Find counter arguments by entering NameVs… or …VsName.
| Disputed term/author/ism | Author Vs Author |
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| Best Explanation | Fraassen Vs Best Explanation | Field I 15 Principle of the Best Explanation/Field: Suppose we have a) certain beliefs about the "phenomena" that we do not want to give up b) this class of phenomena is large and complex c) we have a pretty good (simple) explanation that is not ad hoc and from which the consequences of the phenomena follow d) one of the assumptions in the explanation is assertion S and we are sure that no explanation is possible without S. Best Explanation: then we have a strong reason to believe S. False: "The phenomena are as they would be if explanation E was correct": As If/Field: As-if assertions that are piggyback passengers on true explanations may not be constructed as explanations themselves (at least not ad hoc). Then the principle is not empty: it excludes the possibility that we accept a large and complex set of phenomena as a brute fact. (van FraassenVsBest Explanation: 1980) Best Explanation/BE/Field: the best explanation often leads us to believe something that we could also test independently by observation, but also to beliefs about unobservable things, or unobservable beliefs about observable things. Observation: should not make a difference here! In any case, our beliefs go beyond what is observed. I 16 Important argument: if no test was done, it should make no difference in the status of the evidence between cases where an observation is possible and those where no observation is possible! A stronger principle of the best explanation could be limited to observable instances of belief. FieldVs: but that would cripple our beliefs about observable things and would be entirely ad hoc. Unobserved things: a principle could be formulated that allowed the inference on observed things - that have been unobserved so far! - while we do not believe the explanation as such. FieldVs: that would be even more ad hoc! I 25 VsBenacerraf: bases himself on an outdated causal theory of knowledge. I 90 Theory/Properties/Fraassen: theories have three types of properties: 1) purely internal, logical: axiomatization, consistency, various kinds of completeness. Problem: It was not possible to accommodate simplicity here. Some authors have suggested that simple theories are more likely to be true. FraassenVsSimplicity: it is absurd to suppose that the world is more likely to be simple than that it was complicated. But that is metaphysics. 2) Semantic Properties: and relations: concern the relation of theory to the world. Or to the facts in the world about which the theory is. Main Properties: truth and empirical adequacy. 3) pragmatic: are there any that are philosophically relevant? Of course, the language of science is context-dependent, but is that pragmatic? I 91 Context-Dependent/Context-Independent/Theory/Science/Fraassen: theories can also be formulated in a context-independent language, what Quine calls Def "External Sentence"/Quine. Therefore it seems as though we do not need pragmatics to interpret science. Vs: this may be applicable to theories, but not to other parts of scientific activity: Context-Dependent/Fraassen: are a) Evaluations of theories, in particular, the term "explained" (explanation) is radically context-dependent. b) the language of the utilization (use) of theories to explain phenomena is radically context-dependent. Difference: a) asserting that Newton’s theory explains the tides ((s) mention). b) explaining the tides with Newton’s theory (use). Here we do not use the word "explains". Pragmatic: is also the immersion in a theoretical world view, in science. Basic components: speaker, listener, syntactic unit (sentence or set of sentences), circumstances. Important argument: In this case, there may be a tacit understanding to let yourself be guided when making inferences by something that goes beyond mere logic. I 92 Stalnaker/Terminology: he calls this tacit understanding a "pragmatic presupposition". (FraassenVsExplanation as a Superior Goal). I 197 Reality/Correspondence/Current/Real/Modal/Fraassen: Do comply the substructures of phase spaces or result sequences in probability spaces with something that happens in a real, but not actual, situation? ((s) distinction reality/actuality?) Fraassen: it may be unfair to formulate it like that. Some philosophical positions still affirm it. Modality/Metaphysics/Fraassen: pro modality (modal Interpretation of frequency), but that does not set me down on a metaphysical position. FraassenVsMetaphysics. I 23 Explanatory Power/Criterion/Theory/Fraassen: how good a choice is explanatory power as a criterion for selecting a theory? In any case, it is a criterion at all. Fraassen: Thesis: the unlimited demand for explanation leads to the inevitable demand for hidden variables. (VsReichenbach/VsSmart/VsSalmon/VsSellars). Science/Explanation/Sellars/Smart/Salmon/Reichenbach: Thesis: it is incomplete as long as any regularity remains unexplained (FraassenVs). |
Fr I B. van Fraassen The Scientific Image Oxford 1980 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 |
| Copenhague Interpr. | Fraassen Vs Copenhague Interpr. | I 175 Copenhagen Interpretation/CI/Double Slit/Quantum Mechanics/QM/Fraassen: revolutionary: the number that results from the formula Pmw(E) is the conditional probability of a result that is within E, given that the observable m was measured in a system in state w - VsBorn: no trajectory through the upper slit: instead. I a I ² is the probability (prob.) that if a measurement is made, we obtain a light spot - to say that a system is in a certain state only indicates a relation of conditional probabilities of measurements - FraassenVsCopenhagen Interpretation: it is not certain whether the concepts of probability and conditional probability are applicable - I 177 but the Copenhagen Interpretation allows viewing probability as a measure of objective variables: the frequency of results - problem: when no measurements are made. |
Fr I B. van Fraassen The Scientific Image Oxford 1980 |
| Cresswell, M.J. | Stechow Vs Cresswell, M.J. | I 154 Lambda-Operator/λ-Operator/Stechow: the language used here corresponds pretty much to the λ categorial of Cresswell 1973. Only difference: Cresswell: does not differentiate between syntactic categories and types. The type symbols act at the same time as category symbols. StechowVsCresswell: this is impractical, because different categories can have the same type. For example intransitive verbs as well as nomina are of type ep. Here: we choose a language with meaning*types, so e, p etc. Lambda-Operator/Semantics/Linguistics/Stechow: interprets the motion index. Thus the logical properties of the operator are transferred to the Interpretation of the movement. Movement: (on LF) creates a lambda operator that binds its track and thus all the same variables (pronouns) that it commands c. 1. Interpretation: of a closed expression does not depend on the choice of a certain occupancy. This is a consequence of the so-called Def Coincidence Lemma: this means that two expressions, which differ only by free variables, can be interpreted in the same way by suitable assignments. 2. The syntax of the λ language contains the principle of the Def λ conversion, which is our function conversion. The principle says that you can break down a λ operator if you use an expression of the variable type for the variables bound by the operator. This follows from the >transition lemma. (>binding). 3. Bound Renaming/Stechow: if two expressions differ only in the choice of their bound variables, they mean the same thing. ^These are the alphabetical variants. |
A. von Stechow I Arnim von Stechow Schritte zur Satzsemantik www.sfs.uniï·"tuebingen.de/~astechow/Aufsaetze/Schritte.pdf (26.06.2006) |
