt/M. 2002 A VIII Theodor W. Adorno Gesammelte Schriften in 20 Bänden: Band 2: Kierkegaard. Konstruktion des Ästhetischen Frankfurt/M. 2003 A IX Theodor W. Adorno Gesammelte Schriften in 20 Bänden: Band 8: Soziologische Schriften I Frankfurt/M. 2003 A XI Theodor W. Adorno Über Walter Benjamin Frankfurt/M. 1990 A XII Theodor W. Adorno Philosophische Terminologie Bd. 1 Frankfurt/M. 1973 A XIII Theodor W. Adorno Philosophische Terminologie Bd. 2 Frankfurt/M. 1974 |
| Prior Knowledge | Norvig | Norvig I 777 Prior knowledge/AI Research/Norvig/Russell: To understand the role of prior knowledge, we need to talk about the logical relationships among hypotheses, example descriptions, and classifications. Let Descriptions denote the conjunction of all the example descriptions in the training set, and let Classifications denote the conjunction of all the example classifications. Then a Hypothesis that “explains the observations” must satisfy the following property (recall that |= means “logically entails”): Hypothesis ∧ Descriptions |= Classifications. Entailment constraint: We call this kind of relationship an entailment constraint, in which Hypothesis is the “un-known.” Pure inductive learning means solving this constraint, where Hypothesis is drawn from some predefined hypothesis space. >Hypotheses/AI Research. Software agents/knowledge/learning/Norvig: The modern approach is to design agents that already know something and are trying to learn some more. An autonomous learning agent that uses background knowledge must somehow obtain the background knowledge in the first place (…). This method must itself be a learning process. The agent’s life history will therefore be characterized by cumulative, or incremental, development. Norvig I 778 Learning with background knowledge: allows much faster learning than one might expect from a pure induction program. Explanation based learning/EBL: the entailment constraints satisfied by EBL are the following: Hypothesis ∧ Descriptions |= Classifications Background |= Hypothesis. Norvig I 779 (…) it was initially thought to be a way to learn from examples. But because it requires that the background knowledge be sufficient to explain the hypothesis, which in turn explains the observations, the agent does not actually learn anything factually new from the example. The agent could have derived the example from what it already knew, although that might have required an unreasonable amount of computation. EBL is now viewed as a method for converting first-principles theories into useful, special purpose knowledge. Relevance/observations/RBL: the prior knowledge background concerns the relevance of a set of features to the goal predicate. This knowledge, together with the observations, allows the agent to infer a new, general rule that explains the observations: Hypothesis ∧ Descriptions |= Classifications , Background ∧ Descriptions ∧ Classifications |= Hypothesis. We call this kind of generalization relevance-based learning, or RBL. (…) whereas RBL does make use of the content of the observations, it does not produce hypotheses that go beyond the logical content of the background knowledge and the observations. It is a deductive form of learning and cannot by itself account for the creation of new knowledge starting from scratch. Entailment constraint: Background ∧ Hypothesis ∧ Descriptions |= Classifications. That is, the background knowledge and the new hypothesis combine to explain the examples. Knowledge-based inductive learning/KBIL algorithms: Algorithms that satisfy [the entailment] constraint are called knowledge-based inductive learning, or KBIL, algorithms. KBIL algorithms, (…) have been studied mainly in the field of inductive logic programming, or ILP. Norvig I 780 Explanation-based learning: The basic idea of memo functions is to accumulate a database of input–output pairs; when the function is called, it first checks the database to see whether it can avoid solving the problem from scratch. Explanation-based learning takes this a good deal further, by creating general rules that cover an entire class of cases. Norvig I 781 General rules: The basic idea behind EBL is first to construct an explanation of the observation using prior knowledge, and then to establish a definition of the class of cases for which the same explanation structure can be used. This definition provides the basis for a rule covering all of the cases in the class. Explanation: The “explanation” can be a logical proof, but more generally it can be any reasoning or problem-solving process whose steps are well defined. The key is to be able to identify the necessary conditions for those same steps to apply to another case. Norvig I 782 EBL: 1. Given an example, construct a proof that the goal predicate applies to the example using the available background knowledge. Norvig I 783 2. In parallel, construct a generalized proof tree for the variabilized goal using the same inference steps as in the original proof. 3. Construct a new rule whose left-hand side consists of the leaves of the proof tree and whose right-hand side is the variabilized goal (after applying the necessary bindings from the generalized proof). 4. Drop any conditions from the left-hand side that are true regardless of the values of the variables in the goal. Norvig I 794 Inverse resolution: Inverse resolution is based on the observation that if the example Classifications follow from Background ∧ Hypothesis ∧ Descriptions, then one must be able to prove this fact by resolution (because resolution is complete). If we can “run the proof backward,” then we can find a Hypothesis such that the proof goes through. Norvig I 795 Inverse entailment: The idea is to change the entailment constraint Background ∧ Hypothesis ∧ Descriptions |= Classifications to the logically equivalent form Background ∧ Descriptions ∧ ¬Classifications |= ¬Hypothesis. Norvig I 796 An inverse resolution procedure that inverts a complete resolution strategy is, in principle, a complete algorithm for learning first-order theories. That is, if some unknown Hypothesis generates a set of examples, then an inverse resolution procedure can generate Hypothesis from the examples. This observation suggests an interesting possibility: Suppose that the available examples include a variety of trajectories of falling bodies. Would an inverse resolution program be theoretically capable of inferring the law of gravity? The answer is clearly yes, because the law of gravity allows one to explain the examples, given suitable background mathematics. Norvig I 798 Literature: The current-best-hypothesis approach is an old idea in philosophy (Mill, 1843)(1). Early work in cognitive psychology also suggested that it is a natural form of concept learning in humans (Bruner et al., 1957)(2). In AI, the approach is most closely associated with the work of Patrick Winston, whose Ph.D. thesis (Winston, 1970)(3) addressed the problem of learning descriptions of complex objects. Version space: The version space method (Mitchell, 1977(4), 1982(5)) takes a different approach, maintaining the set of all consistent hypotheses and eliminating thosefound to be inconsistent with new examples. The approach was used in the Meta-DENDRAL Norvig I 799 expert system for chemistry (Buchanan and Mitchell, 1978)(6), and later in Mitchell’s (1983)(7) LEX system, which learns to solve calculus problems. A third influential thread was formed by the work of Michalski and colleagues on the AQ series of algorithms, which learned sets of logical rules (Michalski, 1969(8); Michalski et al., 1986(9)). EBL: EBL had its roots in the techniques used by the STRIPS planner (Fikes et al., 1972)(10). When a plan was constructed, a generalized version of it was saved in a plan library and used in later planning as a macro-operator. Similar ideas appeared in Anderson’s ACT* architecture, under the heading of knowledge compilation (Anderson, 1983)(11), and in the SOAR architecture, as chunking (Laird et al., 1986)(12). Schema acquisition (DeJong, 1981)(13), analytical generalization (Mitchell, 1982)(5), and constraint-based generalization (Minton, 1984)(14) were immediate precursors of the rapid growth of interest in EBL stimulated by the papers of Mitchell et al. (1986)(15) and DeJong and Mooney (1986)(16). Hirsh (1987) introduced the EBL algorithm described in the text, showing how it could be incorporated directly into a logic programming system. Van Harmelen and Bundy (1988)(18) explain EBL as a variant of the partial evaluation method used in program analysis systems (Jones et al., 1993)(19). VsEBL: Initial enthusiasm for EBL was tempered by Minton’s finding (1988)(20) that, without extensive extra work, EBL could easily slow down a program significantly. Formal probabilistic analysis of the expected payoff of EBL can be found in Greiner (1989)(21) and Subramanian and Feldman (1990)(22). An excellent survey of early work on EBL appears in Dietterich (1990)(23). Relevance: Relevance information in the form of functional dependencies was first developed in the database community, where it is used to structure large sets of attributes into manageable subsets. Functional dependencies were used for analogical reasoning by Carbonell and Collins (1973)(24) and rediscovered and given a full logical analysis by Davies and Russell (Davies, 1985(25); Davies and Russell, 1987(26)). Prior knowledge: Their role as prior knowledge in inductive learning was explored by Russell and Grosof (1987)(27). The equivalence of determinations to a restricted-vocabulary hypothesis space was proved in Russell (1988)(28). Learning: Learning algorithms for determinations and the improved performance obtained by RBDTL were first shown in the FOCUS algorithm, due to Almuallim and Dietterich (1991)(29). Tadepalli (1993)(30) describes a very ingenious algorithm for learning with determinations that shows large improvements in earning speed. Inverse deduction: The idea that inductive learning can be performed by inverse deduction can be traced to W. S. Jevons (1874)(31) (…). Computational investigations began with the remarkable Ph.D. thesis by Norvig I 800 Gordon Plotkin (1971)(32) at Edinburgh. Although Plotkin developed many of the theorems and methods that are in current use in ILP, he was discouraged by some undecidability results for certain subproblems in induction. MIS (Shapiro, 1981)(33) reintroduced the problem of learning logic programs, but was seen mainly as a contribution to the theory of automated debugging. Induction/rules: Work on rule induction, such as the ID3 (Quinlan, 1986)(34) and CN2 (Clark and Niblett, 1989)(35) systems, led to FOIL (Quinlan, 1990)(36), which for the first time allowed practical induction of relational rules. Relational Learning: The field of relational learning was reinvigorated by Muggleton and Buntine (1988)(37), whose CIGOL program incorporated a slightly incomplete version of inverse resolution and was capable of generating new predicates. The inverse resolution method also appears in (Russell, 1986)(38), with a simple algorithm given in a footnote. The next major system was GOLEM (Muggleton and Feng, 1990)(39), which uses a covering algorithm based on Plotkin’s concept of relative least general generalization. ITOU (Rouveirol and Puget, 1989)(40) and CLINT (De Raedt, 1992)(41) were other systems of that era. Natural language: More recently, PROGOL (Muggleton, 1995)(42) has taken a hybrid (top-down and bottom-up) approach to inverse entailment and has been applied to a number of practical problems, particularly in biology and natural language processing. Uncertainty: Muggleton (2000)(43) describes an extension of PROGOL to handle uncertainty in the form of stochastic logic programs. Inductive logic programming /ILP: A formal analysis of ILP methods appears in Muggleton (1991)(44), a large collection of papers in Muggleton (1992)(45), and a collection of techniques and applications in the book by Lavrauc and Duzeroski (1994)(46). Page and Srinivasan (2002)(47) give a more recent overview of the field’s history and challenges for the future. Early complexity results by Haussler (1989) suggested that learning first-order sentences was intractible. However, with better understanding of the importance of syntactic restrictions on clauses, positive results have been obtained even for clauses with recursion (Duzeroski et al., 1992)(48). Learnability results for ILP are surveyed by Kietz and Duzeroski (1994)(49) and Cohen and Page (1995)(50). Discovery systems/VsILP: Although ILP now seems to be the dominant approach to constructive induction, it has not been the only approach taken. So-called discovery systems aim to model the process of scientific discovery of new concepts, usually by a direct search in the space of concept definitions. Doug Lenat’s Automated Mathematician, or AM (Davis and Lenat, 1982)(51), used discovery heuristics expressed as expert system rules to guide its search for concepts and conjectures in elementary number theory. Unlike most systems designed for mathematical reasoning, AM lacked a concept of proof and could only make conjectures. It rediscovered Goldbach’s conjecture and the Unique Prime Factorization theorem. AM’s architecture was generalized in the EURISKO system (Lenat, 1983)(52) by adding a mechanism capable of rewriting the system’s own discovery heuristics. EURISKO was applied in a number of areas other than mathematical discovery, although with less success than AM. The methodology of AM and EURISKO has been controversial (Ritchie and Hanna, 1984; Lenat and Brown, 1984). 1. Mill, J. S. (1843). 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The Principles of Science. Routledge/Thoemmes Press, London. 32. Plotkin, G. (1971). Automatic Methods of Inductive Inference. Ph.D. thesis, Edinburgh University. 33. Shapiro, E. (1981). An algorithm that infers theories from facts. In IJCAI-81, p. 1064. 34. Quinlan, J. R. (1986). Induction of decision trees. Machine Learning, 1, 81–106. 35. Clark, P. and Niblett, T. (1989). The CN2 induction algorithm. Machine Learning, 3, 261–283. 36. Quinlan, J. R. (1990). Learning logical definitions from relations. Machine Learning, 5(3), 239–266. 37. Muggleton, S. H. and Buntine, W. (1988). Machine invention of first-order predicates by inverting resolution. In ICML-88, pp. 339–352. 38. Russell, S. J. (1986). A quantitative analysis of analogy by similarity. In AAAI-86, pp. 284–288. 39. Muggleton, S. H. and Feng, C. (1990). Efficient induction of logic programs. In Proc. Workshop on Algorithmic Learning Theory, pp. 368–381. 40. Rouveirol, C. and Puget, J.-F. (1989). A simple and general solution for inverting resolution. In Proc. European Working Session on Learning, pp. 201–210. 41. De Raedt, L. (1992). Interactive Theory Revision: An Inductive Logic Programming Approach. Academic Press. 42. Muggleton, S. H. (1995). Inverse entailment and Progol. New Generation Computing, 13(3-4), 245- 286. 43. Muggleton, S. H. (2000). Learning stochastic logic programs. Proc. AAAI 2000 Workshop on Learning Statistical Models from Relational Data. 44. Muggleton, S. H. (1991). Inductive logic programming. New Generation Computing, 8, 295–318. 45. Muggleton, S. H. (1992). Inductive Logic Programming. Academic Press. 46. Lavrauc, N. and Duzeroski, S. (1994). Inductive Logic Programming: Techniques and Applications. Ellis Horwood 47. Page, C. D. and Srinivasan, A. (2002). ILP: A short look back and a longer look forward. Submitted to Journal of Machine Learning Research. 48. Duzeroski, S., Muggleton, S. H., and Russell, S. J. (1992). PAC-learnability of determinate logic programs. In COLT-92, pp. 128–135. 49. Kietz, J.-U. and Duzeroski, S. (1994). Inductive logic programming and learnability. SIGART Bulletin, 5(1), 22–32. 50. Cohen, W. W. and Page, C. D. (1995). Learnability in inductive logic programming: Methods and results. New Generation Computing, 13(3–4), 369-409. 51. Davis, R. and Lenat, D. B. (1982). Knowledge-Based Systems in Artificial Intelligence. McGraw- Hill. 52. Lenat, D. B. (1983). EURISKO: A program that learns new heuristics and domain concepts: The nature of heuristics, III: Program design and results. AIJ, 21(1–2), 61–98. 53. Ritchie, G. D. and Hanna, F. K. (1984). AM: A case study in AI methodology. AIJ, 23(3), 249–268. 54. Lenat, D. B. and Brown, J. S. (1984). Why AM and EURISKO appear to work. AIJ, 23(3), 269–294. |
Norvig I Peter Norvig Stuart J. Russell Artificial Intelligence: A Modern Approach Upper Saddle River, NJ 2010 |
| Probability Theory | Schurz | I 110 Probability theory/theorems/Schurz: a) unconditioned probability: (objective und subjective) (T1) p(~A) = 1 – p(A) (complementary probability) (T2) p(A) ≤ 1 (upper bound) (T3) p(A u ~A) = 0 (contradiction) (T4) p(A1 v A2) = p(A1) + p(A2) – p(A1 u A2) (general law of addition). b) conditioned probability (for formulas X in antecedens position) (PT1) If B > A is exhaustive, gilt p(A I B) = 1. The converse is not valid. (PT2) p(A u B) = p(A I B) mal p(B) (PT3) Für jede Partition B1,...Bn: p(A) = ∑ 1≤i≤n p(A I Bi) times p(Bi) (general law of multiplication) (PT4): Def Bayes-Theorem, 1st version: p(A I B) = p(B I A) times p(A)/p(B) (PT5) Def Bayes-Theorem, 2nd version: for each partition A1,...An: p(Ai I B) = p(B I Ai) times p (Ai) /∑ 1≤i≤n p(B I Ai) times p(Ai). (PT6) Symmetry of probabilistic dependence: p(A I B) > p(A) iff p(B I A) > p(B) iff p(B I A) > p(B I ~A) (analog for ≥). Def Partition/Schurz: exhaustive disjunction. I 110 Consequence relation/probability/consequence/probability theory/Schurz: the probability-theoretic inference relation can be characterized as follows: a probability statement A follows probabilistically from a set D of probability statements iff. A follows logically from D and the Kolmogorov axioms (plus mathematical definitions). >Probability. I 112 Probability theory/Schurz: still unsolved problems: (a) objective probability: definitional problems. Definition of statistical probability: problem: with one random experiment one can potentially produce infinitely many infinitely increasing sequences of results, Why should they all have the same frequency limit? Why should they have one at all? Problem: even worse: from a given sequence of results, one can always construct a sequence with an arbitrarily deviating frequency limit value by arbitrary rearrangement or place selection. I 113 Law of large numbers/Schurz: ("naive statistical theory"): is supposed to be a solution for this problem: the assertion "p(Fx) = r" does not say then that in all random sequences the frequency limit is r, but only that it is r with probability 1. StegmüllerVs/KutscheraVs: This is circular! In the definiens of the expression "the probability of Fx is r" the expression "with probability 1" occurs again. Thus the probability is not reduced to frequency limits, but again to probability. >Circularity. Rearrangement/(s): only a problem with infinite sets, not with finite ones. Mises/solution: "statistical collective". 1. every possible outcome E has a frequency threshold in g, identified with probability p(E), and 2. this is insensitive to job selection. From this follows the general product rule/statistic: the probability of a sum is equal to the product of the individual probabilities: p(Fx1 u Gx2) = p(Fx1) times p(Gx2). Probability /propensity//Mises: this result of Mises is empirical, not a priori! It is a substantive dispositional statement about the real nature of the random experiment (>Ontology/Statistics). The Mises probability is also called propensity. >Propensity. Singular Propensity/Single Case Probability/Single Probability/Popper: many Vs. Probability theory/Schurz: problem: what is the empirical content of a statistical hypothesis and how is it tested? There is no observational statement that logically follows from this hypothesis. >Verification. That a random sequence has a certain frequency limit r is compatible for any n, no matter how large, with any frequency value hn unequal to r reached up to that point. Bayes/Schurz: this is often raised as an objection by Bayesians, but it merely expresses the fact that no observational theorems follow from statistical hypotheses. I 115 Verification/Statistics/Schurz: Statistical hypotheses are not deductively testable, but they are probabilistically testable, by sampling. I 115 Principal Principle/PP/Statistics/Schurz: subjective probabilities, if objective probabilities are known, must be consistent with them. Lewis (1980): singular PP: subjectivist. Here "objective" singular propensities are simply postulated. >Propensities. SchurzVsPropensity/SchurzVsPopper: it remains unclear what property a singular propensity should correspond to in the first place. Solution/de Finetti: one can also accept the objective notion of probability at the same time. Conditionalization/Statistics/Schurz: on an arbitrary experience datum E(b1...bn) over other individuals b1,..bn is important to derive two further versions of PP: 1. PP for random samples, which is needed for the subjective justification of the statistical likelihood intuition. 2. the conditional PP, for the principle of the closest reference class and subject to the inductive statistical specialization inference. PP: w(Fa I p(Fx) = r u E(b1,...bn)) = r PP for random samples: w(hn(Fx) = k/n I p(Fx) = r) = (nk) rk times (1 r)n k. Conditional PP: w(Fa I Ga u p(Fx I Gx) = r u E(b1,...bn)) = r. Principal principle: is only meaningful for subjective a priori probability. I.e. degrees of belief of a subject who has not yet had any experience. Actual degree of belief: for him the principle does not apply in general: e.g. if the coin already shows heads, (=Fa) so the act. dgr. of belief of it is of course = 1, while one knows that p(Fx) = ½. a priori probability function: here all background knowledge W must be explicitly written into the antecedent of a conditional probability statement w( I W). Actual: = personalistic. Apriori probability: connection with actual probability: Strict conditionalization/Schurz: let w0 be the a priori probability or probability at t0 and let w1 be the actual probability I 116 Wt the knowledge acquired between t0 and t1. Then for any A holds: Wt(A) = w0(A I Wt). Closest reference class/principle/Schurz: can be justified in this way: For a given event Fa, individual a can belong to very many reference classes assigning very different probabilities to Fx. Then we would get contradictory predictions. Question: But why should the appropriate reference class be the closest one? Because we can prove that it maximizes the frequency threshold of accurate predictions. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Problem Solving | Minsky | I 74 Problem Solving/Minsky: In principle, we can use the generate and test method - that is, trial and error - to solve any problem whose solution we can recognize. But in practice, it can take too long for even the most powerful computer to test enough possible solutions. Solution: The Progress Principle: Any process of exhaustive search can be greatly reduced if we possess some way to detect when progress has been made. Then we can trace a path toward a solution (...).Many easy problems can be solved this way, but for a hard problem, it may be almost as difficult to recognize progress as to solve the problem itself. Solution: [identify] goals and subgoal[s]. [And use] knowledge. It often turned out easier to program machines to solve specialized problems that educated people considered hard - such as playing chess or proving theorems about logic or geometry - than to make machines do things that most people considered easy (...). >Learning/Minsky. |
Minsky I Marvin Minsky The Society of Mind New York 1985 Minsky II Marvin Minsky Semantic Information Processing Cambridge, MA 2003 |
| Propositional Knowledge | Propositional knowledge, philosophy: the knowledge of whether certain propositions are true or false in contrast to a knowledge-how or possessing an ability. A problem with propositional knowledge are indexical theorems because the determination of the truth value (true or false) is context-dependent and situation-dependent here. See also propositions, opacity, example of the two omniscient Gods. |
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| Radical Interpretation | Quine | VI 64 String of Symbols/Chain/Radical Interpretation/RI/Quine: recurring segments can be treated as words. V 73 Radical interpretation/RI/Quine: also for them a question answer game is indispensable. V 74 The field researcher has to ask for approval. (>Gavagai). Criterion for consent: the willingness to express an observation sentence of one's own accord. >Observation Sentence/Quine XII 27 Object/Translation/Indefiniteness/Expression Conditions/Language Learning/Radical Interpretation/Quine: the expression conditions are not sufficient to be able to say with certainty what a speaker of a foreign language regards as objects. >Language/Quine Problem: how can assertions of existence (theorems of existence) ever be empirically invalidated? Solution: the knowledge of the conditions of utterance does not ensure the reference to the subject, but it does help to clarify what serves as empirical confirmation of the truth of the whole sentence. XII 28 We then project our own acceptance of objects onto the indigenous language. We can be sure that the assumed object is an observed object in the sense that the amplified stimuli emanate quite directly from it. >Language Learning/Quine Language Learning/Object/Reference/Quine: Phases: 1. "Mum", "water" etc. are subsequently recognized as names of recurring objects 2. Occurrence individuates terms (general term): true concept of objects. "Which one of them" 3. Demonstrative singular term: Example "this apple". Problem: may not name anything: may be a dummy. N.B.: the dummy is also an observable spatial temporal object. 4. Attributive combination of two general terms: new: now we can create general terms that do not apply to anything: Example "blue apple", "round square". XII 29 N.B.: but if they are true, the items in question are nothing new. 5. New types of objects, new understanding: compound terms by comparatives: e.g. "smaller than this spot": While the non-existence of observable blue apples means the non-existence of blue apples at all. I.e. we have theoretical terms. N.B.: these are only gradual differences of terms for observable objects. XII 62 Def Original Translation/Terminology/Quine/Spohn: = radical interpretation (RI). >Translation/Quine |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Rational Reconstruction | Rational Reconstruction, theory of science, philosophy: rational reconstruction is a collective term for attempts to justify a theory by constructing models of it that meet certain requirements such as rationality, economy, area-specific adequacy and general validity as well as verifiability. Models are the structures which result from the use of designations for objects instead of the abstract designations used in the theorems. Models can only be created for consistent statements. See also reduction, interpretation, models, empiricism, rationality. |
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| Reason | Ryle | I 384ff Mind/reason/Ryle: the mind is not a seperated organ. Thinking does not cause anything. The mind is not a search for truth. Chess and engineering is not a discovery of truth and legislation does not lead to theorems. Memories of youth do not lead to discoveries. >Memory/Ryle, >Discoveries, >Thinking/Ryle, >Thinking, >Truth, cf. >Chess, |
Ryle I G. Ryle The Concept of Mind, Chicago 1949 German Edition: Der Begriff des Geistes Stuttgart 1969 |
| Redundancy Theory | Logic Texts | Hoyningen-Huene II 56 E.g. "The house is beautiful" is about a house - B. "It is true that the house is beautiful" does not speak of a house, but of a statement (Hoyningen-HueneVsRedundancy Theory). >Levels (Order), >Description level, >Object language, >Meta language. --- Read III 40 Redundancy theory VsCorrespondence theory: denies that truth is a predicate. Truth is redundant, it says, inasmuch as the predication of truth from a statement says no more than the assertion of that statement itself. "It is true that A" is the same as "A". >Correspondence theory, >Fact. It does not need a theory of truth, because there is no such thing as truth. Tarski's theorems are true because the right and left sides are essentially identical. They differ only by their notation. Redundancy Theory Vs Metaphysical Object. Thesis: Truth is not a property. VsRedundancy Theory: "is true" is grammatically required, truth is more than repetition: it is force and universality. Truth is not a property - true statements have no common characteristic. >Truth criterion. The truth-predicate adds universality to the fact. >Truth predicate, >Truth. |
Logic Texts Me I Albert Menne Folgerichtig Denken Darmstadt 1988 HH II Hoyningen-Huene Formale Logik, Stuttgart 1998 Re III Stephen Read Philosophie der Logik Hamburg 1997 Sal IV Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983 Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001 Re III St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 |
| Referential Quantification | Kripke | III 378 Referential quantification: if sentences are substitutes, it is again about referential quantification: are (s) sentences treated as objects? Kripke: in any case there is a dispute: are the variables going over sentences, propositions or truth values? III 377 Referential quantification/interpretation/KripkeVsSubstitutionalism: the point is that an uninterpreted formal system is exactly what it is: uninterpreted! Then it is simply impossible to ask for the "right interpretation"! >Interpretation/Kripke, >Substitutional quantification/Kripke. III 378 1. Kripke: surely there are certain formal systems that allow referential interpretation but not substitutional interpretation. Example Quine: If (Ex)φ(x) is provable but ~φ(t) (negation!) is provable for any expression t that can be used for x, resulting in a meaningful sentence φ(t), it is obviously impossible to give the system a substitutional interpretation, but if the formation rules are standard, and it is formally consistent, a referential interpretation is possible. ((s) Although the referential interpretation makes "ontologically stronger assumptions"!). If ~φ(t) is provable for each expression in a class C, while ((s) simultaneously) (Ex)φ(x) is provable, it is impossible to let all theorems be true and interpret the quantifier as replaceable with the substitution class C. These conditions are sufficient, but demonstrably not necessary, so that a first-stage theory does not receive a substitutional interpretation that makes all theorems true. 2. What about the common problem? (Referential interpretation excluded but substitutional interpretation allowed): The autonymous interpretation (see section 3 above, where each term denotes itself) could suggest a negative answer. And this will be one reason why many mathematical logicians did not want to treat substitutional quantification as an independent model-theoretical topic. KripkeVs: however, there may be cases where substitutional quantification is more appropriate than referential quantification. For example, if the substitution class insists on sentences of L0, a referential interpretation with sentences as substitutes leads to a philosophical dispute: do the variables go over propositions, over sentences or over truth values? Are the entities in the area denoted by the sentences? Connectives/Kripke: connectives do not play a threefold role now: as a) sentence connectives, b) function symbols and c) predicates. However, in Frege's system they play such a threefold role! >Connective/Kripke, >Logical constant. |
Kripke I S.A. Kripke Naming and Necessity, Dordrecht/Boston 1972 German Edition: Name und Notwendigkeit Frankfurt 1981 Kripke II Saul A. Kripke "Speaker’s Reference and Semantic Reference", in: Midwest Studies in Philosophy 2 (1977) 255-276 In Eigennamen, Ursula Wolf Frankfurt/M. 1993 Kripke III Saul A. Kripke Is there a problem with substitutional quantification? In Truth and Meaning, G. Evans/J McDowell Oxford 1976 Kripke IV S. A. Kripke Outline of a Theory of Truth (1975) In Recent Essays on Truth and the Liar Paradox, R. L. Martin (Hg) Oxford/NY 1984 |
| Regularities | Lewis | II 198 Regularity: there is always an alternative regularity that could have fulfilled the same function if the whole process had only started differently. II 224 Regularity/Lewis: rules of syntax and semantics are not even regularities. II 234 Communication depends not only on truthfulness, but also on principles of usefulness and relevance. However, these regularities are not independent language conventions. They are by-products. >Convention/Lewis. V XI Natural Laws/Lewis: at least they are regularities without exception. Not all regularities are laws, of course. Def Natural Laws/Ramsey: Laws are those that enter into the truth systems (buy into) that are unsurpassed in severity and simplicity. This is enough for the Humean Supervenience. >Humean supervenience. Simplicity/Lewis: what is simple is certainly not contingent. And the regularities (or candidates for truth systems) are supervised on the arrangement of qualities. V XIII Probability/Lewis: Probabilities are in play from the beginning. If Ramsey says that laws are regularities that enter into the best systems, the question is: what kind of systems? >Probability/Lewis. V 70 Zeit/Lewis: in the life of ordinary people there is a regularity: For example, hair grows, relative to the external time. Time traveller: no regularity at external time, but there is a way of assigning coordinates to his or her travel stages and only one, so that the regularities, as they correspond to his or her attribution, match with those normally assumed in relation to external time: This is the personal time of the time traveler: for example his hair grows, etc. but it is not really time, it only plays the same role in his life as the role it plays in the life of a normal person. (functional, not operational). >Time traveller/Lewis. V 122 Law/natural law/Lewis: this is a kind of regularity theory of lawfulness, but a collective and selective one at the same time: collective: because regularities do not acquire their status as a law from themselves, but through a system within which they are either axioms or theorems, selective: because not every regularity is worthy of being called a law. Laws should have at least the following characteristics (based on chance). V 123 (1) Simplicity, rigour and their balance can only be determined in the light of competing hypotheses. But I don't want to make lawfulness dependent on the kind of access. Nevertheless, our laws would be different if our approach were different, at least in the sense that we can keep our standards fixed and ask what the laws would be like in counterfactual situations. >Simplicity. (2) With this approach, it is not possible to say whether certain generalisations are lawful, whether they are true or false, and whether the laws are the true lawful ones. Three possibilities: something can be wrong, randomly true, or lawfully true. (3) I do not say that the competing systems of truths must consist entirely of regularities. Nevertheless, the regularities in the best systems should be laws. >Best explanation. Laws: should not mention indiviuals, not even the Big Bang, but such laws should not be excluded a priori. (4) Simplicity: in order to be able to compare them, we must not allow our theories to be simply formulated with particularly trivial terms. V 124 This means that the theory must not make all properties the same! Really simple systems may only be called those that integrate real natural characteristics as simply as possible. But then it is also useless to say that natural properties are those which occur in laws ((s) that would be circular). (5) What about a regularity that occurs in some but not all systems? Three options: 1. it is not a law, (you can take the average) 2. it is a law (association), 3. It is uncertain whether it is a law. Lewis pro 1, but I hope that nature is kind enough to show us the right system in the end. I also hope that some systems are completely out of the question. Then it will not matter whether the standards themselves are unfounded. |
Lewis I David K. Lewis Die Identität von Körper und Geist Frankfurt 1989 Lewis I (a) David K. Lewis An Argument for the Identity Theory, in: Journal of Philosophy 63 (1966) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (b) David K. Lewis Psychophysical and Theoretical Identifications, in: Australasian Journal of Philosophy 50 (1972) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (c) David K. Lewis Mad Pain and Martian Pain, Readings in Philosophy of Psychology, Vol. 1, Ned Block (ed.) Harvard University Press, 1980 In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis II David K. Lewis "Languages and Language", in: K. Gunderson (Ed.), Minnesota Studies in the Philosophy of Science, Vol. VII, Language, Mind, and Knowledge, Minneapolis 1975, pp. 3-35 In Handlung, Kommunikation, Bedeutung, Georg Meggle Frankfurt/M. 1979 Lewis IV David K. Lewis Philosophical Papers Bd I New York Oxford 1983 Lewis V David K. Lewis Philosophical Papers Bd II New York Oxford 1986 Lewis VI David K. Lewis Convention. A Philosophical Study, Cambridge/MA 1969 German Edition: Konventionen Berlin 1975 LewisCl Clarence Irving Lewis Collected Papers of Clarence Irving Lewis Stanford 1970 LewisCl I Clarence Irving Lewis Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991 |
| S 4 / S 5 | Bigelow | I 107 System S4/Bigelow/Pargetter: contains T and in addition: A10 Axiom S4 (Na > Nna) Everyday language translation: if something has to be true, it must be true that it has to be true. System B/Brouwer/Bigelow/Pargetter: contains T plus A11. Axiom B: (a > NMa) Everyday language translation: if something is true, it must be true that it is possible. System S4/Bigelow/Pargetter: some of his theorems are not theorems of B, and some of B are not theorems of S4. With an additional Axiom S5, we can prove both S4 and B as theorems: A12. Axiom S5: (Ma > NMa) System S5/Bigelow/Pargetter: contains all theorems of S4 and of B and nothing else. I 108 Systems/Proveability/Bigelow/Pargetter: T plus S5 can prove S4 and B, but also T plus S4 and B together can prove S5. Nevertheless: T plus S4 without B cannot prove S5 T plus B without S4 cannot prove S5. Logical necessity/S5/Bigelow/Pargetter: the system S5 is a plausible characterization of the logical necessity. System S4/Bigelow/Pargetter: when we interpret: Rhomb/diamond/possibility/M: "cannot be proved by logic alone" Box/Necessity/N: "can be proved by logic alone" Then S4 becomes: Everyday language translation: "If something can be proved by logic alone, then one can prove by logic alone that one can prove it by logic alone". Bigelow/Pargetter: that is plausible. System B/Bigelow/Pargetter: Everyday language translation: "If something is true, one can show with logic alone that it cannot be refuted by logic alone. System S5/Bigelow/Pargetter: Everyday language translation: If something cannot be refuted by logic alone, it can be proved by logic alone that it cannot be refuted by logic alone. >Axioms, >Axiom systems. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| Satisfaction | Putnam | I (c) 91 Satisfaction/Tarski: satisfaction is the terminus for reference. Putnam: there is a relation between words and things, more precisely, between formulas and finite sequences of things. Tarski: "The sequence of length only existing of x, satisfies the formula "electron (y)" iff x is an electron". The sequence Abraham: Isaac meets the formula "x is the father of y". If there are more binary relations one does not speak of Reference. > Correspondence Theory, -> picture theory. Putnam: Tarski's theory is not suitable for the correspondence theory because satisfaction is explained by a list (instead > meaning postulates: "electron" refers to electrons, etc.). "True" is the zero digit case of fulfillment: a formula is true if it has no free variables and if it meets the zero sequence. I (c) 92 Zero Digit Relation: e.g. Tarski: "true" is the zero digit case of satisfaction: that means, a formula is true if it has no free variables and if the zero sequence is met. Zero Sequence: converges to 0. Example 1, 1/4, 1/9, 1/16, ... I (c) 92 Satisfaction/Putnam: criterion T can be extended to the criterion E: (E) an adequate definition of fulfilled-in-S must generate all instances of the following scheme as theorems: "P(x1 ... xn) is only fulfilled by the sequence y1. ..yn when P (y1 .... yn). Reformulated: "electron (x)" is then and only then fulfilled by y1 when y1 is an electron. This is determined by truth and reference (not by provability) and is therefore even preserved in intuitionistic interpretation. PutnamVsField: Field's objection fails: for the realists the Tarski schema is correct. FieldVsTarski: this is similar to a "definition" of chemical valence by enumeration of all elements and their valence. The causal involvement in our explanations is lacking. PutnamVsField: truth and reference are not causally explanatory terms, we still need them for formal logic, even if scientific theories are wrong. |
Putnam I Hilary Putnam Von einem Realistischen Standpunkt In Von einem realistischen Standpunkt, Vincent C. Müller Frankfurt 1993 Putnam I (a) Hilary Putnam Explanation and Reference, In: Glenn Pearce & Patrick Maynard (eds.), Conceptual Change. D. Reidel. pp. 196--214 (1973) In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (b) Hilary Putnam Language and Reality, in: Mind, Language and Reality: Philosophical Papers, Volume 2. Cambridge University Press. pp. 272-90 (1995 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (c) Hilary Putnam What is Realism? in: Proceedings of the Aristotelian Society 76 (1975):pp. 177 - 194. In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (d) Hilary Putnam Models and Reality, Journal of Symbolic Logic 45 (3), 1980:pp. 464-482. In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (e) Hilary Putnam Reference and Truth In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (f) Hilary Putnam How to Be an Internal Realist and a Transcendental Idealist (at the Same Time) in: R. Haller/W. Grassl (eds): Sprache, Logik und Philosophie, Akten des 4. Internationalen Wittgenstein-Symposiums, 1979 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (g) Hilary Putnam Why there isn’t a ready-made world, Synthese 51 (2):205--228 (1982) In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (h) Hilary Putnam Pourqui les Philosophes? in: A: Jacob (ed.) L’Encyclopédie PHilosophieque Universelle, Paris 1986 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (i) Hilary Putnam Realism with a Human Face, Cambridge/MA 1990 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (k) Hilary Putnam "Irrealism and Deconstruction", 6. Giford Lecture, St. Andrews 1990, in: H. Putnam, Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992, pp. 108-133 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam II Hilary Putnam Representation and Reality, Cambridge/MA 1988 German Edition: Repräsentation und Realität Frankfurt 1999 Putnam III Hilary Putnam Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992 German Edition: Für eine Erneuerung der Philosophie Stuttgart 1997 Putnam IV Hilary Putnam "Minds and Machines", in: Sidney Hook (ed.) Dimensions of Mind, New York 1960, pp. 138-164 In Künstliche Intelligenz, Walther Ch. Zimmerli/Stefan Wolf Stuttgart 1994 Putnam V Hilary Putnam Reason, Truth and History, Cambridge/MA 1981 German Edition: Vernunft, Wahrheit und Geschichte Frankfurt 1990 Putnam VI Hilary Putnam "Realism and Reason", Proceedings of the American Philosophical Association (1976) pp. 483-98 In Truth and Meaning, Paul Horwich Aldershot 1994 Putnam VII Hilary Putnam "A Defense of Internal Realism" in: James Conant (ed.)Realism with a Human Face, Cambridge/MA 1990 pp. 30-43 In Theories of Truth, Paul Horwich Aldershot 1994 SocPut I Robert D. Putnam Bowling Alone: The Collapse and Revival of American Community New York 2000 |
| Social Movements | Social Choice Theory | Gaus I 268 Social movements/Social choice theory/rational choice theory/West: recognition of the potential rationality of collective action is (...) reflected in theoretical attempts to explain social movement activity. Resource mobilization theory: in the USA, in particular, the influential paradigm of 'rational choice theory' has applied the methods of neoclassical economics to the explanation of social behaviour, giving rise to 'resource mobilization theory' (RMT) (...). RMT treats social movements as more or less successful attempts by individuals to mobilize human and other resources for the sake of collective goals. The availability of resources, the capacity of 'political entrepreneurs' to mobilize these resources and the 'political opportunity structure' of the surrounding political system, all contribute to the distinctive trajectory of success and failure, growth and decline - or 'life cycle' - of movements (Oberschall, 1973(1); Tilly, 1978(2); Zald and McCarthy, 1987(3)). Problems: (...) RMT addresses the formal properties of social movements in general, rather than the substantive characteristics of new social movements in particular. It considers general preconditions, problems and determinants of collective action. But like other rational choice theories, it has nothing to say about the particular goals, values or ideology of new social movement agents (Piven and Cloward, 1992(4)). 1) VsRational choice/West: Rational choice theories may be able to deduce theorems predicting the 'rational' choices that agents make on the basis of particular 'preferences', but they are notoriously unable to cast light on the formation of these preferences or their possible replacement by others (Hindess, 1988)(5). 2) VsRational choice: Rational choice approaches have, for example, been much engaged by the 'problem of voting' - the apparent irrationality of exerting even minimal effort when the chances of influencing the outcome of elections are infinitesimally small (Brennan and Lomasky, 1993)(6). They must surely have difficulty, then, in understanding why people expend considerable long-term effort and even undergo serious (sometimes mortal) risk for the sake of political goals. Gaus I 269 Recently, indeed, there has been consideration of such concepts (Johnston and Klandermans, 1995)(7). >Rational decision, >Rationality, >Altruism. 1. Oberschall, Anthony (1973) Social Conflict and Social Movements. Englewood Cliffs, NJ: Prentice Hall. 2. Tilly, Charles (1978) From Mobilization to Revolution. Reading, MA: Addison-Wesley. 3. Zald, Mayer N. and John McCarthy (1987) Social Movements in an Organizational Society. New Brunswick, NJ: Transaction. 4. Piven, F. F. and R. A. Cloward (1992) 'Normalizing collective protest'. In A. Morris and C. M. Mueller, eds, Frontiers in Social Movement Theory. New Haven, CT: Yale University Press. 5. Hindess, Barry (1988) Choice, Rationality and Social Theory. London: Unwin Hyman. 6. Brennan, Geoffrey and Loren Lomasky (1993) Democracy and Decision: The Pum Theory of Electoral Preference. Cambridge: Cambridge University Press. 7. Johnston, Hank and Bert Klandermans, eds (1995) Social Movements and Culture. Minneapolis: University of Minnesota Press. West, David 2004. „New Social Movements“. In: Gaus, Gerald F. & Kukathas, Chandran 2004. Handbook of Political Theory. SAGE Publications |
Gaus I Gerald F. Gaus Chandran Kukathas Handbook of Political Theory London 2004 |