| Extensionalism | Verschiedene Vs Extensionalism | Lewis IV 256 Lewis: I really do not know what the Intensionalist (I) Vs Extensionalism (E) should say! I know several unsatisfactory arguments. ("I" in the English text also for "I, Lewis") (in vain) Vs Extensionalism: 1. one could say that the extensionalism is more complicated. It needs two more categories and one more lexicon object. VsVs: this is bad for two reasons: a) Extensionality itself is generally regarded as an important dimension of simplicity. b) I agree with E that a complete approach must also take into account the speaker's pause at the beginning of the sentence. E has already done this with its syntax and semantics! The intensionalist still has to find a place for it. (in vain) Vs Extensionalism: 2. One could object that it goes against our paradigm that extensions must be shared: Example "Boston" simply names Boston and not instead a function of indices. Problem: this paradigm applies to English, Polish, German, etc. but not necessarily to unexplored indigenous languages. Even if the intensionalist suspected that the language is very related to ours, one cannot expect E to agree that the paradigms are applicable! For E and I do not agree which language is theirs! Tarski's convention W: does not help here: because the native language does not correspond by the way not uncontroversially to our metalanguage of their language. Therefore the only versions of these principles that are applicable are stated in translations of these terms. Example E and I may agree that a meta-linguistic sentence of the form "_____ designates ___ in their language" or IV 256/257 "_____ is a name that has ____ as an extension in your language." should be true whenever the first blank space is filled with a name (in our language) with a name of the native language and the second with a translation of into our language. But that does not lead us anywhere, because we do not agree at all about names and what their correct translations are! (in vain) Vs Extensionalism: 3. I could try to argue that native language cannot be extensional because in it some inference patterns are invalid that are valid in any extensional language. For example, identity: inferences with Leibniz's identity (Leibniz' Law) or existential generalization lead from true premises to false conclusions in native language. Extensionalist/VsLewis: should agree that Leibniz's law receives truth in every extensional language and that it is not preserved in my counter-examples (which?). But he should not agree that such inferences are cases of Leibniz identity! Identity/Leibniz/Lewis: an inference with Leibniz' law needs an identity premise and how to identify it? Not by looking at three or four horizontal lines! Semantic: an expression with two gaps expresses identity, if and only if 1. the result of inserting names into the gaps is a sentence, 2. the sentence thus formed is true if the names are coextensive, otherwise false. Def Identity Premise: is a sentence thus formed. Problem: since E and I disagree on what the coextensive names are, they disagree on what the expressions are that express identity, which propositions are the identity premises, and which inferences are real instances of Leibniz's law. We are ignoring the difference of opinion here about whether a phrase S must be introduced by a pause to be a sentence at all. To be precise, if ",/so " is a non truth-preserving inference in Li, then " ,/so " is a non truth-preserving inference in Le. The original version without is no inference at all in Le, because its "premises" and "conclusions" are S names and not sentences. ((s) Extensional Language/(s): how is it possible at all, if no predicates (properties) are allowed - then is not the form subject predicate at all?) Vs: the form is then: a is an element of the set B. (in vain) VsExtensionalism: 4. I could argue ad hominem that E has not really escaped intentionality because the things he takes as extensions are intensional entities. Functions of indices to truth values are usually identified with propositions (especially if the indices consist of possible worlds and little more). And these functions are identified equally with individual terms. How can such intensional entities then be extensions? LewisVsVs: this is just a mix-up! Intension is relational! ((s) It depends on the consideration whether something is an intension or an extension). Intensions are things ((s) entities) that play a certain role in semantics and not things of a certain sort. E and I agree that in a suitable language the same thing that is the intention of one expression is also the extension of another. For example, when we speak technical English in a fragment that is suitable as the meta-meta-language of a smaller fragment, we agree that one and the same thing is both, the intention of expression in the object language "my hat" IV 258 and the extension of the metaphorical expression "intension of "my hat"". ((s) The same thing, not the same expression). Lewis: the thing itself is neither extension nor intension. It is true that some entities can only serve as extensions, while other functions of indices can serve as both. But there is no thing that would be unsuitable to be an extension. Ontology/(in vain) Vs Extensionalism: 5. one might think that the extensionalist attributes an extravagant ontology to the natives: For example, if the intensionalist says that a word of the natives designates a concrete material mountain, then E says he designates something more esoteric: a set-theoretical object, formed from a realm of individuals that includes unrealized possibilities. But also E and I believe in esoteric things if they do not want to contradict themselves. We have no doubt that we can name them. We agree that the natives have names for even more far-fetched things like gods (according to the Intensionalist) or functions of indices to such gods (according to the Extensionalist). Ontology/Vs Extensionalism: I should perhaps argue better that certain unesoteric things are missing! Ontology/Kripke: (conversational, 1972): it is wrong to attribute to someone an ontology that contains sets without elements or functions without arguments and values, etc. LewisVsVs: this is a plausible principle. But did E violate it by saying that the names of the natives are functions of indices and not names of concrete things? I do not think so. The ascribed ontology is not the same as the ascribed set of name carriers. For example, if our language is attributed an ontology, it contains all natural numbers, not just the small minority of them that actually bear names! It is not significant that the amount of name carriers violates Kripke's closure principle unless it can be shown that this is the totality of the attributed ontology. But it is difficult to say what ontology, if any, is attributed by the use of Le. One should look at the range of quantifiers, but Le has no quantifiers at all! Quantifiers: make sentences. But in Le only the predicate does that and that is not a quantifier. The transformation Lp of Parsons is different: it has a range. The set D, so that we get intended truth conditions for the propositions of Lp that transform the propositions of Li, then and only when D is included in the range of bound variables. (This assumes that the predicates of Lp have intended Interpretations). The set D is the same as the set of extensions of expressions in Le. It violates Kripke's closing principle ((s) that no empty sets should be attributed, see above), so it cannot be attributed to anyone as ontology. ((s) because there are no bound variables in Le.). I.e. if an extensionalist claims that the native speaks Lp, veiled by transformations, we have a remedy against him. But E himself does not represent that! Perhaps one can show that if it is bad to attribute the use of Lp, IV 259 that it is also bad to attribute the use of Le? But I do not see that yet. |
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, H. | Putnam Vs Field, H. | Field IV 405 Internal realism/metaphysical/Putnam/Field: (ad Putnam: Reason, Truth, and History): FieldVsPutnam: the contrast between internal realism and metaphysical realism is not defined clearly enough. >Internal realism, >metaphysical realism. Metaphysical realism/Field: comprises three theses, which are not separated by Putnam. 1. metaphysical realism 1: thesis, the world is made up of a unity of mentally independent objects. 2. metaphysical realism 2: thesis, there is exactly one true and complete description (theory) of the world. Metaphysical realism 2/Field: is not a consequence of the metaphysical realism 1 ((s) is independent) and is not a theory that any metaphysical realist would represent at all. Description/world/FieldVsPutnam: how can there only be a single description of the world ((s) or of anything)? The terms that we use are never inevitable; Beings that are very different from us, could need predicates with other extensions, and these could be totally indefinable in our language. Field IV 406 Why should such a strange description be "the same description"? Perhaps there is a very abstract characterization that allows this, but we do not have this yet. wrong solution: one cannot say, there is a single description that uses our own terms. Our current terms might not be sufficient for a description of the "complete" physics (or "complete" psychology, etc.). One could at most represent that there is, at best, a true and complete description that uses our terms. However, this must be treated with caution because of the vagueness of our present terms. Theory/world/FieldVsPutnam: the metaphysical realism should not only be distinguished from his opponent, the internal realism, by the adoption of one true theory. 