| Strategic Voting | Economic Theories | Parisi I 504 Strategic voting/Economic theories/Nitzan/Paroush: (…) it is possible that individuals have an incentive to vote insincerely. Using a game-theoretic analysis, Austen-Smith and Banks (1996)(1) show that non-strategic voting may be inconsistent with Nash equilibrium, Parisi I 505 equilibrium, even when all members have identical preferences and beliefs. >Nash equilibrium. More precisely, if the number of voters is sufficiently large, then voting based on private information only (informative voting) is generically not a Nash equilibrium of a Bayesian game that formally represents a CJT [Condorcet Jury Theorem]. >Condorcet Jury Theorem, >Jury theorem. The general idea is that an individual’s vote affects the collective decision only when it is pivotal. But if all the others vote informatively, the fact that they are tied may be very informative in the sense that this reveals more precise information than that privately held by the individual. Following this newly revealed information, it may be rational not to vote according to one’s own private information. [E.g.,] consider three individuals with identical preferences over two alternatives, A and B. There is uncertainty about the true state of the world, which may be either state A or state B. In each state, individuals receive a pay-off of one if the alternative of the specific state is chosen and a payoff of zero otherwise. There is a common prior probability that the true state is A. Individuals have private information about the true state of the world. Majority rule is used to select an alternative. There are two additional assumptions on individuals’ beliefs: (1) sincere voting is informative; and (2) the common prior belief that the true state is A is sufficiently strong, such that if any individual were to observe all the three individual signals, then that individual believes B is the true state only if all the available evidence supports the true state being B. In this example sincere voting is not rational. Suppose that you are playing this game and the two other individuals vote sincerely. You must then be in one of the three following situations: (1) the others have observed that the state is A and accordingly vote for A; (2) the others have both observed B and vote for B; or (3) the others have observed different signals and one votes for A and the other for B. In the first two scenarios the aggregated outcome is independent of your own vote, and in the third scenario your vote is decisive. However, if you are in the third scenario your best decision is to vote for A. Therefore, voting sincerely is not a Nash equilibrium. In response to the above finding, McLennan (1998)(2) and Wit (1998)(3) found conditions under which Nash equilibrium behavior, although it may be inconsistent with non-strategic voting, still predicts that groups are more likely to make correct decisions than individuals. Feddersen and Pesendorfer (1997(4), 1998(5)) adapt the general framework of Austen-Smith and Banks (1996)(1) to the specific case of jury procedures in criminal trials. In their model it is never a Nash equilibrium for all jurors to vote non-strategically under the unanimity rule. Moreover, Nash equilibrium behavior leads to higher probabilities of both convicting the innocent and acquitting the guilty under the unanimity rule than under alternatives rules, including the simple majority rule. Ben-Yashar and Milchtaich (2007)(6) examine the question of strategic voting when voters are solely concerned with the common collective interest. They find that under the optimal WMR, individuals do not have an incentive to vote strategically and non-informatively. >Decision rules. Such strategy-proofness does not hold under second-best anonymous voting rules. Thus, assigning the proper weight to each voter achieves the optimal team performance and guarantees sincere voting. 1. Austen-Smith, D. and J. Banks (1996). “Information aggregation, rationality and the Condorcet jury theorem.” American Political Science Review 90(1): 34-45. 2. McLenan, A. (1998). “Consequences of the Condorcet jury theorem for beneficial information aggregation by rational agents.” American Political Science Review 92(2): 413-418. 3. Wit, J. (1998). “Rational choice and the Condorcet jury theorem.” Games and Economic Behavior 22(2): 364–376. 4. Feddersen, T. J. and W. Pesendorfer (1997). “Voting behavior and information aggregation in elections with private information.” Econometrica 65(5): 1029-1058. 5. Feddersen, T. J. and W. Pesendorfer (1998). “Convicting the innocent: The inferiority of unanimity jury verdicts under strategic voting.” American Political Science Review 92(1): 23-35. 6. Ben-Yashar, R. and I. Milchtaich (2007). “First and second best voting rules in committees.” Social Choice and Welfare 29(3): 453-486. Shmuel Nitzan and Jacob Paroush. “Collective Decision-making and the Jury Theorems”. In: Parisi, Francesco (ed) (2017). The Oxford Handbook of Law and Economics. Vol 1: Methodology and Concepts. NY: Oxford University. |
Parisi I Francesco Parisi (Ed) The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017 |
| Strength of Theories | Quine | IX 237ff Stronger/weaker/theory/system/Quine: Problem: Comparability: it fails if both of the two systems have theorems that cannot be found in the other - it also depends on contingencies of interpretation and not on structure. >Comparisons, >Comparability. If we can interpret the primitive logic characters (only "ε" in set theory) new so that we can ensure that all theorems of this system are made to translations of the theorems of the other system, then the latter system is at least as strong as the other. >Systems. If this is not possible in the other direction, one system is stronger than the other one. Definition "ordinal strength"/set theory: numerical measure: the smallest transfinite ordinal number whose existence you cannot prove anymore in the system. The smallest transfinite number after blocking of the apparatus shows how strong the apparatus was. Relative strength/proof theory: Goedel incompleteness sentence: since the number theory can be developed in set theory, this means that the class of all theorems (in reality all Goedel numbers of theorems) of a present set theory can be defined in this same set theory, and different things can be proven about them. >Incompletenes/Goedel. One can produce an endless series of further based on a arbitrary set theory, of which each in the proof-theoretic sense is stronger than its predecessors, and which is consistent when its predecessors were. - One must only add via Goedel numbering a new arithmetic axiom of the content so that the previous axioms are consistent. Ordinal strength: is the richness of the universe. >Goedel numbers. --- X 71 Metalanguage/Set Theory/Quine: in the metalanguage a stronger set theory is possible than in the object language. In the metalanguage a set of z is possible so that satisfaction relation z applies. - ((s) A set that is the fulfillment relation (in form of a set of arranged pairs) - not in the object language, otherwise Grelling paradox. >Meta language, >Set theory, >Grelling's paradox, >Metalanguage. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Supervenience | Chalmers | I 33 Supervenience/Chalmers: supervenience is in general a relation between two sets of properties: B properties: higher-level properties A properties: lower-level properties (for us physical properties). The specific nature of these properties is not relevant to us. >Levels/order, >Description Levels. Basic pattern: Definition Supervenience/Chalmers: B-properties supervene on A-properties, if two possible situations are not identical with regard to their A-properties and at the same time differ in their B-properties. For example, biological properties supervene on physical ones insofar as two possible physically identical situations are also biologically identical. Local/Global Supervenience/Chalmers: we distinguish global supervenience, depending on how the situations under consideration, refer to individuals or possible worlds. Local Supervenience/Chalmers: B supervenes locally on A when the A properties of an individual determine the B properties of that individual. I 34 E.g. form supervenes on physical properties. Definition Global Supervenience/Chalmers: when A facts about the world determine B facts about the world. That is, there are no two possible worlds which are identical with respect to A, which are not also identical with regard to B. For example biological properties supervene globally on physical properties. Definition local supervenience implies global supervenience, but not vice versa. E.g. two physical organisms can differ in certain biological characteristics, one individual can be fitter than the other, triggered by environmental conditions. >Extrinsic properties,> Niches. Chalmers: For example, one could imagine that two physically identical organisms might belong to different species, if they had different evolutionary stories. Consciousness: here it will be more about local supervenience. I 35 Logical Supervenience/Chalmers: logical supervenience is conceptual and stronger than natural supervenience. Natural Supervenience/Chalmers: this term is used to distinguish between logical supervenience. I 38 A situation would be conceivable in which laws that automatically produce B facts might not produce these for once. (Kripke 1972, 1980)(1). I 39 Logical Supervenience/Chalmers: Problem: There could be a possible world which is identical to our actual world, but not additionally with non-physical elements such as angels and ghosts. These could be physically identical with us, but biologically different from us. This has led some authors (Haugeland 1982(2), Petrie 1987(3)) to say that the logical possibility and logical necessity are too strong terms for our supervenience relations. Solution/Chalmers: we must explicitly refer to our actual world or specified possible worlds. I 40 Other problems have to do with negative existence statements about what does not exist in our world, or does not exist in other possible worlds. Such problems can never be determined by local facts or local characteristics. Supervenience should always be determined by reference to positive facts and characteristics. I 84 Name/Supervenience/Explanation/Chalmers: E.g. according to Kaplan (1989)(4) the name "Rolf Harris" simply picks out its speaker directly. Does that mean that the property to be Rolf Harris does not logically supervene on physical facts? >Names, >Reference, >Identification, >Vivid name/Kaplan. Secondary intension of the name: what resulted from a certain egg and sperm in all possible worlds. This supervenes logically on facts. Primary intension of the name: is that what results from the linguistic usage, of those who have, or had assiociate with Rolf Harris, or heard of Rolf Harris. The primary intension may be absent, which is a problem for the supervenience >Propositions/Chalmers, >Terminology/Chalmers. I 87 Logical Supervenience/Chalmers: apart from conscious experience, indexicality, and negative existence theorems everything supervenes logically on physical facts, including physical laws. >Indexicality, >Experience, >Non-existence, >Existence statements. I 88 Supervenience/Horgan/Blackburn/Chalmers: Question: (Blackburn 1985)(5), Horgan (1993)(6): How do we explain the supervenience relation itself? Primary Intension/Chalmers: For logical supervenience on primary intensions, we simply need to present a conceptual analysis, together with the determination that the reference over possible worlds remains preserved (is rigid). Thereby, the supervenience conditional is an a priori conceptual truth. I 89 Secondary Intension: here, the logical supervenience can be explained by saying that the primary intension of the concept picks out a referent of the actual world, which is projected unchanged to other physically identical worlds (by rigidifying operations). Such facts are contingent. (See Horgan and Timmons 1992b.(7)) Natural Supervenience/Chalmers: natural supervenience is - as opposed to the logical - contingent. This is ontologically expensive, so we can be glad that logical supervenience is the ussual case. I 124 Supervenience/Consciousness/Chalmers: we have seen that conscious experience does not logically supervene on the physical facts, but not that it does not supervene at all! 1. S. A. Kripke, Naming and Necessity, Reprint: Cambridge 1980 2. J. Haugeland, Weak supervenience. American Philosophical Quarterly 19, 1982: pp. 93-103 3. B. Petrie, Global supervenience and reduction. Philosophical and Phenomenological Research 48, 1987: pp. 119-30 4. D. Kaplan, Demonstratives. In: J. Almog, J. Perry and H. Wettstein (Eds) Themes from Kaplan. New York 1989 5. S. Blackburn, Supervenience revisited. In: I. Hacking (ed) Exercises in Analysis: Essay by Students of Casimir Lewy. Cambridge 1985 6. T. Horgan, From supervenience to superdupervenience: Meeting the demands of a material world. Mind 102, 1993: pp. 555-86 7. T. Horgan and M. Timmons, Troubles for new ware moral sentiments; The "open question argument" revived. Philosophical Papers 1992. |
Cha I D. Chalmers The Conscious Mind Oxford New York 1996 Cha II D. Chalmers Constructing the World Oxford 2014 |
| Systems | Cresswell | Hughes I 65 System/Part/Hughes/Cresswell(s):parts of formulas are not themselves parts of the system already to which the formulas belong to. - ((s) "p" can never be an axiom, otherwise all sentences would be true.) Hughes I 237 Non-regular systems/Modal Logic/Hughes/Cresswell: can include formulas of the form p. ~ p where the eradication of the modal operator simply results in p, E.g. systems with e.g. C 13 MMp - "no statement is necessarily necessary" >Modal operators, >Deletion. MMp simply results in p - p. ~ p. Hughes I 243 >" I 258 Def regular: is a system in which the modal status is maintained. >Modalities Hughes I 238 Non-regular systems/modal logics/Hughes/Cresswell: Problem: in S1 - S3, neither a nor b are themselves a thesis - they also have no common variable either. - Problem in the case of (a v b): could be valid while neither a nor b would be valid. Solution/Halldén: "normal interpretation": here either a or b is valid, but neither I-a nor I-b is valid. So there are valid formulas that are not theorems. >Theorems, >Logic, >Formulas. |
Cr I M. J. Cresswell Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988 Cr II M. J. Cresswell Structured Meanings Cambridge Mass. 1984 Hughes I G.E. Hughes Maxwell J. Cresswell Einführung in die Modallogik Berlin New York 1978 |
| Systems | Quine | VII (e) 91 Abbreviations/Quine: defining abbreviations are always outside of a formal system - that's why we need to get an expression in simple notation before we examine it in relation to hierarchy. IX 190 System/Quine: a new system is not introduced by new definitions, but by new distinctions. ((s) Example (s): if I always have to note "n + 1" to mark the difference between real and rational numbers, I did not eliminate the real numbers, but kept the old difference. I only changed the notation, not the ontology.) IX 232 Theory/Enlargement/Extension/System/Quine: an enlargement is not an extension! Extension: addition of axioms, can create contradictions. Magnification/Quine: means to relativize an added scheme to already existing axioms of a system, e.g. to "Uϑ", (s) so if something exists in "Uϑ", it must be a set. Such a magnification never creates a contradiction. IX 237 Theory/stronger/weaker/Quine: if a deductive system is an extension of another in the sense that its theorems include all of the other and others, then in a certain way one is stronger than the other. But this basis of comparison is weak: 1. It fails if each of the two systems has theorems that are not found in the other. (Comparability). 2. It depends on randomness of interpretation and not simply on structural properties. Example: suppose we would have exactly "=" and "R" as primitive two-digit predicates with an ordinary identity axiom and transitivity. Now we extend the system by adding the reflexivity "x(xRx)". The extended system is only stronger if we equate its "R" with the original "R". But if we reinterpret its "xRy" as "x = y v x R y" using the original "R", then all its theorems are provable in the non-extended system. (>Löwenheim, >Provability), Example (less trivial): Russell's method ((1) to (4), Chapter 35) to ensure extensionality for classes without having to accept them for attributes. Given is a set theory without extensionality. We could extend it by adding this axiom, and yet we could show that all theorems of the extended system could be reinterpreted with Russell's method as theorems already provable in the non-extended system. Stronger/weaker/Quine: a better standard for the comparison of strength is the "comparison by reinterpretation": if we can reinterpret the primitive logical signs (i.e. in set theory only "e") in such a way that all theorems of this system become translations of the theorems of the other system, then the latter system is at least as strong as the first one. IX 238 If this is not possible in the other direction, one system is stronger than the other. Def "ordinal strength"/Quine: another meaningful sense of strength of a system is the following surprising numerical measure: the smallest transfinite ordinal number, whose existence can no longer be proven in the system. Any normal set theory can, of course, prove the existence of infinitely many transfinite numbers, but that does not mean that you get them all. Transfinite/Quine: what is so characteristic about it is that we then iterate the iteration further and iterate the iteration of iterations until our apparatus somehow blocks. The smallest transfinite number after blocking the apparatus then indicates how strong the apparatus was. An axiom that can be added to a system with the visible goal of increased ordinal strength is the axiom that there is an unattainable number beyond w (omega). (End of Chapter 30). An endless series of further axioms of this kind is possible. Strength of systems/Ordinal Numbers/Quine: another possibility to use ordinal numbers for strength: we can extend the theory of cumulative types to transfinite types by accrediting to the x-th type for each ordinal number x, all classes whose elements all have a type below x. So the universe of the theory of cumulative types in chapter 38, which lacks the transfinite types, is even the ω-th type. Def "Natural Model"/Montague/Vaught/Quine: this is what they call this type, if the axioms of set theory are fulfilled, if one takes their universe as such a type. So Zermelo's set theory without infinity axiom has the ω-th type as a natural model. (We have seen this in chapter 38). So the ordinal strength of this system is at most ω, obviously not smaller. With infinity axiom: ω + ω. Strength of the system of von Neumann-Bernays: one more than the first unattainable number after w. XII 33 Object/existence/system/Quine: systematic considerations can lead us to reject certain objects XII 34 or to declare certain terms as non-referring. Occurrence: also individual occurrences of terms. This is Frege's point of view: an event can refer to something on one occasion, not on another (referential position). Example "Thomas believes that Tullius wrote the Ars Magna". In reality he confuses Tullius with Lullus. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Theories | Duhem | I XIII Theory/Duhem: Thesis: The goal of physical theory formation is not the knowledge of reality, because it would move in a metaphysical field of concepts, but the design of a formal system that has optimal order properties for the world of phenomena. >Physics, >Phenomena, >Goals. The structure of science is a holistic context, not a combination of single sentences whose truth values are determined in isolation. Only the whole of science can be compared with the totality of facts and examined. Observations are "theory-laden". >Observations, >Theory-ladenness. Theories are not inductively gained knowledge of experience, but designs of the human mind, agreements of a formal nature, whose empirical utility is found only in practice. Conventionalist science-perception, nevertheless Poincaré: it is not the definitive status of the fundamental laws, which deprives them of the revision, such revisions, even of the fundamental laws, can become necessary and meaningful, they cannot be forced experimentally. I XVII Delimitation from metaphysics, which does not allow refutation by observation. (Also Popper, 1934) autonomy of physics. Today one would say: theory is supposed to explain phenomena. The performance of theories or laws can be characterized by the logical link with verifiable statements. For Duhem (in contrast to today's language usage): "Description". "Explanation"/Duhem: reserved for the metaphysicians' claim for knowledge. Metaphysics: (DuhemVs): Premises must be distinguished ontologically, they must concern "things in themselves". Observable properties are "explained" in such a way that they are attributed to another (unobservable) reality layer. E.g. "ether", heat: atomic movement. This is the Cartesian concept of explanation, which Duhem does not grant physics. His physics conception is antimetaphysical, unlike Mach, but he does not consider metaphysics to be pointless. I 22 Definition Physical Theory/Duhem: A physical theory is not an explanation. It is a system of mathematical theorems that are derived from a small number of principles and have the purpose of presenting a group of experimental laws as simple as they are complete and accurate. I 22 A correct theory does not explain reality, but presents a group of experimental laws satisfactorily. A false theory is a set of equations that do not agree with the experimental laws. (Comparison with reality would be metaphysics). >Metaphysics, >Reality. I 29 Revision of a theory: the relationships remain, but their nature is understood differently. I 37 Theories/Duhem: consist of 2 parts A) descriptive B) explanatory The explanatory part is by no means the adequate basis of the descriptive. It is not the seed or the root. >Method, >Explanation. |
Duh I P. Duhem La théorie physique, son objet et sa structure, Paris 1906 German Edition: Ziel und Struktur der physikalischen Theorien Hamburg 1998 |
| Theories | Fraassen | I 3 Theory/Science/Fraassen: Fraassen also tries to find an explanation for unobservable processes which explains the observable and also merely possible processes. I 4 Theories/Fraassen: a theory must preserve the phenomena, i.e. describe correctly. - Then "accepting the theory" means believing that it is true. I 43f Theory/Semantics/Syntax/Fraassen: We evaluate theories better semantically (e.g., via models) rather than syntactically. >Evaluation. I 44 Syntactic: takes theory as a corpus of theorems. - There is a certain language for this theory. Semantics: class of structures or models. - Language is not fundamental here! - (s) Are isomorphic theories then semantically identical? - Fraassen: in other languages, the theories have other limitations, - This is about models, not about the language. E.g. Bohr's atom modell does not refer to a single structure, but to a single structure type - for example, hydrogen and helium atoms, etc. (class of structures, model type). >Models, >Structures. I 48 Theory/Fraassen: different theories must have different empirical meaning (empirical import). - N.B.: even false theories can be empirically adequate. I 49 Maxwell/Hertz: Maxwell's theory is his equations. - I.e. it is not a mechanical theory, but it has mechanical models - N.B.: the electromagnetic forces depend on velocities, not just on acceleration. I 59 Theory/Unobservable/Fraassen: a physical theory cannot be translated without a rest into a corpus of sentences, which only states observable phenomena. - It must always take the unobserved into account. I 67 Theory/Fraassen: two groups: 1. Tarski-Suppes: set theoretically, extensionalist (FraassenVs) 2. Weyl-Evert Beth: state space, modal approach (Fraassen pro). Both initially designed language-dependent, later Vs. |
Fr I B. van Fraassen The Scientific Image Oxford 1980 |
| Theories | Lewis | I (b) 31 Theory/Lewis: has more theorems than follow logically from its postulate (the definition of the theoretical terms) - namely the claim that the theoretical entities are the only ones to implement the theory. I (b) 22 Theoretical identifications are not determined, they rather follow from the theories that they make possible. I (b) 21f Theory: theoretical terms: can be functionally defined, with recourse to causal roles. >Theoretical term/Lewis, >Causal role/Lewis. Theory: In our present case, the theoretical terms are to name components of the near-implementation. (The closest implementation of the theory). We should only use the escape route of treating theoretical terms like failed descriptions when the story comes close to realization. (closest possible worlds). >Similarity metrics/Lewis. I (b) 27 We know very well that scientific theories are often almost implemented and rarely implemented. I (b) 31 Theory: If I am right, theoretical terms can be eliminated. We can always replace them with their definientia. This does not mean that theories are fictions or their entities are unreal. On The Contrary! Because we understand the A terms and the theoretical terms can be defined with their help, theories have a meaning without compromising. And then their entities actually exist. >Terminology/Lewis. I (b) 32 These theoretical identifications are no stipulations. They are deductive conclusions. And in this way we will conclude one day that the mental states G1, G2,... are the neural states N1, N2,.... --- IV 93 Theory/Unambiguousness/Implementation/Lewis: a theory which claims to explain everything (e.g. a machine) cannot have a second implementation - ((s) > functionalism). |
Lewis I David K. Lewis Die Identität von Körper und Geist Frankfurt 1989 Lewis I (a) David K. Lewis An Argument for the Identity Theory, in: Journal of Philosophy 63 (1966) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (b) David K. Lewis Psychophysical and Theoretical Identifications, in: Australasian Journal of Philosophy 50 (1972) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (c) David K. Lewis Mad Pain and Martian Pain, Readings in Philosophy of Psychology, Vol. 1, Ned Block (ed.) Harvard University Press, 1980 In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis II David K. Lewis "Languages and Language", in: K. Gunderson (Ed.), Minnesota Studies in the Philosophy of Science, Vol. VII, Language, Mind, and Knowledge, Minneapolis 1975, pp. 3-35 In Handlung, Kommunikation, Bedeutung, Georg Meggle Frankfurt/M. 1979 Lewis IV David K. Lewis Philosophical Papers Bd I New York Oxford 1983 Lewis V David K. Lewis Philosophical Papers Bd II New York Oxford 1986 Lewis VI David K. Lewis Convention. A Philosophical Study, Cambridge/MA 1969 German Edition: Konventionen Berlin 1975 LewisCl Clarence Irving Lewis Collected Papers of Clarence Irving Lewis Stanford 1970 LewisCl I Clarence Irving Lewis Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991 |
| Theories | Schurz | I 176 Theory/Science/Schurz: Ex A good scientific theory must have 1. have system character and verification holism, 2. distinction between axioms and the consequences derived from them. 3. within axioms, a gradual distinction between the core of the theory and its periphery. >Holism, >Verification, >Review, >Periphery, >Axioms, >System, >Theorems. I 179 Theory association: physical theories organize themselves in the form of hierarchical theory associations. Core laws: are at the top. >Physics, >Laws of nature, >Assignment. I 184 Theory/Schurz: A theory can be divided into components in three ways: 1. with respect to language: comprise. Theoretical total language, subsystem: empirical (resp. pre-theoretical) which contains only empirical terms of T besides the logical mathematical ones. 2. with respect to the logical nature of the propositions of T: difference: axioms, and logical (resp. probabilistic) consequences. 3. with respect to the conceptual nature of the propositions: Difference: purely theoretical laws (contain only theoretical terms in addition to logically mathematical ones; I 185 Mixed propositions: contain also empirical Empirical consequences: contain empirical and logically mathematical terms. Assignment laws: are a part of mixed propositions. 4. regarding epistemic status of sentences of T: gradual difference core/periphery. Core/core axioms/Schurz: define the historical identity of the theory. If you change them, you get a different theory. Periphery: peripheral hypotheses characterize the current version of the theory. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Thought Experiments | Duhem | I 270 Thought experiment/Duhem's fictitious experiment: has no foundation other than belief in the principle: what follows is a cirulus vitiosus. >Fictions, >Circular reasoning. I 273 Physics does not grow like geometry, while it continues to produce new theorems, which are proved once and for all, which it adds to already proven ones. >Experiments, >Theories, >Methods. |
Duh I P. Duhem La théorie physique, son objet et sa structure, Paris 1906 German Edition: Ziel und Struktur der physikalischen Theorien Hamburg 1998 |
| Truth | Davidson | I (c) 56 Immanence Theory of Truth/Davidson: The sentence of another could be true for him, even though, when I translate it correctly, it makes no sense for me. The truth predicate defined in the meta-language can be translated back into the object language and the state before the elimination can be restored of the "true". >Truth predicate, >Object language, >Metalanguage. Object language and meta-language should contain the predicate "true". >Expressiveness, >Richness, >Truth theory. Davidson, however, can avoid the dilemma by not defining a definition at all. He calls this a truth definition in the style of Tarski in the following called "truth theory". DavidsonVsTarski: empirical instead of formal - Empiricism excludes false additions of law (Goodman) - Convention: truth is not sufficiently empirical. >Convention T. The truth of an utterance depends only on two things: of what the words, as they were used, mean, and of the world. Glüer II 131 VsTranscendentalism: one cannot separate language competence and influence on the world. "Negative Transcendentalism". Rorty VI 51 Davidson/Truth: We collect information and patterns about whether actors agree to sentences or not. And this, without knowing the meaning of the sentences of actor. But after a while we do the step from the "nonpropositional to the propositional". A theory of truth is at the same time automatically a theory of meaning and rationality. Every intensional concept is intertwined with every other intensional concept. Glüer II 28 Interpretation Theory/Glüer: must not assume that their theorems were derived with the help of a translation (circle) - therefore DavidsonVsTarski: presupposing truth to explain meaning. >Interpretation theory. Horwich I 443 Truth/Davidson/Rorty: should be identified with nothing. - There is no correspondence, no truth-making. DavidsonVsPragmatism: Truth is not equal to assertion. Richard Rorty (1986), "Pragmatism, Davidson and Truth" in E. Lepore (Ed.) Truth and Interpretation. Perspectives on the philosophy of Donald Davidson, Oxford, pp. 333-55. Reprinted in: Paul Horwich (Ed.) Theories of truth, Dartmouth, England USA 1994 Rorty VI 189 Truth/Norms/Davidson: (according to Brandom): the pursuit of truth cannot go beyond our own practices (also Sellars). |
Davidson I D. Davidson Der Mythos des Subjektiven Stuttgart 1993 Davidson I (a) Donald Davidson "Tho Conditions of Thoughts", in: Le Cahier du Collège de Philosophie, Paris 1989, pp. 163-171 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson I (b) Donald Davidson "What is Present to the Mind?" in: J. Brandl/W. Gombocz (eds) The MInd of Donald Davidson, Amsterdam 1989, pp. 3-18 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson I (c) Donald Davidson "Meaning, Truth and Evidence", in: R. Barrett/R. Gibson (eds.) Perspectives on Quine, Cambridge/MA 1990, pp. 68-79 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson I (d) Donald Davidson "Epistemology Externalized", Ms 1989 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson I (e) Donald Davidson "The Myth of the Subjective", in: M. Benedikt/R. Burger (eds.) Bewußtsein, Sprache und die Kunst, Wien 1988, pp. 45-54 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson II Donald Davidson "Reply to Foster" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 Davidson III D. Davidson Essays on Actions and Events, Oxford 1980 German Edition: Handlung und Ereignis Frankfurt 1990 Davidson IV D. Davidson Inquiries into Truth and Interpretation, Oxford 1984 German Edition: Wahrheit und Interpretation Frankfurt 1990 Davidson V Donald Davidson "Rational Animals", in: D. Davidson, Subjective, Intersubjective, Objective, Oxford 2001, pp. 95-105 In Der Geist der Tiere, D Perler/M. Wild Frankfurt/M. 2005 D II K. Glüer D. Davidson Zur Einführung Hamburg 1993 Rorty I Richard Rorty Philosophy and the Mirror of Nature, Princeton/NJ 1979 German Edition: Der Spiegel der Natur Frankfurt 1997 Rorty II Richard Rorty Philosophie & die Zukunft Frankfurt 2000 Rorty II (b) Richard Rorty "Habermas, Derrida and the Functions of Philosophy", in: R. Rorty, Truth and Progress. Philosophical Papers III, Cambridge/MA 1998 In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty II (c) Richard Rorty Analytic and Conversational Philosophy Conference fee "Philosophy and the other hgumanities", Stanford Humanities Center 1998 In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty II (d) Richard Rorty Justice as a Larger Loyalty, in: Ronald Bontekoe/Marietta Stepanians (eds.) Justice and Democracy. Cross-cultural Perspectives, University of Hawaii 1997 In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty II (e) Richard Rorty Spinoza, Pragmatismus und die Liebe zur Weisheit, Revised Spinoza Lecture April 1997, University of Amsterdam In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty II (f) Richard Rorty "Sein, das verstanden werden kann, ist Sprache", keynote lecture for Gadamer’ s 100th birthday, University of Heidelberg In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty II (g) Richard Rorty "Wild Orchids and Trotzky", in: Wild Orchids and Trotzky: Messages form American Universities ed. Mark Edmundson, New York 1993 In Philosophie & die Zukunft, Frankfurt/M. 2000 Rorty III Richard Rorty Contingency, Irony, and solidarity, Chambridge/MA 1989 German Edition: Kontingenz, Ironie und Solidarität Frankfurt 1992 Rorty IV (a) Richard Rorty "is Philosophy a Natural Kind?", in: R. Rorty, Objectivity, Relativism, and Truth. Philosophical Papers Vol. I, Cambridge/Ma 1991, pp. 46-62 In Eine Kultur ohne Zentrum, Stuttgart 1993 Rorty IV (b) Richard Rorty "Non-Reductive Physicalism" in: R. Rorty, Objectivity, Relativism, and Truth. Philosophical Papers Vol. I, Cambridge/Ma 1991, pp. 113-125 In Eine Kultur ohne Zentrum, Stuttgart 1993 Rorty IV (c) Richard Rorty "Heidegger, Kundera and Dickens" in: R. Rorty, Essays on Heidegger and Others. Philosophical Papers Vol. 2, Cambridge/MA 1991, pp. 66-82 In Eine Kultur ohne Zentrum, Stuttgart 1993 Rorty IV (d) Richard Rorty "Deconstruction and Circumvention" in: R. Rorty, Essays on Heidegger and Others. Philosophical Papers Vol. 2, Cambridge/MA 1991, pp. 85-106 In Eine Kultur ohne Zentrum, Stuttgart 1993 Rorty V (a) R. Rorty "Solidarity of Objectivity", Howison Lecture, University of California, Berkeley, January 1983 In Solidarität oder Objektivität?, Stuttgart 1998 Rorty V (b) Richard Rorty "Freud and Moral Reflection", Edith Weigert Lecture, Forum on Psychiatry and the Humanities, Washington School of Psychiatry, Oct. 19th 1984 In Solidarität oder Objektivität?, Stuttgart 1988 Rorty V (c) Richard Rorty The Priority of Democracy to Philosophy, in: John P. Reeder & Gene Outka (eds.), Prospects for a Common Morality. Princeton University Press. pp. 254-278 (1992) In Solidarität oder Objektivität?, Stuttgart 1988 Rorty VI Richard Rorty Truth and Progress, Cambridge/MA 1998 German Edition: Wahrheit und Fortschritt Frankfurt 2000 Horwich I P. Horwich (Ed.) Theories of Truth Aldershot 1994 |
| Truth Predicate | Field | II 28 "True"/Truth-Predicate/Purpose/Generalization/Generality/Quine/Field: (Quine, 1970)(1): above all, the truth-predicate has the role of generalization. - That is his whole value. - Leeds dito. Field: E.g. "All true sentences of this theory are theorems". Camp/Grover/Belnap/CGB: (CGB, 1975(2), dito). E.g.: "There are true sentences that no one will ever have a reason to believe". --- II 120 Truth-Predicate/Generalization/Truth/Field: E.g. the desire to express only true sentences: "I utter "p" only if p". --- II 121 E.g. "Not every (of infinitely many) axioms is true". - Or, for example, they are contingent: "Not every had to be true". - N.B.: this is only possible with purely disquotational truth. >Disquotationalism, >Disquotational truth, >Speaker meaning. 1. Quine, W.V.O. 1970. Philosophy of Logic. Harvard University Press (1970) 2. Dorothy L. Grover, Joseph L. Camp & Nuel D. Belnap. 1975. A Prosentential theory of truth. Philosophical Studies 27 (1):73--125. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Truthmakers | Simons | Chisholm II 166 Truthmaker/Simons: truthmakers are only things, not facts. Therefore, we introduce expressions for complexes and replace normal sentences by truth functions of existence theorems. >Sentences, >Truth functions, >Facts, >Situations, >Complex. |
Simons I P. Simons Parts. A Study in Ontology Oxford New York 1987 Chisholm I R. Chisholm The First Person. Theory of Reference and Intentionality, Minneapolis 1981 German Edition: Die erste Person Frankfurt 1992 Chisholm II Roderick Chisholm In Philosophische Aufsäze zu Ehren von Roderick M. Ch, Marian David/Leopold Stubenberg Amsterdam 1986 Chisholm III Roderick M. Chisholm Theory of knowledge, Englewood Cliffs 1989 German Edition: Erkenntnistheorie Graz 2004 |
| Universals | Lewis | Armstrong II 18 Universals/Lewis/Armstrong: economical theory: only postulate those properties and relations that are needed a posteriori for a scientific approach. Armstrong II 181 Universals/Lewis/Armstrong: I am not set on them. - More neutral: truth supervenes on what things there are and what completely natural properties and relations they instantiate. Negative existence theorems and = predications are innocent. LewisVsphenomenalistic counterfactual conditionals (VsCounterfactual conditionals). - ((s) my perception would have been somewhat different.) >Counterfactual conditionals. --- Lewis V 244 Universal/Armstrong/Lewis: properties are not universals, - and not a substitute for universals. - And vice versa, properties are probably not a substitute for universals. - Lewis: I am committed to properties - If universals, then only a few. - Which there are, is important for the sciences. - Universals are not divisible. - Otherwise, they lead to exact duplicates. - None of this applies to properties. >Properties/Lewis. |
Lewis I David K. Lewis Die Identität von Körper und Geist Frankfurt 1989 Lewis I (a) David K. Lewis An Argument for the Identity Theory, in: Journal of Philosophy 63 (1966) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (b) David K. Lewis Psychophysical and Theoretical Identifications, in: Australasian Journal of Philosophy 50 (1972) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (c) David K. Lewis Mad Pain and Martian Pain, Readings in Philosophy of Psychology, Vol. 1, Ned Block (ed.) Harvard University Press, 1980 In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis II David K. Lewis "Languages and Language", in: K. Gunderson (Ed.), Minnesota Studies in the Philosophy of Science, Vol. VII, Language, Mind, and Knowledge, Minneapolis 1975, pp. 3-35 In Handlung, Kommunikation, Bedeutung, Georg Meggle Frankfurt/M. 1979 Lewis IV David K. Lewis Philosophical Papers Bd I New York Oxford 1983 Lewis V David K. Lewis Philosophical Papers Bd II New York Oxford 1986 Lewis VI David K. Lewis Convention. A Philosophical Study, Cambridge/MA 1969 German Edition: Konventionen Berlin 1975 LewisCl Clarence Irving Lewis Collected Papers of Clarence Irving Lewis Stanford 1970 LewisCl I Clarence Irving Lewis Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991 Armstrong I David M. Armstrong Meaning and Communication, The Philosophical Review 80, 1971, pp. 427-447 In Handlung, Kommunikation, Bedeutung, Georg Meggle Frankfurt/M. 1979 Armstrong II (a) David M. Armstrong Dispositions as Categorical States In Dispositions, Tim Crane London New York 1996 Armstrong II (b) David M. Armstrong Place’ s and Armstrong’ s Views Compared and Contrasted In Dispositions, Tim Crane London New York 1996 Armstrong II (c) David M. Armstrong Reply to Martin In Dispositions, Tim Crane London New York 1996 Armstrong II (d) David M. Armstrong Second Reply to Martin London New York 1996 Armstrong III D. Armstrong What is a Law of Nature? Cambridge 1983 |
| Universe | Field | I 104 Universe/Classes/Sets/Model/"all"/Field: as the universe of all classes is too large to form a countable model, it is too big to form a class and therefore too large, to form any (over-countable) model. >Models, >Infinity, >Paradoxes. --- II 335 Universe/Standard-Platonism/Field: (thesis: "There's only one universe"). >Platonism. Problem: PutnamVsPlatonism: How can we make it at all possible to pick out the "full" (universal) universe and to make it face a partial universe, and accordingly the standard-element-relation in contrast to a non-standard-element-relation? (Putnam 1980)(1). Putnam: Thesis: we cannot do that - i.e. that the "incomplete content" of the concepts "quantity" and "element of" is not sufficient to determine the truth value of all set theoretical theorems. >Element relation, >Truth, >Truth values, >Theorems, >Theories. 1. Putnam, Hilary. 1980. Models and Reality. Journal of Symbolic Logic 45. (3):464-482 |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Validity | Quine | VII (f) 116 Validity/Quine: even validity and extension of predicates can be eliminated in favor of truth value tables - validity in the quantifier theory can be eliminated by proof theory. --- VII (i) 161 Validity/Quine: sentences that are valid for a universe, are also valid for a small universe - except for an empty universe. - Therefore, laws for large universes also should consider possible smaller universes. - Test, whether theorems are also valid for empty universes: put all universal quantifiers as true and all existential quantifiers as false. --- X 77 Validity/valid/Quine: There are two definitions of validity, a) (so far) as a property of schemes that refer to insertion. b) uses the set theory: therefore two auxiliary terms: 1. Auxiliary term "set-theoretic analogue": a logical scheme, open sentence of set theory: instead of predications "Fx", "Fy", "Gx" etc., so we write "X ε a" y ε α "x ε β" etc. the values of the variable "α", "β" etc. are amounts. Two-digit predicate letters. For "Hxy" we use ordered pairs Existential quantification: E.g. (Ex)(Fx.Gx): Set-theoretic analogue: the open sentence "Ex(x ε α. x ε β)". N.B.: This sentence talks about quantities and allows quantification about them. E.g. "(α)". Schematic letters "F" etc. on the other hand, only predicates represent and are not variables that take values. >Schematic letters, >Quantification. Set-theoretic analogue/s.a.: while the scheme is only the logical form of sentences, the set-theoretic analogue is actually a sentence of this form. 2. Auxiliary term for the new definition of validity: model. >Models. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Validity | Stalnaker | I 148 Validity/expressiveness/modal/quantification/Stalnaker: the validity of the generalization schema is unlike the identity scheme. >Generality, >Generalization. It depends on limitations of the expressiveness of the extensional theory. If the language is richer, some new instances will be no theorems. >Extensions, >Extensionality, >Expressivivity, >Expressibility, >Richness. |
Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
| Verifiability | Schurz | I 98 Def Verifiability/Schurz: A hypothesis H is verifiable iff there is a finite and consistent set B of observation propositions from which H follows logically. This means only possible (actual) verifiability. >Verification, >Actuality, >Hypotheses, >Confirmation. Def Falsifiability/Schurz: H is falsifiable iff there is a finite consistent set B of observation propositions, from which the negation of H follows logically. This means only possible falsifiability (actual). >Falsification. Def Confirmability/Schurz: (resp. weakenable) is hypothesis H if there is a finitely consistent set B of observation propositions, which hears resp. degrades the validity resp. plausibility of H. Falsification/Asymmetry/Popper: Falsification is restricted to strict spatiotemporally unrestricted empirical all-hypotheses. Dual to this, unrestricted existence propositions Ex "There is a white raven" are verifiable, but not falsifiable. I 99 Spatiotemporally restricted hypotheses: are in principle verifiable and falsifiable by observing the finitely many individuals of a domain. Verifiability: no unrestricted generalization and no theoretical theorem is verifiable. Allexistence theorem/statistical generalization: not verifiable also not falsifiable because they do not imply observation theorems. Theories/falsification: neither whole theories nor single theoretical hypotheses are falsifiable. Even if they are strictly general. And this is because of holism. >Holism. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Vocabulary | Mates | I 193 Identity/is/analytical/intensional/Mates: it is disputed whether A is A is to be considered as formal analytical or analytical because of the meaning of . >Is, >Copula, >Analyticity/Synthetic, >Synthetic, cf. >Predication. Just as statements of the scheme E.g. If A is warmer than B and B is warmer than C, so A is warmer than C analytically because of the sense of "being warmer than". The dispute is about whether "is" can be seen as a logical constant as "not", and so on or if it belongs to the non-logical vocabulary. >Logical constants, cf. >Lexicon/Quine, >Logic, >Everyday language. Language L: here was "is" non-logical. - That was arbitrary. >Convention. I 195 If non-logical, then independent theory of identity possible. >Identity. On the other hand: if "is" logical constant (which always means the relation of identity above this region) we construct with that a new language. >Formal language, >Formalization, cf. >Equal sign. I 231 Theory/Mates: is always determined by the amount of their doctrines. - ((S) because these contain the entire non-logical vocabulary.) I 248 Definitions/Mates: are needed to represent formalized theories. - They introduce designations that do not belong to the vocabulary of the language, but which improve readability. >Definitions, >Definability. I 250 Definition creative Definition/Mates: leads to new theorems in which the defined symbol does not occur. >Elimination. Demand: a satisfactory definition should not be creative. |
Mate I B. Mates Elementare Logik Göttingen 1969 Mate II B. Mates Skeptical Essays Chicago 1981 |