3. Metaphysical realism 3/Field: Thesis, truth involves a kind of correspondence theory between words and external things. VsMetaphysical Realism 3/VsCorrespondence Theory/Field: the correspondence theory is rejected by many people, even from representatives of the metaphysical realism 1 (mentally independent objects). Field IV 429 Metaphysical realism/mR/FieldVsPutnam: a metaphysical realist is someone who accepts all of the three theses: Metaphysical realism 1: the world consists of a fixed totality of mentally independent objects. Metaphysical realism 2: there is only one true and complete description of the world. Metaphysical realism 3: truth involves a form of correspondence theory. PutnamVsField: these three have no clear content, when they are separated. What does "object" or "fixed totality", "all objects", "mentally independent" mean outside certain philosophical discourses? However, I can understand metaphysical realism 2 when I accept metaphysical realism 3. I: is a definite set of individuals. Williams II 430 P: set of all properties and relations Ideal Language: Suppose we have an ideal language with a name for each element of I and a predicate for each element of P. This language will not be countable (unless we take properties as extensions) and then only countable if the number of individuals is finite. But it is unique up to isomorphism; (but not further, unique up to isomorphism). Theory of World/Putnam: the amount of true propositions in relation to each particular type (up to any definite type) will also be unique. Whole/totality/Putnam: conversely, if we assume that there is an ideal theory of the world, then the concept of a "fixed totality" is (of individuals and their properties and relations) of course explained by the totality of the individuals which are identified with the range of individual variables, and the totality of the properties and relations with the region of the predicate variables within the theory. PutnamVsField: if he was right and there is no objective justification, how can there be objectivity of Interpretation then? Field/Putnam: could cover two positions: 1. He could say that there is a fact in regard to what good "rational reconstruction" of the speaker's intention is. And that treatment of "electron" as a rigid designator (of "what entity whatsoever", which is responsible for certain effects and obeys certain laws, but no objective fact of justification. Or. 2. He could say that Interpretation is subjective, but that this does not mean that the reference is subjective. Ad 1.: here he must claim that a real "rational reconstruction" of the speaker's intention of "general recognition" is separated, and also of "inductive competence", etc. Problem: why should then the decision that something ("approximately") obeys certain laws or disobeys, (what then applies to Bohr's electrons of 1900 and 1934, but not for phlogiston) be completely different by nature (and be isolable) from decisions on rationality in general? Ad 2.: this would mean that we have a term of reference, which is independent of procedures and practices with which we decide whether different people in different situations with different background beliefs actually refer on the same things. That seems incomprehensible. Reference/theory change/Putnam: We assume, of course, that people who have spoken 200 years ago about plants, referred, on the whole, to the same as we do. If everything would be subjective, there would be no inter-theoretical, interlinguistic term of reference and truth. If the reference is, however, objective, then I would ask why the terms of translation and Interpretation are in a better shape than the term of justification. --- Putnam III 208 Reference/PutnamVsField: there is nothing that would be in the nature of reference and that would make sure that the connection for two expressions would ever result in outcomes by "and". In short, we need a theory of "reference by description". --- Putnam V 70 Reference/FieldVsPutnam: recently different view: reference is a "physicalist relationship": complex causal relationships between words or mental representations and objects. It is a task of empirical science to find out which physicalistic relationship this is about. PutnamVsField: this is not without problems. Suppose that there is a possible physicalist definition of reference and we also assume: (1) x refers to y if and only if x stands in R to y. Where R is a relationship that is scientifically defined, without semantic terms (such as "refers to"). Then (1) is a sentence that is true even when accepting the theory that the reference is only determined by operational or theoretical preconditions. Sentence (1) would thus be a part of our "reflective equilibrium" theory (see above) in the world, or of our "ideal boundaries" theory of the world. V 71 Reference/Reference/PutnamVsOperationalism: is the reference, however, only determined by operational and theoretical preconditions, the reference of "x is available in R y" is, in turn, undetermined. Knowing that (1) is true, is not of any use. Each permissible model of our object language will correspond to one model in our meta-language, in which (1) applies, and the interpretation of "x is in R to y" will determine the interpretation of "x refers to y". However, this will only be in a relation in each admissible model and it will not contribute anything to reduce the number of allowable models. FieldVs: this is not, of course, what Field intends. He claims (a) that there is a certain unique relationship between words and things, and (b) that this is the relationship that must also be used when assigning a truth value to (1) as the reference relation. PutnamVsField: that cannot necessarily be expressed by simply pronouncing (1), and it is a mystery how we could learn to express what Field wans to say. Field: a certain definite relationship between words and objects is true. PutnamVsField: if it is so that (1) is true in this view by what is it then made true? What makes a particular correspondence R to be discarded? It appears, that the fact, that R is actually the reference, is a metaphysical inexplicable fact. (So magical theory of reference, as if referring to things is intrinsically adhered). (Not to be confused with Kripke's "metaphysically necessary" truth). ---- Putnam I (c) 93 PutnamVsField: truth and reference are not causally explanatory terms. Anyway, in a certain sense: even if Boyd's causal explanations of the success of science are wrong, we still need them to do formal logic. |
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 Field I H. Field Realism, Mathematics and Modality Oxford New York 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 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 |
| Harrah, D. | Prior Vs Harrah, D. | I 72 Questions/Logic/Prior: we distinguish: a) questions b) the act of questioning c) interrogative sentences d) the things that they are about. Interrogabilia/Middle Ages/Prior: the "questionable thing", "questionable nature", "subject of the question", etc.? Any objectivity? (see below). "Objective questions? Would probably have to be based on a theory of propositions. Questions/Prior: it is quite reasonable to say that there are questions that were never asked. Study 1) interrogabilia and then 2) enuntiabilia (remarks): Adam of Balsham/Middle Ages/Questions/Interrogabilia/Logic/Prior. Aristotle: (de Interpretatione): first affirmative and negative responses. Balsham: had proof that interrogabilia could be put in a one-to-one relationship with a part of themselves. Questions/Ontology/Prior: we need not be Platonists regarding interrogabilia and we can avoid considering what is asked as "part of the sentence"as if it were a name. Content/Command/Questions/Prior: as with the command, also with questions there are no special features or something "behind" the indicative sentences which constitutes a special content. Def Questions/Harrah, David: Thesis: a question is simply an indicative statement which consists in the disjunction or the set of possible answers. PriorVsHarrah: we need not go this far. (But pro: see below) Questions/Prior: We can rules for equivalents for statements of the form "He asked the question Q" and "He knows Q" for different types of Q (questions). E.g. "He knows whether 2 + 2 = 4" This is equivalent to "Either he knows that 2 + 2 = 4, or he knows that 2 + 2 unequal 4". E.g. "He knows what is 2 + 2 is." turns into: "For some x, he knows that 2 + 2 is x". (He knows only that they have a sum). Questions/variables/Prior: unasked questions: Problem: "For some p, no one has ever asked if p" is not the same as "There are questions that were never asked." Because there are other kinds of questions than those of the "whether variety". It would be arbitrary to single out this translation and not I 74 E.g. "For some , it has never been asked for which x it is the case that x t" or: "For some x, it has never been asked for which it is the case that x t" Would we have to ask then if "questions of type A were ever asked? In ordinary language that's nonsense. The alternative seems to be to introduce variables for questions for questioning sub-sentences: E.g. "whether 2 + 2 = 4" or "what is 2 + 2", etc., and then to say: "For some p, it was never asked, p". ((s) here no longer "if p" or "what is p"). Question variables/Prior: could then be put in front of any indicative sentence. E.g. "Is it the case that..." (variable), thus producing an understandable question. Command/Variable/Prior: in the case of commands only a not accurately defined subset seems to be accessible for this treatment. Mainly because of the cases that refer to the past or to logical truths. E.g. "Make (variable) that 2 + 2 = 4", e.g. "Make that yesterday the glass was on the table". Questions/Command/Variable/Prior: our language can also express that someone has asked a question or gave a command. It can be formalized like this: a) first convert the indicative sentence into a question or command, and then introduce an operator. b) couple an operator directly to the question or command. (Quote). In everyday language, it does not quite work like in formal logic. The sentence structure is changed. I 75 For commands we found b) good enough Questions: here we will need a). The "question sub-sentences" are of course not names of questions or interrogabilia. Questions/Prior: are not supposed to be a "relations" between a questioner and any interrogabilia. The argument is not a name but an interrogative sentence. Knowledge/Questions/Meaning/Prior: Problem: 1) It should seem that if "whether p" and "what t" are different components, if they follow "He asks __", just as they should be different if they follow "He knows __". Because they do not seem to have any other meaning, when they appear in this different context. Vs: but then "knows" would function for itself as a special ((s) operator?) that forms a sentence from a name and a question. Operator/Prior: (see above), we have seen above that we have to use parentheses: not "__ knows __", but "__ knows, that __". Knowledge/Questions/Prior: nevertheless "knows" seems to have no different meaning in a) "He knows that 2 + 2 = 4" and b) "He knows what 2 + 2 is". Knowing That/Knowing What/Prior: has the same meaning, but if it should be a different sentence-forming operator in each case (as we assume here for questions), then a different meaning would have to turn up! (PriorVs). I 76 Solution/Prior: in "He knows what t" and "He knows if p" is understood as something, but not explicitly: what is meant: "He knows the answer to the question..." In that, we assume a different form which consists of an indicative sentence and a sub-sentence of the question. Then there are two forms: a) "For some p, he knows that p" b) "...that p is the answer to the question q". A "logic of the question" will work out the following thesis, among others: "For some y, that y t is the answer to the question for which x applies that x t" or "Either, the answer to the question whether p is that p or it is that not p". From this we can then deduce the above forms. ("He knows what 2 + 2 is", etc.) Questions/variables/Prior: that still does not seem to be easy and economical enough with repsect to to the internal question sentences and variables. Surely there is a now better understood relation between the forms: "He asked whether p" and "It is the case that p": the latter is part of the former. This can also be done with commands. But the relation that we want is not syntactic, but a semantic one and that can best be brought out in a meta-language: "For all x, if x expresses p?" then he will ask, under normal circumstances, if p", etc. What initially prevented us from using this, was the fact that "There are questions that have never been asked" cannot be formally presented as "For some p, no one asked whether p". Because that only covers the specific question type "whether" and not e.g. "which are?" or "Who stole my pencil?" I 77 Perhaps "Is it the case that p?" is reducible to "For which ?" Where "d" is somehow distributed on the operators "It is the case that" and "it is not the case that". But that is a bit odd. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
| Hintikka, J. | Quine Vs Hintikka, J. | I 73 Possibilia/Hintikka: Thesis: talk about human experience makes the assumption of possibilia necessary. (Unrealized possibilities). HintikkaVsQuine. Intentionality/Husserl/Hintikka: according to Husserl the essence of human thought is in relation with unrealized possibilities. Possibilia/Hintikka: we need them to deal with logically incompatible entities of the same logical type. Possible World Semantics/Hintikka: is the corresponding model theory. I 137 QuineVsModal Logic: Problem of cross-world identification. Cross-World Identificatin/Cross-Identification/Quine/(s): Problem of identity conditions. If no identity conditions (IC) are given, the question is pointless whether an individual is "the same as" one in a different possible world. HintikkaVsQuine: my modified approach goes beyond the scope of Quine's criticism. Worldlines/Hintikka: are fixed by us, not by God. Nevertheless, they are not arbitrary. Their boundaries are given by the continuity of time and space, memory, location, etc. I 138 It may even be that our presuppositions prove to be incorrect. Therefore, there can be no set of world lines that comprise all possible worlds we need in alethic modal logic. Modal Logic/Quantification/Quine/Hintikka: a realistic Interpretation of quantified alethic ML is impossible. But for reasons more profound than Quine assumed. Cross-World Identification/HintikkaVsQuine: is not intrinsically impossible. Quine/Hintikka: has even accepted this lately, with limitations. Solution/Hintikka: Cross-world identification as re-identification. I 139 Propositional Attitude/Epistemic Logic/Hintikka: we will focus here on the problem of propositional attitudes. I 140 Quantification in Epistemic Contexts/Belief Contexts/Intensional/Hintikka: Ex (1) Albert knows who wrote Coningsby (2) (Ex) K Albert (x wrote Coningsby) Notation: (Ex) perspective (perceptual) identification (acquaintance) in the book: not reflected E). Uniqueness Condition/Hintikka: e.g. (2) can only then be inferred from (3) K Albert (Beaconsfield wrote Coningsby) i.e. (3) * Albert knows that Beaconsfield wrote Coningsby. ... Only then can be concluded when we have an additional premise: (4) (Ex) K Albert (Beaconsfield = x) i.e. (5) Albert knows who Beaconsfield is. Quine per Hintikka: this solution is better than a criterion for rigid designators (rigidity, QuineVsKripke). Everyday Language: it's of course simply very natural to speak in a way that you say you know who or what something is. HintikkaVsQuine: he praises me for the wrong reasons. He turns things upside down. Although he does not commit the mistake I criticize, he forgives it. I 141 Formal Language/Logic/Canonical Notation/HintikkaVsQuine: we should view logical language as our native language and not set so much store by the translation into everyday language. It is only about semantic clarity anyway. I 145 HintikkaVsQuine: does not understand the role my uniqueness conditions play: Quine: says you can also transfer these conditions to belief, knowledge, etc. Quine: Hintikka requires that the subject know who or what the person or thing is. Who or what the term designates. HintikkaVsQuine: he thinks I only use some type of uniqueness condition. Solution: the semantic situation shows the difference: the relation between the conditions for different propositional attitudes (beliefs, see, know) is one of analogy, not of identity. Solution: the sets of compatible possible worlds in the case of knowing, seeing, memory, belief are different ones every time. I 146 