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| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| Anti-Objectivism | Field Vs Anti-Objectivism | II 318 Undecidability/VsAnti-Objectivism/AO/Field: other examples are less favorable for the anti-objectivism: E.g. Gödel. Even very simple sentences may be undecidable. E.g. (*) for all natural numbers x, B(x) where B(x) is a decidable predicate, i.e. a predicate, so that for each numeral n we can either prove B(n) or ~B(n). (Through an uncontroversial proof). Problem: you may say now that every undecidable sentence must be objectively correct (see above, must follow from the axioms). Then proof of ~B(n) would be proof of the negation of (*), as opposed to its undecidability. So, because of the assumption about B(x) B(n) must be provable for each number n, thus presumably objectively correct. This seems to show, however, that the generalization (*) is also objectively correct. (This is not undisputed, because it requires as a final step that it is objectively the case that there are no other natural numbers than those for which there are names. ((s)> "not enough names"). FieldVs extreme Anti-Objectivism: if that can be believed, however, he must adopt a more moderate position. Elementary Number Theory/ENT/Undecidability/Field: in fact, almost everyone believes that the choice between an undecidable proposition and its negation is objective, also for the generalized ENT. That would be hard to give up, because many assertions about provability and consistency are actually undecidable number-theoretic assertions, so that the anti-objectivist would have to say that they lack objectivity. Only few of them want that. Nevertheless, it is not obvious that if the ENT is granted objectivity, it would also have to be conceded to the higher regions. I 347 Anti-Objectivism/Gödel/Field/Conclusion/(s): Gödel gives no reason to assume that some undecidable propositions have certain truth values. (pro extreme anti-objectivism, by Field). VsAnti-Objectivism/Gödel/Field: It may be objected that the Gödel sentences of the candidates for our most mathematical theory should not only have a certain truth value, but that they are true! The argument goes by. Induction: all logical and non-logical premises of M are true. The rules of inference receive truth, therefore, all theorems must be true. So the theory must be consistent, therefore the Gödel sentence must be unprovable and therefore true. Gödel sentence: is true only if unprovable; if provable, it is not true. Problem: this induction can of course not be formalized in M. But one often feels that it is somehow "informally valid". If that is true, only the truth of the Gödel theorem is proved, not its particular truth. Solution: we might be able to fill the gap by establishing a principle that if we can prove something informally, it must certainly be true. (Vs: That’s plausible, but not undisputed!). In any case, the arguments for the particular truth of the Gödel theorem are weaker than those for its simple truth. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Boyd, R. | Putnam Vs Boyd, R. | Williams II 492 Scientific Realism/Richard Boyd/M. Williams: Boyd's defense of scientific realism is much more complex than what we have considered so far: Williams II 493 Is a substantial (explanatory) truth concept necessary? Boyd: more indirect approach than Putnam: the (approximate) truth of our theories explains the instrumental reliability of our methods. Method/Boyd: is not theory neutral! On the contrary, because they are formed by our theories, it is their truth that explains the success of the methods. Boyd/M. Williams: thus it turns a well-known argument on its head: BoydVsPositivism. Positivism/Theory: Thesis: the observing language must be theory neutral. The methodological principles likewise. IdealismVsPositivism: VsTheory Neutrality. E.g. Kuhn: the scientific community determines the "facts". Boyd/M. Williams: Boyd turns the >theory ladenness of our methodological judgments very cleverly into the base of his realism. Thesis: Methods that are as theory-laden as ours would not work if the corresponding theories were not "approximately true in a relevant way". Point: thus he cannot be blamed of making an unacceptably rigid separation between theory and observation. Ad. 1) Vs: this invalidates the first objection Ad. 2) Vs: Boyd: it would be a miracle if our theory-laden methods functioned even though the theories proved to be false. For scientific realism, there is nothing to explain here. Ad. 3) Vs: Williams II 494 M. Williams: this is not VsScientific Realism, but VsPutnam: PutnamVsBoyd: arguments like that of Boyd do not establish a causal explanatory role for the truth concept. BoydVsPutnam: they don't do that: "true" is only a conventional expression which adds no explanatory power to the scientific realism. Truth/Explanation/Realism/Boyd/M. Williams: explaining the success of our methods with the truth of our theories boils down to saying that the methods by which we examine particles work, because the world is composed of such particles that are more or less the way we think. Conclusion: but it makes no difference whether we explain this success (of our methods) by the truth of the theories or by the theories themselves! M. Williams pro Deflationism: so we do not need a substantial truth concept. Putnam I (c) 80 Convergence/Putnam: there is something to the convergence of scientific knowledge! Science/Theory/Richard Boyd: Thesis: from the usual positivist philosophy of science merely follows that later theories imply many observation sentences of earlier ones, but not that later theories must imply the approximate truth of the earlier ones! (1976). Science/Boyd: (1) terms of a mature science typically refer (2) The laws of a theory that belongs to a mature science are typically approximately true. (Boyd needs more premises). I (c) 81 Boyd/Putnam: the most important thing about these findings is that the concepts of "truth" and "reference" play a causally explanatory role in epistemology. When replacing them in Boyd with operationalist concept, for example, "is simple and leads to true predictions", the explanation is not maintained. Truth/Theory/Putnam: I do not only want to have theories that are "approximately true", but those that have the chance to be true. Then the later theories must contain the laws of the earlier ones as a borderline case. PutnamVsBoyd: according to him, I only know that T2 should imply most of my observation sentences that T1 implies. It does not follow that it must imply the truth of the laws of T1! I (c) 82 Then there is also no reason why T2 should have the property that we can assign reference objects to the terms of T1 from the position of T2. E.g. Yet it is a fact that from the standpoint of the RT we can assign a reference object to the concept "gravity" in the Newtonian theory, but not to others: for example, phlogiston or ether. With concepts such as "is easy" or "leads to true predictions" no analogue is given to the demand of reference. I (c) 85/86 Truth/Boyd: what about truth if none of the expressions or predicates refers? Then the concept "truth value" becomes uninteresting for sentences containing theoretical concepts. So truth will also collapse. PutnamVsBoyd: this is perhaps not quite what would happen, but for that we need a detour via the following considerations: I (c) 86 Intuitionism/Logic/Connectives/Putnam: the meaning of the classical connectives is reinterpreted in intuitionism: statements: p p is asserted p is asserted to be provable "~p" it is provable that a proof of p would imply the provability of 1 = 0. "~p" states the absurdity of the provability of p (and not the typical "falsity" of p). "p u q" there is proof for p and there is proof for q "p > q" there is a method that applied to any proof of p produces proof of q (and proof that this method does this). I (c) 87 Special contrast to classical logic: "p v ~p" classical: means decidability of every statement. Intuitionistically: there is no theorem here at all. We now want to reinterpret the classical connectives intuitionistically: ~(classical) is identical with ~(intuitionist) u (classical) is identified with u (intuitionist) p v q (classical) is identified with ~(~p u ~q)(intuitionist) p > q (classical) is identified with ~(p u ~q) (intuitionist) So this is a translation of one calculus into the other, but not in the sense that the classical meanings of the connectives were presented using the intuitionistic concepts, but in the sense that the classical theorems are generated. ((s) Not translation, but generation.) The meanings of the connectives are still not classical, because these meanings are explained by means of provability and not of truth or falsity (according to the reinterpretation)). E.g. Classical means p v ~p: every statement is true or false. Intuitionistically formulated: ~(~p u ~~p) means: it is absurd that a statement and its negation are both absurd. (Nothing of true or false!). |
Putnam I Hilary Putnam Von einem Realistischen Standpunkt In Von einem realistischen Standpunkt, Vincent C. Müller Frankfurt 1993 Putnam I (a) Hilary Putnam Explanation and Reference, In: Glenn Pearce & Patrick Maynard (eds.), Conceptual Change. D. Reidel. pp. 196--214 (1973) In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (b) Hilary Putnam Language and Reality, in: Mind, Language and Reality: Philosophical Papers, Volume 2. Cambridge University Press. pp. 272-90 (1995 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (c) Hilary Putnam What is Realism? in: Proceedings of the Aristotelian Society 76 (1975):pp. 177 - 194. In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (d) Hilary Putnam Models and Reality, Journal of Symbolic Logic 45 (3), 1980:pp. 464-482. In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (e) Hilary Putnam Reference and Truth In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (f) Hilary Putnam How to Be an Internal Realist and a Transcendental Idealist (at the Same Time) in: R. Haller/W. Grassl (eds): Sprache, Logik und Philosophie, Akten des 4. Internationalen Wittgenstein-Symposiums, 1979 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (g) Hilary Putnam Why there isn’t a ready-made world, Synthese 51 (2):205--228 (1982) In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (h) Hilary Putnam Pourqui les Philosophes? in: A: Jacob (ed.) L’Encyclopédie PHilosophieque Universelle, Paris 1986 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (i) Hilary Putnam Realism with a Human Face, Cambridge/MA 1990 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (k) Hilary Putnam "Irrealism and Deconstruction", 6. Giford Lecture, St. Andrews 1990, in: H. Putnam, Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992, pp. 108-133 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam II Hilary Putnam Representation and Reality, Cambridge/MA 1988 German Edition: Repräsentation und Realität Frankfurt 1999 Putnam III Hilary Putnam Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992 German Edition: Für eine Erneuerung der Philosophie Stuttgart 1997 Putnam IV Hilary Putnam "Minds and Machines", in: Sidney Hook (ed.) Dimensions of Mind, New York 1960, pp. 138-164 In Künstliche Intelligenz, Walther Ch. Zimmerli/Stefan Wolf Stuttgart 1994 Putnam V Hilary Putnam Reason, Truth and History, Cambridge/MA 1981 German Edition: Vernunft, Wahrheit und Geschichte Frankfurt 1990 Putnam VI Hilary Putnam "Realism and Reason", Proceedings of the American Philosophical Association (1976) pp. 483-98 In Truth and Meaning, Paul Horwich Aldershot 1994 Putnam VII Hilary Putnam "A Defense of Internal Realism" in: James Conant (ed.)Realism with a Human Face, Cambridge/MA 1990 pp. 30-43 In Theories of Truth, Paul Horwich Aldershot 1994 SocPut I Robert D. Putnam Bowling Alone: The Collapse and Revival of American Community New York 2000 EconWilliams I Walter E. Williams Race & Economics: How Much Can Be Blamed on Discrimination? (Hoover Institution Press Publication) Stanford, CA: Hoover Institution Press 2011 WilliamsB I Bernard Williams Ethics and the Limits of Philosophy London 2011 WilliamsM I Michael Williams Problems of Knowledge: A Critical Introduction to Epistemology Oxford 2001 WilliamsM II Michael Williams "Do We (Epistemologists) Need A Theory of Truth?", Philosophical Topics, 14 (1986) pp. 223-42 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Cantor, G. | Frege Vs Cantor, G. | I 117 Infinity/Cantor: only the finite numbers should be considered as real. They are as little perceptible as negative numbers, fractions, irrational and complex numbers. FregeVsCantor: we do not need any sense perceptions as proofs for our theorems. It suffices if they are logically consistent. I 118 The infinite is no extension of the natural numbers, they were infinite from the beginning! In Cantor, unlike Frege, the order is still to be established; for him, E.g. 0 can follow 13. |
F I G. Frege Die Grundlagen der Arithmetik Stuttgart 1987 F II G. Frege Funktion, Begriff, Bedeutung Göttingen 1994 F IV G. Frege Logische Untersuchungen Göttingen 1993 |
| Carnap, R. | Lewis Vs Carnap, R. | Field II 196 Theoretical Terms/TT/Ramsey sentence/Carnap/Lewis/Field: (Carnap 1956, Kap.26, Lewis 1979b,1972). Theoretical Term/Introduction/Content/Ramsey sentence/Carnap: if a new TT was introduced by a theory Θ(T), then the content of the theory is equal to the content of the Ramsey sentence (Ex)Θ(x). Only realization: In a special case in which (E!x)Θ(x) is, we can say that T denotes the only object that fulfills Θ(x). multiple realization: Problem: what does the theoretical term denote here? (>Functionalism/Lewis, >Turing machine). It seems to need to denote something, if this were not possible we cannot explain why Θ(T) is true (and this must be according Carnap's thesis that it "has the content" of(Ex)Θ(x).) Solution/Carnap: if Θ (x) is realized multiple times, then T denotes one random object which fulfills Θ(x). LewisVsCarnap: This is not plausible because it is not explained how it is possible for a user of T to take a particular object instead of another one. Field II 197 Content/TT/Ramsey sentence/Lewis/Field: Lewis felt obliged (probably reluctantly) to not take the content of the Ramsey sentence Ex Θ (x), but the modified sentence of Ramsey: (E! x) Θ (x) ((s) which only presumes one object). I.e. the theory is wrong if Θ(x) is realized multiple times, so that T can be seen as without denotations. Then there is no ambiguity. LewisVs: (1970b): This is costly: Then if somebody states Θ (T), then it is absolutely implausible that he thereby has asserted that nothing than T Θ (x) can be fulfilled. LewisVs: (1972): even worse: it has been applied here on functionalism, which is after all based on multiple realization. Multiple Realization/Functionalism/Field: Many authors actually want to accept mR in one and the same organism at the same time. Partial Denotation/Lösung/Field: Lewis could simply say that (as Carnap says) the content of Θ (T) is simply the Ramsey sentence (Ex) Θ (x), and if Θ (x) is realized multiple ways, then T partially denotes each of the "Realisierer". Lewis IV 88 Theoretical Terms/TT/Definition/Description/Lewis: After having defined the TT through descriptions, we can eliminated the latter with their help. This is how we obtain O sentences. Def Extended Postulation/Lewis: the postulate of T that we get by replacing the TT by descriptions (O sentence). It says that the theory T is realized by the n tuple of the first, second...component of the only realization of T. The extended postulate is equivalent in definition to the postulate. It says that the theory is uniquely realized. It is logically equivalent to a shorter O phrase, which says the same in a shorter form. This is what we call the "sentence of the only realization of T": IV 89 Ey1...yn (x) x1...xn (T[x1,,,xn] ↔ . y1 = x1 & ..& yn = xn LewisVsCarnap: then the postulate is true if and only if the theory is realized once. Problem: the expanded postulate is an O phrase that is stronger than the Ramsey phrase that merely says that there is at least one realization. Nevertheless, if the definition sentences are part of T, then the extended postulate is a theorem of T. Then the definitions give us theorems that could not have been derived without them. This means that the definitions themselves, unlike the Carnap theorem, are not logically implied by the postulate. Therefore, if we want to say that the definition sets of T are correct definitions, we must abandon the idea that the theorems are all and only the logical consequences of T's postulate. And we like to give that up. |
Lewis I David K. Lewis Die Identität von Körper und Geist Frankfurt 1989 Lewis I (a) David K. Lewis An Argument for the Identity Theory, in: Journal of Philosophy 63 (1966) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (b) David K. Lewis Psychophysical and Theoretical Identifications, in: Australasian Journal of Philosophy 50 (1972) In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis I (c) David K. Lewis Mad Pain and Martian Pain, Readings in Philosophy of Psychology, Vol. 1, Ned Block (ed.) Harvard University Press, 1980 In Die Identität von Körper und Geist, Frankfurt/M. 1989 Lewis II David K. Lewis "Languages and Language", in: K. Gunderson (Ed.), Minnesota Studies in the Philosophy of Science, Vol. VII, Language, Mind, and Knowledge, Minneapolis 1975, pp. 3-35 In Handlung, Kommunikation, Bedeutung, Georg Meggle Frankfurt/M. 1979 Lewis IV David K. Lewis Philosophical Papers Bd I New York Oxford 1983 Lewis V David K. Lewis Philosophical Papers Bd II New York Oxford 1986 Lewis VI David K. Lewis Convention. A Philosophical Study, Cambridge/MA 1969 German Edition: Konventionen Berlin 1975 LewisCl Clarence Irving Lewis Collected Papers of Clarence Irving Lewis Stanford 1970 LewisCl I Clarence Irving Lewis Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Conceptualism | Quine Vs Conceptualism | VII (f) 126 Classes/Conceptualism/Quine: does not require classes to exist beyond expressible conditions of membership of elements. ((s) VsPlatonism: Quasi requires that there should also be classes without such conditions, as classes should be independent of speakers.) Cantor's proof: would lead to something else: He namely appeals to a class h of those members of the class k that are not elements of the subclasses of k to which they refer. VII (f) 127 But thus the class h is specified impredicatively! h is in fact itself part of the subclass of k. Thus a theorem of classical mathematics goes overboard in conceptualism. The same fate also applies to Cantor's proof of the existence of hyper-countable infinities. QuineVsConceptualism: which is indeed a welcome relief, but there are problems with much more fundamental and desirable theorems of mathematics: Ex proof that every limited sequence of numbers has an upper limit. ConceptualismVsReducibility Axiom: because it reintroduces the entire Platonist class logic. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Davidson, D. | Strawson Vs Davidson, D. | III 189 Truth theory/tr.th./meaning theory/m.th./Strawson: sentences that ascribe actions are sensitive to adverbial modification, for example, if the expressed proposition includes any other proposition if one omits the modifiers. M.th./tr.th./Davidson/Strawson: a theory like his refers to well-understood logical structures that lie beneath the surface of action ascribing sentences. "Adverbial theory"/StrawsonVsDavidson: I prefer a theory which examines the explanation closer to the surface of everyday language, and thus recognizes, however, more complex basal syntax than Davidson's theory. ("Adverbial access"). The contrast between the two theories is a question of depth and universality: StrawsonVsDavidson: if we seek our understanding in logic (surface) structures that differ from the grammar. III 193 VsVs/StrawsonVsDavidson: but it remains mysterious that the actual mastering of the current language would have to be explained by the mastering of a potential language (Davidson's theorems). adverbial access/StrawsonVsDavidson: instead: the adverbial access is much more direct. Here, the success of the claim can also be shown more directly. III 194 This is not to deny that we could take paraphrases as help or equivalent sentences with a different grammatical structure. But by this Davidson's program becomes less attractive, a program that is set from the beginning to explain our grasping by those strongly bounded structures, namely the predicate calculus. III 197 Language forms must of course be taken into account, III 198 when we assess our theory for simplicity, reasonableness and realism. StrawsonVsDavidson: and here his approach has problems. 2. the second reason why it is possible to bring in extra syntactic considerations from outside of linguistic philosophy: Actions and events generally suffer from the identity subordination on substances. Strawson IV 139 StrawsonVsDavidson: one can not expect that an ordinary language speaker masters the predicate calculus. But that is unnecessary. Our conceptual scheme is in space and time. IV 141 Another problem: ontology: nominalization of speech parts e.g. "The Kissing". |
Strawson I Peter F. Strawson Individuals: An Essay in Descriptive Metaphysics. London 1959 German Edition: Einzelding und logisches Subjekt Stuttgart 1972 Strawson II Peter F. Strawson "Truth", Proceedings of the Aristotelian Society, Suppl. Vol XXIV, 1950 - dt. P. F. Strawson, "Wahrheit", In Wahrheitstheorien, Gunnar Skirbekk Frankfurt/M. 1977 Strawson III Peter F. Strawson "On Understanding the Structure of One’s Language" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 Strawson IV Peter F. Strawson Analysis and Metaphysics. An Introduction to Philosophy, Oxford 1992 German Edition: Analyse und Metaphysik München 1994 Strawson V P.F. Strawson The Bounds of Sense: An Essay on Kant’s Critique of Pure Reason. London 1966 German Edition: Die Grenzen des Sinns Frankfurt 1981 Strawson VI Peter F Strawson Grammar and Philosophy in: Proceedings of the Aristotelian Society, Vol 70, 1969/70 pp. 1-20 In Linguistik und Philosophie, G. Grewendorf/G. Meggle Frankfurt/M. 1974/1995 Strawson VII Peter F Strawson "On Referring", in: Mind 59 (1950) In Eigennamen, Ursula Wolf Frankfurt/M. 1993 |
| Description Theory | Kripke Vs Description Theory | Evans I 310/311 Reference/Description/Acquaintance/Kripke: Although the reference is set by the standard meter of Paris, not every speaker must know it or even know that it exists (according to Evans). Strawson: "the mean of different opinions". KripkeVsDescription Theory/Evans: His attacks were only directed against the first variant (speaker designation). They ignore the social character of naming. Field II 117 Reference/Deflationism/Field: Deflationism seems to make the hard work of recent years regarding the study of the reference insignificant. For if truth conditions do not play a central role, neither do the references. E.g.: KripkeVsDescription Theory/Name/Field: (Kripke 1972): This is not correct. Field: At least if they do not use metalanguage. Reference/Deflationism/Field: Problem: When the truth condition does not matter, then it is also valid for the reference since the relevant scheme is: (R) if b exists, "B" refers to b and nothing else; if B does not exist, "b" refers to nothing. Problem: It this is all that can be said about reference, what is the meaning of Kripke’s critique on Description Theory? Description Theory/Gödel-Schmidt Case/Kripke: e.g. Gödel = proves the "Incompleteness Theorems" Then e.g. Schmidt did actually prove it, but was murdered. Everyone would say that "Gödel" nevertheless refers to Gödel and not to Schmidt. Deflationism/Field: Problem: If deflationism is unable to explain this, then something is wrong with it! But it is actually able to: Reference/Deflationism/Field: The reference is not the actual basis, but observations about our practice of closing. That is actually what Kripke shows. Stalnaker I 15 KripkeVsDescription Theory/Stalnaker: Arises from a confusion between semantics and metasemantics. Anti-Essentialism/Kripke/Stalnaker: Arises from a confusion between semantics and metaphysics. |
Kripke I S.A. Kripke Naming and Necessity, Dordrecht/Boston 1972 German Edition: Name und Notwendigkeit Frankfurt 1981 Kripke II Saul A. Kripke "Speaker’s Reference and Semantic Reference", in: Midwest Studies in Philosophy 2 (1977) 255-276 In Eigennamen, Ursula Wolf Frankfurt/M. 1993 Kripke III Saul A. Kripke Is there a problem with substitutional quantification? In Truth and Meaning, G. Evans/J McDowell Oxford 1976 Kripke IV S. A. Kripke Outline of a Theory of Truth (1975) In Recent Essays on Truth and the Liar Paradox, R. L. Martin (Hg) Oxford/NY 1984 EMD II G. Evans/J. McDowell Truth and Meaning Oxford 1977 Evans I Gareth Evans "The Causal Theory of Names", in: Proceedings of the Aristotelian Society, Suppl. Vol. 47 (1973) 187-208 In Eigennamen, Ursula Wolf Frankfurt/M. 1993 Evans II Gareth Evans "Semantic Structure and Logical Form" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 Evans III G. Evans The Varieties of Reference (Clarendon Paperbacks) Oxford 1989 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
| Extensional Language | Prior Vs Extensional Language | I 96 Operator/Sentence Variable/Functor/Sentence Operator/Propositional Operator/Prior: "δ" in (E) forms sentences from sentences, "φ" in (D) forms sentences only from names it cannot have both sentences and names as an argument. "N" cannot have names as an argument. ((s) Russell: names or objects cannot be negated). PriorVsCohen: therefore, there is no possibility for our simplification of (F) in his system. I 96 PriorVsCohen/PriorVsExtensional Language: E.g. brown cow: in his axioms it is not essential that the pregnant animal should be a brown cow, it is not mentioned in the evidence. Paradox like in the foreword: no use is made here of the assumption that ψx, i.e. something in the book is wrong. I 97 Despite the large difference this makes, it could simply be omitted. The other constituents do all the work. I.e. it would make no difference for Cohen's theorem whether the thing in the book did not mean that something in the book is wrong, but that it meant that the sky is blue, for example. The only thing that is necessary is that the thing in the book should be true iff. something in the book is wrong and that it is not determined by ψx, but by the other component: ETx∑yKφyNTy. It is strange that the two components are indeed absolutely irrelevant for each other! For Cohen, it would be the same if we wrote: "For an x, x means that the sky is blue, and x is true iff. grass is green." Reason: "iff." is an extensional propositional function. PriorVsCohen/PriorVsExtensional Language/Extensionality: but it would be extremely strange if you wanted to say "the book says that grass is green." (If in fact you only mean that the book contains a true statement). But that is indeed the reason why this extra determination occurs in Cohen's symbolism. (ψx). PriorVsCohen: my theorems (A) through (G) apply no matter what statement functions we insert for δ, both extensional and intensional. E.g. if we leave "δ": "it is not the case that __" or "grass is green and __", we still have Cd∑pKδpNp∑pKδpNp. For all these theorems tell us that there could possibly only be extensional statement functions! |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