Identification/Belief/Quine/QuineVsHintikka: any belief world (possible worlds) will include countless bodies and objects that are not individually recognizable, simply because the believer believes his world contains countless such objects. Identity: questions about the identity of these objects are pointless. Problem: if you quantify in belief contexts, how can you exclude them? Solution: the scope of variables to those objects about which the subject has a sufficiently clear idea, would have to be limited. Problem: how do you determine how clear these ideas must be? HintikkaVsQuine: the solution is quite simple if we quantify about individuals in doxastic possible worlds: Ex Operator: "in a world w1, compatible with everything Jack believes": Solution/Hintikka: we can quantify about the inhabitants of such worlds, by simply using a quantifier inside the operator. ((s) i.e. Jack, but not we, distinguish). Problem: it could be that we might want to consider the people as our neighbors from the real world w0. ("qua neighbors"). Hintikka: but that is a problem in itself and has nothing to do with uniqueness conditions. Problem: is more due to the notation of conventional modal logic which does not allow that us to turn around the evaluation process which runs from outside to inside so that it extends from the inside out. Solution/Saarinen: "retrospective" operators (see above) Solution/Hintikka: it may still be that we can track an individual back from w1 to w0, even if it does not meet the uniqueness conditions like (16) - (127). (They require an individual to be identifiable in all the possible worlds). HintikkaVsQuine: he is wrong in that the question of identity is pointless if not all the uniqueness conditions are met. On the contrary, it has to make sense for us to ever able to determine that the conditions are not met! Uniqueness Condition/Hintikka: if it is not met, it only means that we cannot find an individual ((s) or its counterpart) in any possible world. Uniqueness Condition/QuineVsHintikka: Quine's most serious objection is that these conditions are always indicated (indexical) i.e. that they are context-dependent. I.e. only in a particular situation it is about whether an individual is the same. I 147 Knowing-Who/Knowing-What/Context/Quine: E.g. "Who is he?" only makes sense in a given situation. HintikkaVsQuine: of course he is right that the truth conditions vary with the situation, but that does not destroy the uniqueness conditions for epistemic logic. HintikkaVsQuine: he only misunderstands the role these conditions play. Truth Value/Hintikka: the truth value of sentences of the form (18) (Ex) K(b = x) and equally of (19) (Ex) K(b = x) become independent of the truth value of other types of simplest sentences! Question/Answer/T Question/Hintikka: we get a new class of atomic sentences! Solution: distinction between identification through acquaintance/description. I 148 World Lines/Identification/Cross-World Identity/Hintikka: Thesis the world lines have to be drawn before the conditions are ever applied. Drawing the world lines is never part of the application of the uniqueness conditions. ((s) otherwise circular). Truth Conditions/Atomic/Atomic Sentence/Hintikka: for my theory, the interplay of specific atomic and non-atomic sentences is essential: it shows how e.g. the truth value of sentences of the form "knows + -one-question-word" sentences depends on the truth value of sentences of the form (18) - (19). HintikkaVsQuine: his criticism is similar to one that would criticize traditional truth value tables, because some of the sentences that are used to put them together are also blurred. Epistemic Logic/Hintikka: is not affected by this criticism. All it claims is that once the world lines are drawn, the rest of the semantics remains as it was. I 160 Def Knowledge/Hintikka: what is true in all knowledge possible worlds (knowledge worlds) of a subject. And, conversely, what is true in all knowledge possible worlds of a person is their knowledge. Important argument: the world lines can be drawn differently, however, while the evaluations (the non-logical constants) remain the same. The variation of the world lines can then be "seen" in the variation of the semantic power of the phrase n of the form know + indirect question. I 161 Quine has used such variation to the reject the possible world semantics of sentences with "knowing-that". HintikkaVsQuine: for him it was actually about the structural (not the referential) system. And this remained untouched. |
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 |
| Modal Logic | Quine Vs Modal Logic | Chisholm II 185 QuineVsModal Logic: instead space time points as quadruples. Reason: permanent objects (continuants) seem to threaten the extensionality. SimonsVsQuine: the Achilles heel is that we must have doubts whether anyone could learn a language that refers not to permanent objects (continuants). --- Lewis IV 32 QuineVsModal Logic: which properties are necessary or accidental, is then dependent on the description. Definition essentialism/Aristotle: essential qualities are not dependent on description. QuineVs: that is as congenial as the whole modal logic. LewisVsQuine: that really is congenial. --- I 338 But modal logic has nothing to do with it. Here, totally impersonal. The modal logic, as we know it, begins with Clarence Lewis "A survey of Symbolic Logic" in 1918. His interpretation of the necessity that Carnap formulates even more sharply later is: Definition necessity/Carnap: A sentence that starts with "it is necessary that", is true if and only if the remaining sentence is analytic. Quine provisionally useful, despite our reservations about analyticity. --- I 339 (1) It is necessary that 9 > 4 it is then explained as follows: (2) "9 > 4" is analytically. It is questionable whether Lewis would ever have engaged in this matter, if not Russell and Whitehead (Frege following) had made the mistake, the philonic construction: "If p then q" as "~ (p and ~ q)" if they so designate this construction as a material implication instead of as a material conditional. C.I.Lewis: protested and said that such a defined material implication must not only be true, but must also be analytical, if you wanted to consider it rightly as an "implication". This led to his concept of "strict implication". Quine: It is best to view one "implies" and "is analytical" as general terms which are predicated by sentences by adding them predicatively to names (i.e. quotations) of sentences. Unlike "and", "not", "if so" which are not terms but operators. Whitehead and Russell, who took the distinction between use and mention lightly, wrote "p implies q" (in the material sense) as it was with "If p, then q" (in the material sense) interchangeable. --- I 339 Material implication "p implies q" not equal to "p > q" (>mention/>use) "implies" and "analytical" better most general terms than operators. Lewis did the same, he wrote "p strictly implies q" and explained it as "It is necessary that not (p and not q)". Hence it is that he developed a modal logic, in which "necessary" is sentence-related operator. If we explain (1) in the form of (2), then the question is why we need modal logic at all. --- I 340 An apparent advantage is the ability to quantify in modal positions. Because we know that we cannot quantify into quotes, and in (2) a quotation is used. This was also certainly Lewis' intention. But is it legitimate? --- I 341 It is safe that (1) is true at any plausible interpretation and the following is false: (3) It is necessary that the number of planets > 4 Since 9 = the number of planets, we can conclude that the position of "9" in (1) is not purely indicative and the necessity operator is therefore opaque. The recalcitrance of 9 is based on the fact that it can be specified in various ways, who lack the necessary equivalence. (E.g. as a number of planets, and the successor to the 8) so that at a specification various features follow necessarily (something "greater than 4 ") and not in the other. Postulate: Whenever any of two sentences determines the object x clearly, the two sentences in question are necessary equivalent. (4) If Fx and only x and Gx and exclusively x, it is necessary that (w)(Fw if and only if when Gw). --- I 342 (This makes any sentence p to a necessary sentence) However, this postulate nullifies modal distinctions: because we can derive the validity of "It is necessary that p" that it plays no role which true sentence we use for "p". Argument: "p" stands for any true sentence, y is any object, and x = y. Then what applies clearly is: (5) (p and x = y) and exclusively x as (6) x = y and x exclusively then we can conclude on the basis of (4) from (5) and (6): (7) It is necessary that (w) (p and w = y) if and only if w = y) However, the quantification in (7) implies in particular "(p and y = y) if and only if y = y" which in turn implies "p"; and so we conclude from (7) that it is necessary that p. --- I 343 The modal logic systems by Barcan and Fitch allow absolute quantification in modal contexts. How such a theory can be interpreted without the disastrous assumption (4), is far from clear. --- I 343 Modal Logic: Church/Frege: modal sentence = Proposition Church's system is structured differently: He restricts the quantification indirectly by reinterpreting variables and other symbols into modal positions. For him (as for Frege) a sentence designated then, to which a modal operator is superior, a proposition. The operator is a predicate that is applied to the proposition. If we treat the modalities like the propositional attitude before, then we could first (1) reinterpret (8) [9 > 4] is necessary (Brackets for class) and attach the opacity of intensional abstraction. One would therefore interpret propositions as that what is necessary and possible. --- I 344 Then we could pursue the model from § 35 and try to reproduce the modality selectively transparent, by passing selectively from propositions to properties: (9) x (x > 4) is necessary in terms 9. This is so far opposed to (8) as "9" here receives a purely designated position in one can quantify and in one can replace "9" by "the number of planets". This seemed to be worth in the case of en, as we e.g. wanted to be able to say (§ 31), there would be someone, of whom is believed, he was a spy (> II). But in the case of modal expressions something very amazing comes out. The manner of speaking of a difference of necessary and contingent properties of an object. E.g. One could say that mathematicians are necessarily rational and not necessarily two-legged, while cyclist are necessarily two-legged but not necessarily rational. But how can a bicycling mathematician be classified? Insofar as we are talking purely indicatively of the object, it is not even suggestively useful to speak of some of its properties as a contingent and of others as necessary. --- I 344 Properties/Quine: no necessary or contingent properties (VsModal Logic) only more or less important properties Of course, some of its properties are considered essential and others unimportant, some permanently and others temporary, but there are none which are necessary or contingent. Curiously, exactly this distinction has philosophical tradition. It lives on in the terms "nature" and "accident". One attributes this distinction to Aristotle. (Probably some scholars are going to protest, but that is the penalty for attributing something to Aristotle.) --- I 345 But however venerable this distinction may be, it certainly cannot be justified. And thus the construction (9) which carries out this distinction so elegantly, also fails. We cannot blame the analyticity the diverse infirmities of modality. There is no alternative yet for (1) and (2) that at least sets us a little on something like modal logic. We can define "P is necessary" as "P = ((x) (x = x))". Whether (8) thereby becomes true, or whether it is at all in accordance with the equation of (1) and (2), will depend on how closely we construct the propositions in terms of their identity. They cannot be constructed so tightly that they are appropriate to the propositional properties. But how particularly the definition may be, something will be the result that a modal logic without quantifiers is isomorphic. --- VI 41 Abstract objects/modal logic/Putnam/Parsons: modal operators can save abstract objects. QuineVsModal Logic: instead quantification (postulating of objects) thus we streamline the truth functions. Modal logic/Putnam/Parsons/Quine: Putnam and Charles Parsons have shown how abstract objects can be saved in the recourse to possibility operators. Quine: without modal operators: E.g. "Everything is such that unless it is a cat and eats spoiled fish, and it gets sick, will avoid fish in the future." ((s) logical form/(s): (x) ((Fx u Gx u Hx)> Vx). Thus, the postulation of objects can streamline our only loosely binding truth functions, without us having to resort to modal operators. --- VI 102 Necessity/opportunity/Quine: are insofar intensional, as they do not fit the substitutivity of identity. Again, vary between de re and de dicto. --- VI 103 Counterfactual conditionals, unreal conditionals/Quine: are true, if their consequent follows logically from the antecedent in conjunction with background assumptions. Necessity/Quine: by sentence constellations, which are accepted by groups. (Goes beyond the individual sentence). --- VI 104 QuineVsModal logic: its friends want to give the necessity an objective sense. --- XI 52 QuineVsModal Logic/Lauener: it is not clear here on what objects we are referring to. --- XI 53 Necessesity/Quine/Lauener: ("Three Grades of Modal Involvement"): 3 progressive usages: 1. as a predicate for names of sentences: E.g. "N "p"": "p is necessarily true". (N: = square, box). This is harmless, simply equate it with analyticity. 2. as an operator which extends to close sentence: E.g. "N p": "it is necessarily true that p" 3. as an operator, too, for open sentences: E.g. "N Fx": through existence generalization: "(Ex) N Fx". |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 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 Lewis I David K. Lewis Die Identität von Körper und Geist Frankfurt 1989 LewisCl I Clarence Irving Lewis Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991 |
| Principia Mathematica | Gödel Vs Principia Mathematica | Russell I XIV Circular Error Principle/VsPrincipia Mathematica(1)/PM/Russell/Gödel: thus seems to apply only to constructivist assumptions: when a term is understood as a symbol, together with a rule to translate sentences containing the symbol into sentences not containing it. Classes/concepts/Gödel: can also be understood as real objects, namely as "multiplicities of things" and concepts as properties or relations of things that exist independently of our definitions and constructions! This is just as legitimate as the assumption of physical bodies. They are also necessary for mathematics, as they are for physics. Concept/Terminology/Gödel: I will use "concept" from now on exclusively in this objective sense. A formal difference between these two conceptions of concepts would be: that of two different definitions of the form α(x) = φ(x) it can be assumed that they define two different concepts α in the constructivist sense. (Nominalistic: since two such definitions give different translations for propositions containing α.) For concepts (terms) this is by no means the case, because the same thing can be described in different ways. For example, "Two is the term under which all pairs fall and nothing else. There is certainly more than one term in the constructivist sense that satisfies this condition, but there could be a common "form" or "nature" of all pairs. All/Carnap: the proposal to understand "all" as a necessity would not help if "provability" were introduced in a constructivist manner (..+...). Def Intensionality Axiom/Russell/Gödel: different terms belong to different definitions. This axiom holds for terms in the circular error principle: constructivist sense. Concepts/Russell/Gödel: (unequal terms!) should exist objectively. (So not constructed). (Realistic point of view). When only talking about concepts, the question gets a completely different meaning: then there seems to be no objection to talking about all of them, nor to describing some of them with reference to all of them. Properties/GödelVsRussell: one could surely speak of the totality of all properties (or all of a certain type) without this leading to an "absurdity"! ((s) > Example "All properties of a great commander". Gödel: this simply makes it impossible to construe their meaning (i.e. as an assertion about sense perception or any other non-conceptual entities), which is not an objection to someone taking the realistic point of view. Part/whole/Mereology/GödelVsRussell: neither is it contradictory that a part should be identical (not just the same) with the whole, as can be seen in the case of structures in the abstract sense. Example: the structure of the series of integers contains itself as a special part. I XVI/XVII Even within the realm of constructivist logic there are certain approximations to this self-reflectivity (self-reflexivity/today: self-similarity) of impredicative qualities, namely e.g. propositions, which as parts of their meaning do not contain themselves, but their own formal provability. There are also sentences that refer to a totality of sentences to which they themselves belong: Example: "Each sentence of a (given) language contains at least one relational word". This makes it necessary to look for other solutions to the paradoxes, according to which the fallacy does not consist in the assumption of certain self-reflectivities of the basic terms, but in other assumptions about them! The solution may have been found for the time being in simple type theory. Of course, all this refers only to concepts. Classes: one should think that they are also not created by their definitions, but only described! Then the circular error principle does not apply again. Zermelo splits classes into "levels", so that only sets of lower levels can be elements of sets of higher levels. Reducibility Axiom/Russell/Gödel: (later dropped) is now taken by the class axiom (Zermelo's "axiom of choice"): that for each level, for any propositional function φ(x) the set of those x of this level exists for which φ(x) is true. This seems to be implied by the concept of classes as multiplicities. I XVIII Extensionality/Classes: Russell: two reasons against the extensional view of classes: 1. the existence of the zero class, which cannot be well a collection, 2. the single classes, which should be identical with their only elements. GödelVsRussell: this could only prove that the zero classes and the single classes (as distinguished from their only element) are fictions to simplify the calculation, and do not prove that all classes are fictions! Russell: tries to get by as far as possible without assuming the objective existence of classes. According to this, classes are only a facon de parler. Gödel: but also "idealistic" propositions that contain universals could lead to the same paradoxes. Russell: creates rules of translation according to which sentences containing class names or the term "class" are translated into sentences not containing them. Class Name/Russell: eliminate by translation rules. Classes/Principia Mathematica/Russell/Gödel: the Principia Mathematica can do without classes, but only if you assume the existence of a concept whenever you want to construct a class. First, some of them, the basic predicates and relations like "red", "colder" must be apparently considered real objects. The higher terms then appear as something constructed (i.e. something that does not belong to the "inventory of the world"). I XIX Ramsey: said that one can form propositions of infinite length and considers the difference finite/infinite as not so decisive. Gödel: Like physics, logic and mathematics are based on real content and cannot be "explained away". Existence/Ontology/Gödel: it does not behave as if the universe of things is divided into orders and one is forbidden to speak of all orders, but on the contrary: it is possible to speak of all existing things. But classes and concepts are not among them. But when they are introduced as a facon de parler, it turns out that the extension of symbolism opens the possibility of introducing them in a more comprehensive way, and so on, to infinity. To maintain this scheme, however, one must presuppose arithmetics (or something equivalent), which only proves that not even this limited logic can be built on nothing. I XX Constructivist posture/constructivism/Russell/Gödel: was abandoned in the first edition, since the reducibility axiom for higher types makes it necessary that basic predicates of arbitrarily high type exist. From constructivism remains only 1. Classes as facon de parler 2. The definition of ~, v, etc. as valid for propositions containing quantifiers, 3. The stepwise construction of functions of orders higher than 1 (of course superfluous because of the R-Axiom) 4. the Interpretation of definitions as mere typographical abbreviations (all incomplete symbols, not those that name an object described by the definition!). Reducibility Axiom/GödelVsRussell: this last point is an illusion, because of the reducibility axiom there are always real objects in the form of basic predicates or combinations of such according to each defined symbol. Constructivist posture/constructivism/Principia Mathematica/Gödel: is taken again in the second edition and the reducibility axiom is dropped. It is determined that all basic predicates belong to the lowest type. variables/Russell/Gödel: their purpose is to enable the assertions of more complicated truth functions of atomistic propositions. (i.e. that the higher types are only a facon de parler.). The basis of the theory should therefore consist of truth functions of atomistic propositions. This is not a problem if the number of individuals and basic predicates is finite. Ramsey: Problem of the inability to form infinite propositions is a "mere secondary matter". I XXI Finite/infinite/Gödel: with this circumvention of the problem by disregarding the difference between finite and infinite a simpler and at the same time more far-reaching interpretation of set theory exists: Then Russell's Apercu that propositions about classes can be interpreted as propositions about their elements becomes literally true, provided n is the number of (finite) individuals in the world and provided we neglect the zero class. (..) + I XXI Theory of integers: the second edition claims that it can be achieved. Problem: that in the definition "those cardinals belonging to each class that contains 0 and contains x + 1 if it contains x" the phrase "each class" must refer to a given order. I XXII Thus whole numbers of different orders are obtained, and complete induction can be applied to whole numbers of order n only for properties of n! (...) The question of the theory of integers based on ramified type theory is still unsolved. I XXIII Theory of Order/Gödel: is more fruitful if it is considered from a mathematical point of view, not a philosophical one, i.e. independent of the question of whether impredicative definitions are permissible. (...) impredicative totalities are assumed by a function of order α and ω . Set/Class/Principia Mathematica(1)/Russell/Type Theory/Gödel: the existence of a well-ordered set of the order type ω is sufficient for the theory of real numbers. Def Continuum Hypothesis/Gödel: (generalized): no cardinal number exists between the power of any arbitrary set and the power of the set of its subsets. Type Theory/VsType Theory/GödelVsRussell: mixed types (individuals together with predications about individuals etc.) obviously do not contradict the circular error principle at all! I XXIV Russell based his theory on quite different reasons, similar to those Frege had already adopted for the theory of simpler types for functions. Propositional functions/statement function/Russell/Gödel: always have something ambiguous because of the variables. (Frege: something unsaturated). Propositional function/p.f./Russell/Gödel: is so to speak a fragment of a proposition. It is only possible to combine them if they "fit together" i.e. are of a suitable type. GödelVsRussell: Concepts (terms) as real objects: then the theory of simple types is not plausible, because what one would expect (like "transitivity" or the number two) to be a concept would then seem to be something that stands behind all its different "realizations" on the different levels and therefore does not exist according to type theory. I XXV Paradoxes in the intensional form/Gödel: here type theory brings a new idea: namely to blame the paradoxes not on the axiom that every propositional function defines a concept or a class, but on the assumption that every concept results in a meaningful proposition if it is claimed for any object as an argument. The objection that any concept can be extended to all arguments by defining another one that gives a false proposition whenever the original one was meaningless can easily be invalidated by pointing out that the concept "meaningfully applicable" does not always have to be meaningfully applicable itself. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
Göd II Kurt Gödel Collected Works: Volume II: Publications 1938-1974 Oxford 1990 |