| Hume, D. | Bigelow Vs Hume, D. | I 226 Non-modal theory/Laws of Nature/LoN/Hume/Bigelow/Pargetter: most non-modal theories of the LON descended from Hume. Then we can assume nomic necessity to be a relative necessity without falling into a circle. Important argument: then we can just assume nomic necessity as a relative necessity and rely on it being based on an independent approach to laws! Explanation: So it makes sense to make use of laws to explain nomic necessity, rather than vice versa. And that’s much less obscure than modal arguments. I 227 BigelowVsVs: modal explanations are not so mysterious. BigelowVsHume: Hume’s theories are unable to explain these non-modal properties of the laws, they have less explanatory power. I 233 "Full generality"/"Pure" generality/Hume/BigelowVsHume/Bigelow/Pargetter: may not contain any reference to an individual: This is too weak and too strong: a) too strong: E.g. Kepler’s laws relate to all the planets, but therefore also to an individual, the sun. b) too weak: it is still no law. E.g. that everything moves towards the earth’s center. I 235 LoN/BigelowVsHume/Bigelow/Pargetter: in our opinion, it has nothing to do with them, E.g. whether they are useful, or whether they contradict our intuitions. Counterfactual conditional/Co.co/LoN/Hume/Bigelow/Pargetter: for the Humean, Counterfactual Conditional are circular, if they are to represent LoN. We ourselves only use a Counterfactual Conditional when we have recognized something as a law! When we ask ourselves whether something is a law, we ask ourselves not whether it fulfils a Counterfactual Conditional. I 236 HumeVsBigelow/Bigelow/Pargetter: our modal approach for LoN is circular. BigelowVsVs: it is not! BigelowVsHume: most of Hume’s theories of the LON are circular themselves, with one exception: the theory that Lewis reads out of Ramsey. Ramsey/Lewis/Bigelow/Pargetter: this theory is based on the logical relations of laws among each other (coherence). (Ramsey 1929, 1931, Lewis 1973a, Mellor 1980). I 237 BigelowVsLewis/BigelowVsHume/Bigelow/Pargetter: Problem: if theories are sets of propositions, propositions must not be sets of possible worlds! For then the best theory for a possible worlds would have to be an axiom: the one-class of this possible worlds All facts of the world are then theorems of the axiom. There would be only one law for each world. No two possible worlds would have a law in common. I 267 BigelowVsHume: went too far in his rejection of necessity in laws. But not far enough in his rejection of the necessity approach to causality. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| Lewis, D. | Fraassen Vs Lewis, D. | Black I 117 Laws of Nature/LoN/Theory/van FrassenVs Lewis: (1989, § 3.3): 1) Lewis does not explain the model force of LoN: E.g. if "all Fs are Gs", then they have to be so in a good sense. Signs for this are counterfactual conditionals, which are connected to LoN (Dretske 1977, 255, Armstrong 1983, §4.4 and 69f). Schw I 118 VsLewis: 2) his analysis does not indicate why LoN play such a large role in explanations (Dretske 1977, 262, van Fraassen 1989 §3,4, Armstrong 1983 §4.2). Is it possible to explain why this F is a G by indicating that all Fs are Gs? LewisVsVs: why should the theorems of the best theories not meet the conditions? Systematic regularities are an important property of the actual world. Therefore, similarity is assigned special weight in the evaluation of counterfactual conditionals. |
Fr I B. van Fraassen The Scientific Image Oxford 1980 Black I Max Black "Meaning and Intention: An Examination of Grice’s Views", New Literary History 4, (1972-1973), pp. 257-279 In Handlung, Kommunikation, Bedeutung, G. Meggle (Hg) Frankfurt/M 1979 Black II M. Black The Labyrinth of Language, New York/London 1978 German Edition: Sprache. Eine Einführung in die Linguistik München 1973 Black III M. Black The Prevalence of Humbug Ithaca/London 1983 Black IV Max Black "The Semantic Definition of Truth", Analysis 8 (1948) pp. 49-63 In Truth and Meaning, Paul Horwich Aldershot 1994 |
| Mundy, B. | Field Vs Mundy, B. | I 199 Representation Theorem/VsRelationism: Relationism cannot take over the representation theorems from substantivalism either, because these depend on structural regularities (regularity of spacetime structure). And this regularity of spacetime is lost in relationalism. ((s) because there should be no empty sp.t., the sp.t. itself is bound to (empirically irregularly) occurring matter). Wrong Solution/Mundy: (1983): has proven a "representation theorem" which is not based on structural regularities. But that does not help heavy duty Platonism, because it generates numerical functors only from other numerical functors. That means he does not take predicates which put matter particles (point particles) in relation to each other, but a functor k: that refers particles to real numbers. E.g. For every three-point particle a real number that represents the inner product of two vectors which have one of these points as a common starting point, and the other two as endpoints. From this he extracts (several) coordinate systems, so that we have a representation theorem of species. FieldVsMundy: this does not serve the purposes for which representation theorems were originally developed, because it does not depart from a non-numeric base. Mundy: also sees that the R should not use any functions of point particles to real numbers as the basis for its formulation of physics. Therefore, he reformulates the equation: old: k(p,q,r) = a (where a is a real number) new: ka(p,q,r) so that we have an uncountable, infinite set of 3-digit space relations, one for every real number. (Mundy, 1983, p 212, 223.) FieldVsMundy: this does not solve any problem, because it’s only a notational trick. ((s) notation, orthography, paraphrasing, renaming >Rorty: "redescription" not a mere renaming, because description (language) necessitates stronger revision than replacing individual predicates with others. Potentially different number of digits). FieldVsMundy: if you really wanted to interpreted the ka’s as 3-digit spatial relations, the a’s would have to be considered as unquantifiable indices. Then we would have uncountably many primitive predicates, and thus no theory would be possible. Index/Quantification/(s): it is impossible to quantify on indices. Indices are not quantifiable. Mundy: of course, does not treat the indices as unquantifiable, but he re-writes them: k(p,q,r) = a if he wants to quantify on a. FieldVsMundy: but a quantifiable index is simply a variable that appears in a different place. And with the re-naming we do not change the fact that we have a 4-digit relation of which one term is a real number. Conclusion: With that you cannot take advantage of the difference between moderate Platonism and heavy duty Platonism. |
Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Parsons, Ter. | Stalnaker Vs Parsons, Ter. | I 73 Bare particulars/modal logic/ML/semantics/Stalnaker: the problem is now to connect the bare particulars-theory with these three restrictions with the quantified modal logic (ML). I 74 Terence ParsonsVs/Stalnaker: T. Parsons attacked this proof theoretically (1969). Anti-essentialism/T. Parsons: question: what axioms do we need for a full and reasoned anti-essentialist theory? That means a theory that prevents any questionable ascription of essential properties? StalnakerVsParsons: problem: some of his propositions are not theorems: e.g. Theorem: (Ex)N(Fx) > (x)N(Fx). ((s) if F is a necessary property for an object then this applies to all such objects x) E.g. if a square is necessary angular, then all squares). Stalnaker: but the following substitution instance is not a theorem: (Ex)N(Rxy) > (x)N(Rxy). ((s) If something is necessary the father of y, all is necessary the father of y.) Stalnaker: that means the atomic predicate "F" does not represent any property as it should normally be but just a random property of a certain kind. This is not bad per se but imposes the semantics additional burdens. Because the rules have to pick out suitable properties as values for atomic predicates. ((s) QuineVs - Quine: predicates do not represent properties). properties/anti-essentialism/predicates/Stalnaker: in distinguishing it is naturally about between intrinsic, qualitative characteristics and referential or possible world-indexed properties. Only the former come into question. StalnakerVsParsons: this one requires this but does not explain it. Atomic predicate/Stalnaker: this concept cannot help because it is purely syntactic and cannot make a semantic job by itself. Anti-essentialism/quantified modal logic/Stalnaker/conclusion: to connect the two, we need real semantic conditions for atomic predicates. |
Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
| Quine, W.V.O. | Russell Vs Quine, W.V.O. | Prior I 39 Ramified type theory/rTT/Prior: first edition Principia Mathematica(1): here it does not say yet that quantification on non-nouns (non nominal) is illegitimate, or that they are only apparently not nominal. (Not on names?) But only that you have to treat them carefully. I 40 The ramified type theory was incorporated in the first edition. (The "simple type theory" is, on the other hand, little more than a certain sensitivity to the syntax.) Predicate: makes a sentence out of a noun. E.g. "φ" is a verb that forms the phrase "φx". But it will not form a sentence when a verb is added to another verb. "φφ". Branch: comes into play when expressions form a sentence from a single name. Here we must distinguish whether quantified expressions of the same kind occur. E.g. "__ has all the characteristics of a great commander." logical form: "For all φ if (for all x, if x is a great commander, then φx) then φ__". ΠφΠxCψxφx" (C: conditional, ψ: commander, Π: for all applies). Easier example: "__ has the one or the other property" logical form: "For a φ, φ __" "Σφφ". (Σ: there is a) Order/Type: here one can say, although the predicate is of the same type, it is of a different order. Because this "φ" has an internal quantification of "φ's". Ramified type theory: not only different types, but also various "orders" should be represented by different symbols. That is, if we, for example, have introduced "F" for a predicative function on individuals" (i.e. as a one-digit predicate), we must not insert non-predicative functions for "f" in theorems. E.g. "If there are no facts about a particular individual ..." "If for all φ, not φx, then there is not this fact about x: that there are no facts about x that is, if it is true that there are no facts about x, then it cannot be true. I.e. if it is true that there are no facts about x, then it is wrong, that there is this fact. Symbolically: 1. CΠφNφxNψx. I 41 "If for all φ not φ, then not ψx" (whereby "ψ" can stand for any predicate). Therefore, by inserting "∏φφ" for "ψ": 2. CΠφNφxNΠφNφx Therefore, by inserting and reductio ad absurdum: CCpNpNp (what implies its own falsehood, is wrong) 3. CΠφNφx. The step of 1 to 2 is an impermissible substitution according to the ramified type theory. Sentence/ramified type theory/Prior: the same restriction must be made for phrases (i.e. "zero-digit predicates", propositions). Thus, the well-known old argument is prevented: E.g. if everything is wrong, then one of the wrong things would be this: that everything is wrong. Therefore, it may not be the case that everything is wrong. logical form: 1. CΠpNpNq by inserting: 2. CΠpNpNPpNp and so by CCpNpNp (reductio ad absurdum?) 3. NΠpNp, Ramified type theory: that is now blocked by the consideration that "ΠpNp" is no proposition of the "same order" as the "p" which exists in itself. And thus not of the same order as the "q" which follows from it by instantiation, so it cannot be used for "q" to go from 1 to 2. RussellVsQuine/Prior: here propositions and predicates of "higher order" are not entirely excluded, as with Quine. They are merely treated as of another "order". VsBranched type theory: there were problems with some basic mathematical forms that could not be formed anymore, and thus Russell and Whitehead introduce the reducibility axiom. By contrast, a simplified type theory was proposed in the 20s again. Type Theory/Ramsey: was one of the early advocates of a simplification. Wittgenstein/Tractatus/Ramsey: Thesis: universal quantification and existential quantification are both long conjunctions or disjunctions of individual sentences (singular statements). E.g. "For some p, p": Either grass is green or the sky is pink, or 2 + 2 = 4, etc.". (> Wessel: CNF, ANF, conjunctive and adjunctive normal form) Propositions/Wittgenstein/Ramsey: no matter of what "order" are always truth functions of indiviual sentences. Ramified Type TheoryVsRamsey/VsWittgenstein: such conjunctions and disjunctions would not only be infinitely long, but the ones of higher order would also need to contain themselves. E.g. "For some p.p" it must be written as a disjunction of which "for some p, p" is a part itself, which in turn would have to contain a part, ... etc. RamseyVsVs: the different levels that occur here, are only differences of character: not only between "for some p,p" and "for some φ, φ" but also between "p and p" and "p, or p", and even the simple "p" are only different characters. Therefore, the expressed proposition must not contain itself. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
Russell I B. Russell/A.N. Whitehead Principia Mathematica Frankfurt 1986 Russell II B. Russell The ABC of Relativity, London 1958, 1969 German Edition: Das ABC der Relativitätstheorie Frankfurt 1989 Russell IV B. Russell The Problems of Philosophy, Oxford 1912 German Edition: Probleme der Philosophie Frankfurt 1967 Russell VI B. Russell "The Philosophy of Logical Atomism", in: B. Russell, Logic and KNowledge, ed. R. Ch. Marsh, London 1956, pp. 200-202 German Edition: Die Philosophie des logischen Atomismus In Eigennamen, U. Wolf (Hg) Frankfurt 1993 Russell VII B. Russell On the Nature of Truth and Falsehood, in: B. Russell, The Problems of Philosophy, Oxford 1912 - Dt. "Wahrheit und Falschheit" In Wahrheitstheorien, G. Skirbekk (Hg) Frankfurt 1996 Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
| Quine, W.V.O. | Verschiedene Vs Quine, W.V.O. | Davidson I 55 CreswellVsQuine: he had a realm of reified experiences or phenomena facing an unexplored reality. Davidson pro - - QuineVsCresswell >Quine III) Kanitscheider II 23 Ontology/language/human/Kanitschneider: the linguistic products of the organism are in no way separated from its producer by an ontological gap. Ideas are certain neuronal patterns in the organism. KanitscheiderVsQuine: Weak point: his empiricism. One must therefore view his epistemology more as a research programme. Quine VI 36 VsQuine: I've been told that the question "What is there?" is always a question of fact and not just a linguistic problem. That is correct. QuineVsVs: but saying or assuming what there is remains a linguistic matter and here the bound variables are in place. VI 51 Meaning/Quine: the search for it should start with the whole sentences. VsQuine: the thesis of the indeterminacy of translation leads directly to behaviorism. Others: it leads to a reductio ad absurdum of Quine's own behaviorism. VI 52 Translation Indeterminacy/Quine: it actually leads to behaviorism, which there is no way around. Behaviorism/Quine: in psychology one still has the choice whether one wants to be a behaviorist, in linguistics one is forced to be one. One acquires language through the behavior of others, which is evaluated in the light of a common situation. It literally does not matter what other kind psychological life is! Semantics/Quine: therefore no more will be able to enter into the semantic meaning than what can also be inferred from perceptible behaviour in observable situations Quine XI 146 Deputy function/Quine/Lauener: does not have to be unambiguous at all. E.g. characterisation of persons on the basis of their income: here different values are assigned to an argument. For this we need a background theory: We map the universe U in V so that both the objects of U and their substitutes are included in V. If V forms a subset of U, U itself can be represented as background theory within which their own ontological reduction is described. XI 147 VsQuine: this is no reduction at all, because then the objects must exist. QuineVsVs: this is comparable to a reductio ad absurdum: if we want to show that a part of U is superfluous, we can assume U for the duration of the argument. (>Ontology/Reduction). Lauener: this brings us to ontological relativity. Löwenheim/Ontology/Reduction/Quine/Lauener: if a theory of its own requires an overcountable range, we can no longer present a proxy function that would allow a reduction to a countable range. For this one needed a much stronger frame theory, which then could no longer be discussed away as reductio ad absurdum according to Quine's proposal. Quine X 83 Logical Truth/Validity/Quine: our insertion definitions (sentences instead of sets) use a concept of truth and fulfillment that goes beyond the framework of object language. This dependence on the concept of ((s) simple) truth, by the way, would also concern the model definition of validity and logical truth. Therefore we have reason to look at a 3rd possibility of the definition of validity and logical truth: it gets by without the concepts of truth and fulfillment: we need the completeness theorem ((s) >provability). Solution: we can simply define the steps that form a complete method of proof and then: Def Valid Schema/Quine: is one that can be proven with such steps. Def Logically True/Quine: as before: a sentence resulting from a valid schema by inserting it instead of its simple sentences. Proof Procedure/Evidence Method/Quine: some complete ones do not necessarily refer to schemata, but can also be applied directly to the propositions, X 84 namely those that emerge from the scheme by insertion. Such methods generate true sentences directly from other true sentences. Then we can leave aside schemata and validity and define logical truth as the sentence generated by these proofs. 1st VsQuine: this tends to trigger protest: the property "to be provable by a certain method of evidence" is uninteresting in itself. It is interesting only because of the completeness theorem, which allows to equate provability with logical truth! 2. VsQuine: if one defines logical truth indirectly by referring to a suitable method of proof, one deprives the completeness theorem of its ground. It becomes empty of content. QuineVsVs: the danger does not exist at all: The sentence of completeness in the formulation (B) does not depend on how we define logical truth, because it is not mentioned at all! Part of its meaning, however, is that it shows that we can define logical truth by merely describing the method of proof, without losing anything of what makes logical truth interesting in the first place. Equivalence/Quine: important are theorems, which state an equivalence between quite different formulations of a concept - here the logical truth. Which formulation is then called the official definition is less important. But even mere terms can be better or worse. Validity/logical truth/definition/Quine: the elementary definition has the advantage that it is relevant for more neighboring problems. 3. VsQuine: with the great arbitrariness of the choice of the evidence procedure it cannot be excluded that the essence of the logical truth is not grasped. QuineVsVs: how arbitrary is the choice actually? It describes the procedure and talks about strings of characters. In this respect it corresponds to the sentence. Insertion definition: it moves effectively at the level of the elementary number theory. And it stays at the level, while the other definition uses the concept of truth. That is a big difference. |
Davidson I D. Davidson Der Mythos des Subjektiven Stuttgart 1993 Davidson I (a) Donald Davidson "Tho Conditions of Thoughts", in: Le Cahier du Collège de Philosophie, Paris 1989, pp. 163-171 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson I (b) Donald Davidson "What is Present to the Mind?" in: J. Brandl/W. Gombocz (eds) The MInd of Donald Davidson, Amsterdam 1989, pp. 3-18 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson I (c) Donald Davidson "Meaning, Truth and Evidence", in: R. Barrett/R. Gibson (eds.) Perspectives on Quine, Cambridge/MA 1990, pp. 68-79 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson I (d) Donald Davidson "Epistemology Externalized", Ms 1989 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson I (e) Donald Davidson "The Myth of the Subjective", in: M. Benedikt/R. Burger (eds.) Bewußtsein, Sprache und die Kunst, Wien 1988, pp. 45-54 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson II Donald Davidson "Reply to Foster" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 Davidson III D. Davidson Essays on Actions and Events, Oxford 1980 German Edition: Handlung und Ereignis Frankfurt 1990 Davidson IV D. Davidson Inquiries into Truth and Interpretation, Oxford 1984 German Edition: Wahrheit und Interpretation Frankfurt 1990 Davidson V Donald Davidson "Rational Animals", in: D. Davidson, Subjective, Intersubjective, Objective, Oxford 2001, pp. 95-105 In Der Geist der Tiere, D Perler/M. Wild Frankfurt/M. 2005 Kanitsch I B. Kanitscheider Kosmologie Stuttgart 1991 Kanitsch II B. Kanitscheider Im Innern der Natur Darmstadt 1996 Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Relativism | Black Vs Relativism | III 68 Scientific realism/Leopold von Franke: "... as it actually was". Black pro. G.H. Hardy/Black: (mathematician, Cambridge, 1940, pp. 63): equals "physical reality" with "mathematical reality", "laws with "theorems" and "notice" with "prove": Hardy: I believe that the is physical reality is outside of us and it is our function to discover it, or to watch it, and that the laws that we celebrate greatly as our "creations" are simply our comments to these observations. Outside world/Reality/Objectivity/Planck: it is of paramount importance that the external world is independent of us, something absolute. (Scientific Autobiography, NY, 1949 p. 13). ((s) Otherwise, there is no difference between knowing and doubting. How are we to determine what we believe and what we doubt if reality is determined by us?). Absolute/Black: we should not shy away from this word. Truth, knowledge and reality are not relative terms. Only their recognition is relative to the owner ((s)> epistemic). Relativism/Roszak: what is true for me is what I am convinced of. (Roszak pro). BlackVsRelativism/BlackVsRoszak: whoever believes that excludes themselves from the scientific pursuit of truth, III 69 reality and knowledge. Even worse: they also exclude themselves from everyday knowledge. Reality/Bishop Butler: Things and actions are what they are and their consequences will be what they will be. Why should we desire to be deceived? |
Black I Max Black "Meaning and Intention: An Examination of Grice’s Views", New Literary History 4, (1972-1973), pp. 257-279 In Handlung, Kommunikation, Bedeutung, G. Meggle (Hg) Frankfurt/M 1979 Black IV Max Black "The Semantic Definition of Truth", Analysis 8 (1948) pp. 49-63 In Truth and Meaning, Paul Horwich Aldershot 1994 |
| Russell, B. | Strawson Vs Russell, B. | Wolf II 17 StrawsonVsRussell: Vs Russell's resolution of singular sentences like "the F, which is G, is H" are general sentences such as "There is exactly one F, which is G, and this F is H" : this is inappropriate. Thus it is not included, that we refer with the singular term to individual things. --- Newen/Schrenk I 92 Reference/StrawsonVsRussell: ("On Referring") in 1950, 45 years after Russell's "On Denoting" (1905)). Strawson: 5 theses (i) one must distinguish between a) the sentence, b) the use, c) the expression (on one occasion) (ii) there is a difference between (logical) implying and presupposition (iii) truth value gaps are allowed (iv) The meaning of an expression is not its referent, but the conventions and rules. In various uses the term can therefore refer to different objects. (v) expressions can be used referential and predicative (attributing properties). Sentence/truth value/tr.v./Strawson: Thesis: sentences themselves cannot be true or false, only their use. Presupposition/implication/Strawson: difference: Definition implication/Strawson: A implies B iff it cannot be that A is true but B is false. On the other hand: Definition presupposition/Strawson: A presupposes B iff B must be true so that A can take a truth value. Existence assertion/uniqueness assertion/Strawson: are only presupposed by a sentence with description, but not implied. E.g. King of France/presupposition/Strawson: the sentence presupposes the existence, however, does not imply it. And also does not claim the existence and uniqueness. Newen/Schrenk VsStrawson: Strawson provides no philosophical-logical arguments for his thesis. Newen/Schrenk I 94 He rather refers to our everyday practice. Truth-value gaps/StrawsonVsRussell: accepted by him. Negative existential statements/existence/existence theorem/Strawson/VsStrawson/Newen/Schrenk: his approach lets the problem of empty existence theorems look even trickier. Referential/predicative/singular term/designation/name/Strawson/Newen/Schrenk: Thesis: Proper names/demonstratives: are largely used referential. Description: have a maximum predicative, so descriptive meaning (but can also simultaneously refer). Identity/informative identity sentences/referential/predicative/Strawson/Newen/Schrenk: here the description has (or two occurring descriptions) such an extreme predicative use that E.g. "Napoleon is identical to the man who ordered the execution of the Duke" is as good as synonymous with the phrase "Napoleon ordered the ...". In principle, both sentences are used for a predication. Thus, the first sentence is informative when it is read predicative and not purely referential. --- Quine I 447 StrawsonVsRussell: has called Russell's theory of descriptions false because of their treatment of the truth value gaps. --- Schulte III 433 StrawsonVsRussell/Theory of descriptions: Strawson brings a series of basic distinctions between types and levels of use of linguistic expressions into play. Fundamental difference between the logical subject and logical predicate. Pleads for stronger focus on everyday language. "The common language has no exact logic" Schulte III 434 King-xample: "The present king of France is bald". Russell: here the description must not be considered a logical subject. Russell: Such sentences are simply wrong in the case of non-existence. Then we also not need to make any dubious ontological conditions. We analyze (according to Russell) the sentence as follows: it is in reality a conjunction of three sentences: 1. There is a king of France. 2. There are no more than a king of France. 3. There is nothing that is King of France and is not bald. Since at least one member in the conjunction is false, it is wrong in total. StrawsonVsRussell: 1. he speaks too careless of sentences and their meanings. But one has to consider the use of linguistic expressions, which shows that there must be a much finer distinction. 2. Russell confused what a sentence says with the terms of the meaningful use of this sentence. 3. The everyday language and not the formal logic determines the meaning. --- Schulte III 435 Reference/Strawson: an expression does not refer to anything by itself. King-Example/StrawsonVsRussell: with the sentence "The present king of France is bald" no existence assertion is pronounced. Rather, it is "implied". Therefore, the sentence does not need to be true or false. The term does not refer to anything. Definition truth value gap (Strawson): E.g. King-Example: refers to nothing. Wittgenstein: a failed move in the language game. --- VII 95 Description/Strawson: sure I use in E.g. "Napoleon was the greatest French soldier", the word "Napoleon", to name the person, not the predicate. StrawsonVsRussell: but I can use the description very well to name a person. There can also be more than one description in one sentence. VII 98 StrawsonVsRussell: seems to imply that there are such logical subject predicate sentences. Russell solution: only logical proper names - for example, "This" - are real subjects in logical sentences. The meaning is exactly the individual thing. This leads him to the fact that he can no longer regard sentences with descriptions as logical propositions. Reference/StrawsonVsRussell: Solution: in "clear referring use" also dscriptions can be used. But these are not "descriptions" in Russell's sense. VII 99 King-Example/StrawsonVsRussell: claims three statements, one of which in any case would be wrong. The conjunction of three statements, one of which is wrong and the others are true, is false, but meaningful. VII 100 Reference/description/StrawsonVsRussell: distinction: terminology: "Unique reference": expression. (Clearly referring description). Sentence begins with clear referring description. Sentences that can start with a description: (A1) sentence (A2) use of a sentence (A3) uttering of a sentence accordingly: (B1) expression (B2) use of an expression (B3) utterance of an expression. King-Example/StrawsonVsRussell: the utterance (assertion (>utterance) "The present king of France is wise" can be true or false at different times, but the sentence is the same. VII 101 Various uses: according to whether at the time of Louis XIV. or Louis XV. Sentence/statement/statement/assertion/proposition/Strawson: Assertion (assertion): can be true or false at different times. Statement (proposition): ditto Sentence is always the same. (Difference sentence/Proposition). VII 102 StrawsonVsRussell: he overlooks the distinction between use and meaning. VII 104 Sense/StrawsonVsRussell: the question of whether a sentence makes sense, has nothing to do with whether it is needed at a particular opportunity to say something true or false or to refer to something existent or non-existent. VII 105 Meaning/StrawsonVsRussell: E.g. "The table is covered with books": Everyone understands this sentence, it is absurd to ask "what object" the sentence is about (about many!). It is also absurd to ask whether it is true or false. VII 106 Sense/StrawsonVsRussell: that the sentence makes sense, has to do with the fact that it is used correctly (or can be), not that it can be negated. Sense cannot be determined with respect to a specific (individual) use. It is about conventions, habits and rules. VII 106/107 King-Example/Russell/Strawson: Russell says two true things about it: 1. The sentence E.g. "The present king of France is wise" makes sense. 2. whoever expresses the sentence now, would make a true statement, if there is now one, StrawsonVsRussell: 1. wrong to say who uttered the sentence now, would either make a true or a false claim. 2. false, that a part of this claim states that the king exists. Strawson: the question wrong/false does not arise because of the non-existence. E.g. It is not like grasping after a raincoat suggests that one believes that it is raining. (> Presupposition/Strawson). Implication/Imply/StrawsonVsRussell: the predication does not assert an existence of the object. VII 110 Existence/StrawsonVsRussell: the use of "the" is not synonymous with the assertion that the object exists. Principia Mathematica(1): (p.30) "strict use" of the definite article: "only applies if object exists". StrawsonVsRussell: the sentence "The table is covered with books" does not only apply if there is exactly one table VII 111 This is not claimed with the sentence, but (commonplace) implied that there is exactly one thing that belongs to the type of table and that it is also one to which the speaker refers. Reference/StrawsonVsRussell: referring is not to say that one refers. Saying that there is one or the other table, which is referred to, is not the same as to designate a certain table. Referencing is not the same as claiming. Logical proper names/StrawsonVsRussell: E.g. I could form my empty hand and say "This is a beautiful red!" The other notes that there is nothing. Therefore, "this" no "camouflaged description" in Russell's sense. Also no logical proper name. You have to know what the sentence means to be able to respond to the statement. VII 112 StrawsonVsRussell: this blurs the distinction between pure existence theorems and sentences that contain an expression to point to an object or to refer to it. Russell's "Inquiry into meaning and truth" contains a logical catastrophic name theory. (Logical proper names). He takes away the status of logical subjects from the descriptions, but offers no substitute. VII 113 Reference/Name/referent/StrawsonVsRussell: not even names are enough for this ambitious standard. Strawson: The meaning of the name is not the object. (Confusion of utterance and use). They are the expressions together with the context that one needs to clearly refer to something. When we refer we do not achieve completeness anyway. This also allows the fiction. (Footnote: later: does not seem very durable to me because of the implicit restrictive use of "refer to".) VII 122 StrawsonVsRussell: Summit of circulatory: to treat names as camouflaged descriptions. Names are choosen arbitrary or conventional. Otherwise names would be descriptive. VII 123 Vague reference/"Somebody"/implication/Strawson: E.g. "A man told me ..." Russell: existence assertion: "There is a man who ..." StrawsonVsRussell: ridiculous to say here that "class of men was not empty ..." Here uniqueness is also implicated as in "the table". VII 124 Tautology/StrawsonVsRussell: one does not need to believe in the triviality. That only believe those who believe that the meaning of an expression is the object. (E.g. Scott is Scott). VII 126 Presupposition/StrawsonVsRussell: E.g. "My children sleep" Here, everyone will assume that the speaker has children. Everyday language has no exact logic. This is misjudged by Aristotle and Russell. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
Strawson I Peter F. Strawson Individuals: An Essay in Descriptive Metaphysics. London 1959 German Edition: Einzelding und logisches Subjekt Stuttgart 1972 Strawson VII Peter F Strawson "On Referring", in: Mind 59 (1950) In Eigennamen, Ursula Wolf Frankfurt/M. 1993 K II siehe Wol I U. Wolf (Hg) Eigennamen Frankfurt 1993 Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 Schulte I J. Schulte Wittgenstein Stuttgart 2001 Schulte II J. Schulte U. J. Wenzel Was ist ein philosophisches Problem? Frankfurt 2001 Schulte III Joachim Schulte "Peter Frederick Strawson" In Philosophie im 20. Jahrhundert, A. Hügli/P. Lübcke Reinbek 1993 |
| Soames, S. | Schiffer Vs Soames, S. | I 217 Compositional Semantics/Comp.sem./Understanding/Explanation/Scott Soames/Schiffer: (Soames 1987) Thesis: comp.sem. is not needed for explaining the language understanding, nevertheless natural languages have a comp.sem .: Language understanding/Soames: you should not look at the semantics to explain semantic competence. Instead one needs comp.sem you. for the explanation of the representational character of the language. The central semantic fact about language is that it is needed to represent the world. Propositions encode systematic information that characterize the world so and so. We need comp.sem. for the analysis of the principles of this encoding. SchifferVsSoames: Instead, I have introduced the expression potential. One might assume that a finally formulated theory should be able to formulate theorems for the attribution of expression potential to each proposition of the language. But would that then not be a compositional theory?. I 218 E.g. Harvey: here we did not need comp.sem. to assume that for each proposition of M (internal language) there is a realization of belief, that means (µ)(∑P)(If μ is a proposition of M and in the box, then Harvey believes that P). (s) Although here no connection between μ and P is specified). Schiffer: Now we could find a picture of formulas of M into German, which is a translation. But that provides no finite theory which would provide a theorem for every formula μ of M as If μ is in the box, then Harvey thinks that snow is sometimes purple. Propositional attitude/Meaning theory/Schiffer: Problem: it is not possible to find a finite theory which ascribes verbs for belief characteristics of this type. Pointe: yet the terms in M have meaning! E.g. "Nemrac seveileb taht emos wons si elprup" would realize the corresponding belief in Harvey and thus also mean trivially. SchifferVsCompositionality: when the word-meaning contributs to the proposition-meaning, then it is this. Then expressions in M have meaning. But these are not characteristics that can be attributed to a finite theory. We could find only the property to attribute to each proposition of M a particular belief, but that cannot happen in a finite theory. mental representation/Mentalese/Schiffer: the formulas in M are mental representations. They represent external conditions. Propositions of E, Harvey's spoken speech, received their representational character via the connection with mental representations. Therefore Mentalese needs no comp.sem. SchifferVsSoames: So he is wrong and we need the comp.sem. not even for an illustration of how our propositions represent the world. I 219 We had already achieved this result via the expresion potentials. Because: representational character: is indistinguishable from the expression potential. |
Schi I St. Schiffer Remnants of Meaning Cambridge 1987 |
| Tarski, A. | Field Vs Tarski, A. | Brendel I 68 T-Def/FieldVsTarski: does not do justice to physicalistic intuitions. (Field 1972). Semantic concepts and especially the W concept should be traceable to physical or logical-mathematical concepts. Tarski/Brendel: advocates for a metalinguistic definition himself that is based only on logical terms, no axiomatic characterization of "truth". (Tarski, "The Establishment of Scientific Semantics"). Bre I 69 FieldVsTarski: E.g. designation: Def Designation/Field: Saying that the name N denotes an object a is the same thing as stipulating that either a is France and N is "France" or a is Germany and N is "Germany"... etc. Problem: here only an extensional equivalence is given, no explanation of what designation (or satisfiability) is. Bre I 70 Explanation/FieldVsTarski/Field: should indicate because of which properties a name refers to a subject. Therefore, Tarski’s theory of truth is not physicalistic. T-Def/FieldVsTarski/Field/Brendel: does not do justice to physicalistic intuitions - extensional equivalence is no explanation of what designation or satisfiability is. Field I 33 Implication/Field: is also in simpler contexts sensibly a primitive basic concept: E.g. Someone asserts the two sentences. a) "Snow is white" does not imply logically "grass is green". b) There are no mathematical entities such as quantities. That does not look as contradictory as Fie I 34 John is a bachelor/John is married FieldVsTarski: according to him, a) and b) together would be a contradiction, because he defines implication with quantities. Tarski does not give the normal meaning of those terms. VsField: you could say, however, that the Tarskian concepts give similar access as the definition of "light is electromagnetic radiation". FieldVsVs: but for implication we do not need such a theoretical approach. This is because it is a logical concept like negation and conjunction. Field II 141 T-Theory/Tarski: Thesis: we do not get an adequate probability theory if we just take all instances of the schema as axioms. This does not give us the generalizations that we need, for example, so that the modus ponens receives the truth. FieldVsTarski: see above Section 3. 1. Here I showed a solution, but should have explained more. Feferman/Field: Solution: (Feferman 1991) incorporates schema letters together with a rule for substitution. Then the domain expands automatically as the language expands. Feferman: needs this for number theory and set theory. Problem: expanding it to the T-theory, because here we need scheme letters inside and outside of quotation marks. Field: my solution was to introduce an additional rule that allows to go from a scheme with all the letters in quotation marks to a generalization for all sentences. Problem: we also need that for the syntax,... here, an interlinking functor is introduced in (TF) and (TFG). (see above). II 142 TarskiVsField: his variant, however, is purely axiomatic. FieldVsTarski/FefermanVsTarski: Approach with scheme letters instead of pure axioms: Advantages: 1) We have the same advantage as Feferman for the schematic number theory and the schematic set theory: expansions of the language are automatically considered. 2) the use of ""p" is true iff. p" (now as a scheme formula as part of the language rather than as an axiom) seems to grasp the concept of truth better. 3) (most important) is not dependent on a compositional approach to the functioning of the other parts of language. While this is important, it is also not ignored by my approach. FieldVsTarski: an axiomatic theory is hard to come by for belief sentences. Putnam I 91 Correspondence Theory/FieldVsTarski: Tarski’s theory is not suited for the reconstruction of the correspondence theory, because fulfillment (of simple predicates of language) is explained through a list. This list has the form "Electron" refers to electrons "DNS" refers to DNS "Gene" refers to genes. etc. this is similar to (w) "Snow is white" is true iff.... (s)> meaning postulates) Putnam: this similarity is no coincidence, because: Def "True"/Tarski/Putnam: "true" is the zero digit case of fulfillment (i.e. a formula is true if it has no free variables and the zero sequence fulfills it). Def Zero Sequence: converges to 0: E.g. 1; 1/4; 1/9; 1/16: ... Criterion W/Putnam: can be generalized to the criterion F as follows: (F for fulfillment): Def Criterion F/Putnam: (F) an adequate definition of fulfilled in S must generate all instances of the following scheme as theorems: "P(x1...xn) is fulfilled by the sequence y1...yn and only if P(y1...yn). Then we reformulate: "Electron (x)" is fulfilled by y1 iff. y1 is an electron. PutnamVsField: it would have been formulated like this in Tarskian from the start. But that shows that the list Field complained about is determined in its structure by criterion F. This as well as the criterion W are now determined by the formal properties we desired of the concepts of truth and reference, so we would even preserve the criterion F if we interpreted the connectives intuitionistically or quasi intuitionistically. Field’s objection fails. It is right for the realist to define "true" à la Tarski. |
Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 Bre I E. Brendel Wahrheit und Wissen Paderborn 1999 Putnam I Hilary Putnam Von einem Realistischen Standpunkt In Von einem realistischen Standpunkt, Vincent C. Müller Frankfurt 1993 SocPut I Robert D. Putnam Bowling Alone: The Collapse and Revival of American Community New York 2000 |
| Tarski, A. | Prior Vs Tarski, A. | I 98 Truth/Falsity/PriorVsTarski: the concepts of truth and falsity discussed in the last chapter are not the concepts of Tarski. Prior: ours could be described as properties not of sentences, but of propositions. I.e. quasi-properties of quasi-objects! Not adjectives "true", "false", but rather adverbs "correctly" (accurate, truthful, rightly) and "falsely". I 99 PriorVsTarski: (A) If someone says that snow is white, he says it truthfully iff. snow is white. Tarski: (B) The sentence "snow is white" is true iff. snow is white. The truth of all true sentences of a language can be derived from Tarski's definition with normal logic. And that is for him the criterion of satisfiability of the truth definition. Quotation Marks/Truth/Truth Definition/PriorVsTarski: for me there are no quotation marks. But in Tarski, these belong more to informal preparation than to strict theory. Use/Mention/Tarski/Prior: left: the sentence is mentioned (by the name of the sentence) right: used. Prior: in my version () there is no mention, only use. (A) is not about sentences from start to finish, but about snow. (B) is about the sentence "snow is white". Self-Reference/Foreword Paradox/Tarski/Paradox/Prior: it remains the case that it looks as if self-reference were involved when we speak about people and what they say, think, fear, etc., which seems to exclude Tarski's semantics. But we must take a closer look: In Tarski, the predicates "true" and "false" do not belong to the same language as the sentences by which they are stated. I 103 PriorVsTarski: we say instead "x says something true if..." Or: "x says during the interval t t'that __" If we abbreviate this last phrase as "Sx!, "Sxp", then we could insert it in theorems like: CSx∑pKSxpNp∑pKSxpNp. Problem: (see above) If I says that he says something wrong between t and t', then it cannot be the only thing he says. This is a problem for very short intervals. How about if poor old x had to express theorems, and only had such a short time available for it? To the above theorem he would also have to express the consequent ∑pKSxpNp, and for that he might not have time! Above all, it may be that I will not do it ex hypothesi! Metalanguage/Point: this means that the language in which these theorems are expressed cannot be the same language that is used for that at some other occasions! |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
| Various Authors | Frege Vs Various Authors | Brandom II 83 FregeVsBoole: no material contents, therefore unable to follow scientific concept formation. Boole: "scope equality". Frege I 32 Addition/Hankel: wants to define: "if a and b are arbitrary elements of the basic series, then the sum of a + b is understood to be that one member of the basic series for which the formula a + (b + e) = a + b + e is true." (e is supposed to be the positive unit here). Addition/Sum/FregeVsHankel: 1) thus, the sum is explained by itself. If you do not yet know what a + b is, you will not be able to understand a + (b + e). 2) if you’d like to object that not the sum, but the addition should be explained, then you could still argue that a + b would be a blank sign if there was no member of the basic series or several of them of the required type. Frege I 48 Numbers/FregeVsNewton: he wants to understand numbers as the ratio of each size to another of the same kind. Frege: it can be admitted that this appropriately describes the numbers in a broader sense including fractions and irrational numbers. But this requires the concepts of size and the size ratio!. I 49 It would also not be possible to understand numbers as quantities, because then the concept of quantity and the quantity ratios would be presumed. I 58 Number/Schlömilch: "Notion of the location of an object in a series". FregeVsSchlömilch: then always the same notion of a place in a series would have to appear when the same number occurs, and that is obviously wrong. This could be avoided if he liked to understand an objective idea as imagination, but then what difference would there be between the image and the place itself?. I 60 Frege: then arithmetic would be psychology. If two were an image, then it would initially only be mine. Then we could perhaps have many millions of twos. I 64 Unit/Baumann: Delimitation. FregeVsBaumann: E.g. if you say the earth has a moon, you do not want to declare it a delimited one, but you rather say it as opposed to what belongs to Venus or Jupiter. I 65 With respect to delimitation and indivisibility, the moons of Jupiter can compete with ours and are just as consistent as our moon in this sense. Unit/Number/Köpp: Unit should not only be undivided, but indivisible!. FregeVsKöpp: this is probably supposed to be a feature that is independent from arbitrariness. But then nothing would remain, which could be counted and thought as a unit! VsVs: then perhaps not indivisibility itself, but the be considering to be indivisible could be established as a feature. FregeVs: 1) Nothing is gained if you think the things different from what they are!. I 66 2) If you do not want to conclude anything from indivisibility, what use is it then? 3) Decomposabiltiy is actually needed quite often: E.g. in the problem: a day has 24 hours, how many hours have three days?. I 69 Unit/Diversity/Number/FregeVsJevons: the emphasis on diversity also only leads to difficulties. E.g. If all units were different, you could not simply add: 1 + 1 + 1 + 1..., but you would always have to write: 1" + 1"" + 1 """ + 1 """", etc. or even a + b + c + d... (although units are meant all the time). Then we have no one anymore!. I 78 ff: ++ Number neither description nor representation, abstraction not a definition - It must not be necessary to define equality for each case. Infinite/Cantor: only the finite numbers should be considered real. Just like negative numbers, fractions, irrational and complex numbers, they are not sense perceptible. FregeVsCantor: we do not need any sensory perceptions as proofs for our theorems. It suffices if they are logically consistent. I 117 - 127 ++ VsHankel: sign (2-3) is not empty, but determinate content! Signs are never a solution! - Zero Class/FregeVsSchröder: (> empty set) false definition of the zero class: there can be no class that is contained in all classes as an element, therefore it cannot be created by definition. (The term is contradictory). IV 14 VsSchröder: you cannot speak of "classes" without already having given a concept. - Zero must not be contained as an element in another class (Patzig, Introduction), but only "subordinate as a class". (+ IV 100/101). II 93 Euclid/FregeVsEuclid: makes use of implied conditions several times, which he states neither under his principles nor under the requirements of the special sentence. E.g. The 19th sentence of the first book of the elements (in each triangle the greater angle is located opposite the larger side) presupposes the following sentences: 1) If a distance is not greater than another, then it is equal to or smaller than the first one. 2) If an angle is equal to another, then it is not greater than the first one. 3) If an angle is less than another, it is not greater than the first one. Waismann II 12 FregeVsPostulates: why is it not also required that a straight line is drawn through three arbitrary points? Because this demand contains a contradiction. Well, then they should proof that those other demands do not contain any contradictions!. Russell: postulates offer the advantages of theft over honest work. Existence equals solvability of equations: the fact that √2 exists means that x² 2 = 0 is solvable. |
F I G. Frege Die Grundlagen der Arithmetik Stuttgart 1987 F IV G. Frege Logische Untersuchungen Göttingen 1993 Bra I R. Brandom Making it exlicit. Reasoning, Representing, and Discursive Commitment, Cambridge/MA 1994 German Edition: Expressive Vernunft Frankfurt 2000 Bra II R. Brandom Articulating reasons. An Introduction to Inferentialism, Cambridge/MA 2001 German Edition: Begründen und Begreifen Frankfurt 2001 Waismann I F. Waismann Einführung in das mathematische Denken Darmstadt 1996 Waismann II F. Waismann Logik, Sprache, Philosophie Stuttgart 1976 |
| Various Authors | Wessel Vs Various Authors | I 17 Tolerance Principle/Carnap: ("Die logische Syntax der Sprache", 1934): "We do not want to establish prohibitions, we want to make determinations. Prohibitions can be replaced by a definitory distinction. There is no morality in logic. Everyone may construct his logic, i.e. his linguistic form, as he wants, but if he wants to discuss with us, he must indicate syntactic determinations instead of philosophical discussions." (The principle of tolerance was first formulated by Karl Menger). I 20 WesselVsTolerance Principle: overall we reject it, but we agree with Menger that the concept of constructiveness is unclear. VsMenger: the broadest concept of constructiveness is not the demand for mere consistency! (Wessel like Chr. Thiel). Justification/Logics/Wessel: all attempts at justification here are ultimately circular! Pro Carnap: of course, every logician and every mathematician has the right to build up arbitrary calculi first, whereby he has to specify the rules correctly. VsCarnap: this does not mean, however, that the possible or existing calculi are equal! That would be a "principle of indifference" . I 136 Def Analytical Implication/Parry/Wessel: (1933): If a formula A analytically implies a formula B, then only those statement variables occur in B that also occur in A. I 137 Axioms: (selection) + A 12. (A ‹-› B) u F(A) -> F[A/B] A 13. F(A) -> (A -> A) Analytical Implication/WesselVsParry: no solution to the problem since > is again an operator and can occur more than once in axioms and theorems. Pro: here for the first time the idea is expressed that only those variables may occur in the conclusion, which are also contained in the prerequisite. Paradoxes/Implication/Non-Classical Direction/Wessel: Questions: 1. Are there any guarantees that paradoxical formulas are not provable? 2. Are there guarantees that non-paradoxical formulas are not erroneously excluded? 3. Are there criteria to decide whether an arbitrary formula is paradox or not? 4. Is it possible to build a system in which all paradox formulas are not provable, but all non-paradox formulas are provable? I 219 Identity/M.Stirner: "to see the human being in each other and to act against each other as human beings...I see in you the human being as I see in myself the human being and nothing but the human being, so I care for you as I would care for myself...both of us are nothing but mathematical propositions: A = C and B = C therefore A = B, i.e. I nothing but human and you nothing but human: I and you the same". WesselVsStirner, Max: this is the same logic as in "J.Kaspar (pseudonym of Stirner) is a living being, a donkey is a living being, so J. Kaspar is a donkey". This is the confusion of different logical forms. ((s) Predication is not a statement of identity: "I am a human being" does not mean "I = human being".) I 314 Euler Diagrams/Borkowski/Lejewski/"ontological table"/Wessel: Extension of Euler diagrams: Inclusion and exclusion of meaning, existence, etc. WesselVsLejewski: his theory is burdened with serious deficiencies. I 315 Term Theory/Wessel: there are unlimited singular terms possible, but each theory gets by with a limited number. WesselVsLejewski: For example, the term "cosmonaut" undergoes a mysterious transformation. first empty term, then singular term, then general term! WesselVs: it is a general term right from the start: the reference has absolutely nothing to do with it. The distinction between empty and non-empty is a completely different classification of terms. This is not a purely logical task. I 352 Intension/WesselVsStegmüller: the term "content-related" problem only shows that it has not yet been solved on the logical level. StegmüllerVsModal Logic: because modal contexts would have intensional character. |
Wessel I H. Wessel Logik Berlin 1999 |
| Whitehead, A.N. | Simons Vs Whitehead, A.N. | I 94 Bowman L. Clarke/topology/mereology/Simons: formal objections against his system cannot be put forward. It is based on Whitehead's basic concept of compound, the relata are informally understood space-time regions. I 95 Def connected/connection/Clarke/Whitehead: connected means sharing a point ((s) common point). But the points and all the other borders are no individuals. Limit/Whitehead/Clarke: the limit is no individual. Individuals/Whitehead/Clarke: individuals have no interiors. This leads to a non-classical mereology. Connection/spelling/Clarke: it is written as a small diamond with double tails up and down. Separated/disconnected/external connection/spelling/Clarke: >< y”: x is externally connected with y, = "x touches y". Non-classical mereology/Simons: here o (overlap) and < (part-relation) do not interact in the way as in the classic. Only when an object touches nothing (that means intuitive, if it is open, see above) we can treat its parts as in classical mereology. I 96 "Quasi-topologically"/Clarke: (Because there is no zero element and no boundary elements): e.g. concepts: "interior of x", "closure (completion, final, closure) of x", "outside of x", "x is open", "x is closed". Product: a product of any two open individuals is again open. Axioms: (...) I 97 Bowman L. Clarke: "Just as the linguistic domain of the classical individuals calculus is a complete Boolean algebra without zero-elements, our theorems are a closing-algebra without zero elements and without boundary elements. It is interesting that this much topology can be operated with as minimal assumptions. SimonsVsClarke: the idea of "removing" the boundary elements can be understood in two ways: a) that they "really exist" and we have an artificial limit by that I 98 (This would explain why the mereology is non-classical.) b) that these elements do not exist at all, then we miss the remainder principle (Principle Remainder, RP, see above). If we remove the interior (of a non-open individual), nothing will change! In fact, nothing is left. Closure/SimonsVsClarke: if we take any individual, its interior is a real part of its closure but there is no real part of its closure that is separate from the inside. So we have not even the weak supplement principle. We should therefore think that there are two types of individuals: a) "weak" (open) that do not touch anything and b) "strong" that are in contact with something. Nevertheless, we must not believe that there are any individuals who reconcile the difference again. We can distinguish individuals who differ only in one point but cannot determine the point. SimonsVs: this is not satisfactory. Nevertheless, if we want to perform topology without points and other limits, it is difficult to see how we can solve the problem. Solution/Simons: a philosophical approach must be more complex and allow vague approximations of sharp boundaries (> Menger, 1940, 107). |
Simons I P. Simons Parts. A Study in Ontology Oxford New York 1987 |
| Wittgenstein | Millikan Vs Wittgenstein | I 221 not/"not"/Tractatus/Wittgenstein/Millikan: thesis: "not" is an operator which operates on the rest of the sentence by changing the meaning of the entire sentence. (s)VsWittgenstein/(s)VsMIllikan: Problem: a) "no" does not belong to the sentence, then it can be applied on the whole sentence "The sun is shining". Wittgenstein: "no" changes the meaning of the sentence, to which it belongs. b) it is part of the sentence, then it would have to be applied twice, the second time on itself. It only changes the meaning, if it is not part of the sentence. Projection theory/image theory/Tractatus/Wittgenstein/Millikan: then the sentence stands for something that does not exist. Problem/Millikan: this leads to a reification of possibilities. negative sentence/negation/existence/Millikan: negative sentences can not have non-existent facts as real value. Justification: negative facts have no causal powers that could play a role in a normal explanation. negative sentence/Millikan: we could assume that negative sentences are not representations. Ex "not-p" is to say "the fact that p does not exist". Wittgenstein has understood it roughly in that way. Pointe: above we said that existence theorems are not representations. projection theory/image theory/Tractatus/Wittgenstein/Millikan: but he does not think that sentences of the form "x does not exist" represent a non-existent fact. Then the variable "X" in "x does not exist" is not about names of individual things (objects, elementary objects) but about representations of possible states (possible facts). Sense/non-existence/negation/Wittgenstein/Millikan: so it was possible for him to maintain that sentences of the form "x does not exist" have a meaning. ((s) > Meinong). Millikan: in our terminology that is, they are representations (MillikanVs). I 222 And at the same time he could argue that the most basic elements of all propositions correspond to real objects. Pointe: this made it possible that he could say "x does not exist" is always equivalent to a sentence of the form "not-p". Millikan: couldn't we keep up at least one half of this equivalence? From "non-p" to "that p does not exist"? MillikanVsWittgenstein: no, not even that we can. When Wittgenstein was right and "not-p" says "that p does not exist", then that would mean for my position that negative sentences dont project world states and aren't representations. Millikan: instead they would project linguistic facts, "not-p" would be an icon, but it does not represent, even though a world state would have the sentence type "p" as a variant. Proto reference/Millikan. "P" would not be an underrepresented reference of "not-p" but a proto reference .Question: would "not-p" be an icon of "p is false"? Vs: then "not" would no longer be an operator! Not/negation/operator/Wittgenstein/Millikan: that is, the projection rule for "not-p" is a function of the projection rule for "p". 1. If "no" would not be an operator, it could happen that someone does not understand the meaning of "p", but still the meaning of "not-p". Absurd. 2. if "not-p" says "that p does not exist", "not-p" would also have to be true if any version of "p" is not completely determined, has no custom meaning. Ex "Pegasus was not a winged horse" Ex "The present king of France is not bald" were true statements! 3. sure, ""p" is wrong" at least reflects (icons) that "p" has no real value. Accordingly: "x does not exist" then reflects the fact that "x" has no reference. Pointe: if "not-p" says "that p" does not exist, it still projects a negative fact. negative fact/Millikan: we should be able to show that a negative fact is still something else than the non-existence of a positive fact. But we can not. We have just moved in circles. non-existent fact/Millikan: can not be a matter of an icon and not the object of a representation. negative fact/Millikan: would have to be something other than a non-existent fact. Pointe: but if we can show that, we don't need to assume any longer that "not-p" says "that p does not exist". negative sentence/projection/fact/negation/Millikan: what I have to claim is that negative sentences depict real or existing world states (facts). It is well known how such a thing is done: Negation/solution: one simply says that the negation is applied only to the logical predicate of the sentence ((S) internal negation). Here, the meaning of the predicate is changed so that the predicate applies to the opposite (depicts) as of what it normally does. I 223 This can then be extended to more complex sentences with external negation: Ex "No A is " becomes "Every A is non-". MilllikanVs: the difficulties with this approach are also well known: 1. Problem: how can the function of "not" be interpreted in very simple sentences of the form "X is not" Ex "Pegasus is not (pause)". Here, "not" can be interpreted as operating through predicates! Sentences of the form "X is not" are of course equivalent to sentences of the form "x does not exist." Problem: we have said that "existing" is no representation. So "not" can not be interpreted as always operating on a predicate of a representative sentence. Ex "Cicero is not Brutus" can not operate on a logical predicate of the sentence, because simple identity sentences have no logical predicate. So "not" must have still other functions. Problem: how do these different functions relate to each other? Because we should assume that "not" does not have different meanings in different contexts. meaningless/meaningless sentences/negation/projection/Millikan: here there is the same problem: Ex "Gold is not square". The sentence does not become true just because gold would have another form than to be a square. Problem: the corresponding affirmative sentences have no sense! Yet Ex "Gold is not square" seems to say something real. Problem: in turn: if "not" has a different function here than in representing sentences, we still need to explain this function. 2. Problem: (Important): the projective rules between simple sentences of the form "X is not " and its real value. real value/negation/Millikan: is the real value of a negative sentence the world state? Ex The fact of John's not-being-tall? Or a precise fact as Johns being-exactly-180cm? I 224 Millikan: the latter is correct. Representation/negation/Millikan: thesis: negative representations have an undefined sense. ((S) But Millikan admits that negations are representations, unlike identity sentences and existence sentences). Millikan: as in vague denotations, real values are determined if they occur in true sentences, but they must not be identified by the hearer to meet their intrinsic function. Opposite/negative sentence/representation/Millikan: thesis: negative sentences whose opposites are normal representative sentences must project positive facts themselves. I 229 "not"/negation/negative sentence/representation/SaD/Millikan: thesis: the law of the excluded third is inapplicable for simple representative negative sentences. Ex additionsally to the possibility that a predicate and its opposite are true, there is the possibility that the subject of the sentence does not exist. And that's just the way that the sentence has no particular Fregean sense. "P or not-p": only makes sense if "p" has a sense. Negation: their function is never (in the context of representative sentences) to show that the sentence would not make sense. sense/Millikan: one can not know a priori if a sentence makes sense. Negation/representation/Wittgenstein/MillikanVsWittgenstein: his mistake (in the Tractatus) was to believe that if everyone sees that "x" in "x does not exist" has a meaning that the negative sentence is then a negative representation. Rationalism/Millikan: the rationalist belief that one could know a priori the difference between sense and non-sense. I 303 Sensation Language/sensation/private language/Wittgenstein/MillikanVsWittgenstein/Millikan: the problem is not quite what Wittgenstein meant. It is not impossible to develop a private language, but one can not develop languages that speak only of what can be seen only once and from a single point of view. |
Millikan I R. G. Millikan Language, Thought, and Other Biological Categories: New Foundations for Realism Cambridge 1987 Millikan II Ruth Millikan "Varieties of Purposive Behavior", in: Anthropomorphism, Anecdotes, and Animals, R. W. Mitchell, N. S. Thomspon and H. L. Miles (Eds.) Albany 1997, pp. 189-1967 In Der Geist der Tiere, D Perler/M. Wild Frankfurt/M. 2005 |
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The author or concept searched is found in the following 6 theses of the more related field of specialization.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Carnap-Sentence | Carnap, R. | Schurz I 214 Carnap - sentence / CS / Carnap / Schurz: C (T): R (T)> T - ((s) if the Ramsey sentence is true, the theory follows from it.) - Hence, the thesis that the meaning the theoretical terms is determined by the theory itself, is brought to their logical concept - RS / CS: the conjunction of the two is L-equivalent to the theory itself - the CS-L does not imply a non-tautological empirical claim - therefore it is analytical - CS: only provides a characterization of meaning for all th.t. together - not individual - but the division analytic / synthetic is still not working for individual axioms or theorems - I 216 Carnap-sentence says that the meaning of the theoretical terms is to denote the entities that meet the claims of the theory. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Truth-Cond. Sem. | Cresswell, M.J. | I 16 Truth Conditional Semantics/Cresswell: there is also a version without explicit reference to possible worlds. I 17 This says that the knowledge of the truth value of (3) is indeed not sufficient, but also not necessary for the knowledge of meaning. But not because there is more to know about it than possible worlds, but because we should know the truth values of other propositions, e.g. (4) (3) is true iff a cat... on 25 Nov... That's Davidson's approach (1969). Also John Wallace (1972a). They try an axiomatic meaning theory where propositions like (4) come out as theorems. Cresswell: For (4) to tell us something, we must understand its meaning. Davidson: ditto, but without having to say too much about how we achieve the meaning of (4). II 145 Meaning/Truth Conditions/Knowledge/Truth Conditional Semantics/tr.cond./Cresswell: Truth Conditional Semantics: Thesis: the knowledge of truth conditions is the knowledge of the meaning of the proposition or to know what a proposition means, means to know what the case should be if it is true. Propositional Attitudes/Cresswell: they show that we often do not know the truth conditions at all ((s) and still know the meaning). For example, it may be because we do not know that "7 + 5 = 11" has the same truth conditions as "56 is a prime". Solution/Partee: (1982, 97): it is more about determining the consequences of what we know. We should make a distinction between "what the speaker knows" and "what characteristics of the language are determined by what the speaker knows". |
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| Theory of Sense | McDowell, J. | II 42 McDowell: Thesis: wants a theory of sense (ST), (Theory of sense) which is at the same time a meaning theory. A theory of sense ascribes a suitable property first to the components and establishes rules according to which the whole proposition is then true or false. Then it shows how for an indicative proposition a theorem of the form "s is true if and only if p" whereby "s" is replaced by an appropriate description of the sentence and "p" by a sentence. EMD II 43 It would be nice to have a general condition for the relation between the substitutions for "s" and "p" of this form: "s is f if and only if p". The hope is then that one replaces "f" with "true" by the general rule. That would seem to be the desired answer to what a truth theory is. II 44 McDowell: Thesis: a theory of sense (ST) and a theory of force in combination makes it possible to determine from a complete description of the utterance to come to it: "He claims that p" or "he asks that p" etc. whereby what replaces "p" is the sentence used on the right side of the theorem. I.e. we have a two-sided theory from the theory of sense and the theory of force. Acceptability in this theory would require that the descriptions of propositional actions fit into a wider context. II 46 Thesis, then, is not the illumination of the concept of meaning by other concepts and even less reduction, but simply a description of its relation to these other concepts. II 47 Sense/Truth/McDowell: Thesis: Sense is not what a truth theory is about, but rather truth is what a sense theory is about. The gap could also be filled quite differently, the above considerations ensure that the theorems would continue to be acceptable if this other filling were again replaced by "true, if and only if". Thus, as Frege thought, a sense theory will specify the truth conditions for sentences, either directly or by justifiable transformation. |
EMD II G. Evans/J. McDowell Truth and Meaning Oxford 1977 Evans III G. Evans The Varieties of Reference (Clarendon Paperbacks) Oxford 1989 |
| Ramsey-Sentence | Ramsey, F. | Schurz I 214 Carnap - sentence / CS / Carnap / Schurz: C (T): R (T)> T - ((s) if the Ramsey sentence is true, the theory follows from it - hence, the thesis, as the meaning of the theoretical terms is determined by the theory itself, brought to its logical concept - Ramsey-Sentence / CS: the conjunction of the two is L-equivalent to the theory itself - the CS-L does not imply a non-tautological empirical claim - therefore it is analytical - CS: provides only one meaning-characterization for all th.t. together - not individual - the division analytic / synthetic still does not work for individual axioms or theorems - I 216 Carnap-sentence says that the meaning of the th. t. is to describe the entities, which satisfy the claims of the theory. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Compositionality | Soames, Sc. | Schiffer I 217 Compositional Semantics/understanding/explanation/Scott Soames/Schiffer: (Soames 1987) Thesis: compositional semantics is not used to explain speech understanding, yet natural languages have a compositional semantics: Language Mastery/Soames: one should not look at semantics to explain semantic competence. Instead, compositional semantics is needed to explain the representational character of the language. The central semantic fact about language is that it is used to represent the world. Sentences systematically encode information that characterizes the world so and so. We need compositional semantics for the analysis of the principles of this coding. SchifferVsSoames: instead I introduced the expression potential. One could assume that a finitely formable theory should be able to formulate theorems for the attribution of AP to each sentence of the language. But wouldn't that be a compositional theory? |
Schi I St. Schiffer Remnants of Meaning Cambridge 1987 |
| Existence Predicate | Woods, M. | EMD II 250 Theorem of Existence/Atomic Sentence/Existence/Universal Quantification/Woods: for individual theorems of existence, the consequence of treating E as "true of all" is less obvious: Some things depend on how we treat names and singular terms. Woods: Thesis: but there is hardly any reason why the predicate of existence E should not be treated as PeS (predicate of the first level), just like "self-identical". But this does not have to be taken as a primitive predicate! If the range of quantifiers is defined so that it only runs over existing objects, then the predicate can be defined with the help of quantification and identity. |
EMD II G. Evans/J. McDowell Truth and Meaning Oxford 1977 Evans III G. Evans The Varieties of Reference (Clarendon Paperbacks) Oxford 1989 |
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