| Putnam, H. | Hacking Vs Putnam, H. | I40 Truth/Reason/Putnam: are very closely connected. HackingVsPutnam. I 148 Meaning/Science/HackingVsPutnam: we should talk about types of objects, not about types of meaning. Meaning is not a very good concept for philosophy of science. I 156 HackingVsPutnam: Reference is ultimately not decisive! (E.g. muon). For physicists, "Meson" was initially synonymous with "whatever corresponds to the presumption of Yukawa". That’s something like Fregean sense. When it became clear that this sense did not correspond to the object, the baptism was annulled and a new name was given. I 163 PutnamVsMetaphysical Realism: Vs idea of "fixed whole of mind-independent objects". HackingVsPutnam: nobody has never represented this!. I 164 HackingVsPutnam: links his different theses, as if they were logically connected. They are not!. HackingVsPutnam: he used to represent a scientific realism. He has not changed party, he has changed war. I 179 HackingVsPutnam: however, actually he has shown nothing but the failure of the reference by naming a number of true statements, which are brought into being in the first-order logic (>Löwenheim, >AustinVsMoore). I 181 Löwenheim-Skolem/Premises/Hacking: 1) the sentence is only about the first-order logic sentences. So far, no one has proved that the language of the physicists could be pressed in this context. Spoken languages contain indicators: "this" and "that". Montague thesis: colloquial language primarily uses second-order quantifiers. Wittgenstein’s arguments against showing, according to which it was not possible to fully specify meaning using rules, do not imply that there was something in our linguistic practice, which is essential undetermined. Löwenheim and Skolem spoke about large numbers and we can only talk about them. About cats or cherries we can do more than merely talk. Putnam asserts that it is possible to reinterpret words such as "designate" and "refer" in turn. HackingVsPutnam: I do not need theory of reference to refer. And it’s a - possibly with reference to Wittgenstein - at least defensible conception that there cannot be a general theory of reference. I 182 scientific articles on muons are full of photographs! - E.g. muons: it has been found that the mass of the muon is 206,786 times the mass of the electron. How have we found out this figure at the time?. I 183 From a whole bunch of complicated calculations with a bunch of variables and a number of relations between nature constants. These consist not only of sentences, but are linked to experimental findings. They also have been found by independent scientists and laboratories. I 184 The Löwenheim-Skolem theorem is not constructive. I.e. in principle there is no method for producing a non-intended interpretation available to man. - E.g. we also speak of "Persian" and "Heart Cherry". These species names do not act like ordinary adjectives of the type "sweet", because sweet heart cherries are sweet fruits and not "heart fruit". - Solution: This is not possible or would be noticed, because the number of subspecies is not the same: the number of cherry species is different from the number of cat species. So no correspondence relation will preserve the structure of the species names. Moreover, you would not bake a cake with cats! How should cherry facts come to light in the cat world?. I 185 Putnam perhaps commits the gravest error possible in philosophy: he takes a sentence as an example that was perhaps never uttered and would be pointless outside logic. The next step is then to assert that just as it is possible to reinterpret "cherries" it is possible to reinterpret "designating". Reference: its warranty does not depend primarily on the expression of true propositions, but on our interactions with the world. Even at the level of the language there is far more structure given than Putnam involves. I 220 HackingVsPutnam: transcendental Nominalist (anti-realist). It is not possible to step out of the system of thought and retain a base of reference that does not belong to one’s own system of reference. HackingVsPutnam: misguided dichotomy of thought and action (like Dewey). Hacking Thesis: man is a representing being. (A tribe without images is not a human tribe for me). |
Hacking I I. Hacking Representing and Intervening. Introductory Topics in the Philosophy of Natural Science, Cambridge/New York/Oakleigh 1983 German Edition: Einführung in die Philosophie der Naturwissenschaften Stuttgart 1996 |
| Russell, B. | Quine Vs Russell, B. | Chisholm II 75 Predicates/Denote/Russell: denoting expressions: proper names stand for individual things and general expressions for universals. (Probleme d. Phil. p. 82f). In every sentence, at least one word refers to a universal. QuineVsRussell: confusion! II 108 Theory of Descriptions/VsRussell/Brandl: thus the whole theory is suspected of neglecting the fact that material objects can never be part of propositions. QuineVsRussell: confusion of mention and use. Quine II 97 Pricipia mathematica, 1903: Here, Russell's ontology is rampant: every word refers to something. If a word is a proper name, then its object is a thing, otherwise it is a concept. He limits the term "existence" to things, but has a liberal conception of things which even includes times and points in empty space! Then there are, beyond the existent things, other entities: "numbers, the gods of Homer, relationships, fantasies, and four-dimensional space". The word "concept", used by Russell in this manner, has the connotation of "merely a concept". Caution: Gods and fantasies are as real as numbers for Russell! QuineVsRussell: this is an intolerably indiscriminate ontology. Example: Take impossible numbers, e.g. prime numbers that are divisible by 6. It must be wrong in a certain sense that they exist, and that is in a sense in which it is right that there are prime numbers! Do fantasies exist in this sense? II 101 Russell has a preference for the term "propositional function" against "class concept". In P.M. both expressions appear. Here: Def "Propositional Function": especially based on forms of notation, e.g. open sentences, while concepts are decidedly independent of notation. However, according to Meinong Russell's confidence is in concepts was diminished, and he prefers the more nominalistic sound of the expression "propositional function" which is now carries twice the load (later than Principia Mathematica.) Use/Mention/Quine: if we now tried to deal with the difference between use and mention as carelessly as Russell has managed to do sixty years ago, we can see how he might have felt that his theory of propositional functions was notation based, while a theory of types of real classes would be ontological. Quine: we who pay attention to use and mention can specify when Russell's so-called propositional functions as terms (more specific than properties and relations) must be construed as concepts, and when they may be construed as a mere open sentences or predicates: a) when he quantifies about them, he (unknowingly) reifies them as concepts. For this reason, nothing more be presumed for his elimination of classes than I have stated above: a derivation of the classes from properties or concepts by means of a context definition that is formulated such that it provides the missing extensionality. QuineVsRussell: thinks wrongly that his theory has eliminated classes more thoroughly from the world than in terms of a reduction to properties. II 102 RussellVsFrege: "~ the entire distinction between meaning and designating is wrong. The relationship between "C" and C remains completely mysterious, and where are we to find the designating complex which supposedly designates C?" QuineVsRussell: Russell's position sometimes seems to stem from a confusion of the expression with its meaning, sometimes from the confusion of the expression with its mention. II 103/104 In other papers Russel used meaning usually in the sense of "referencing" (would correspond to Frege): "Napoleon" particular individual, "human" whole class of such individual things that have proper names. Russell rarely seems to look for an existing entity under any heading that would be such that we could call it the meaning that goes beyond the existing referent. Russell tends to let this entity melt into the expression itself, a tendency he has in general when it comes to existing entities. QuineVsRussell: for my taste, Russell is too wasteful with existing entities. Precisely because he does not differentiate enough, he lets insignificance and missed reference commingle. Theory of Descriptions: He cannot get rid of the "King of France" without first inventing the description theory: being meaningful would mean: have a meaning and the meaning is the reference. I.e. "King of France" without meaning, and "The King of France is bald" only had a meaning, because it is the short form of a sentence that does not contain the expression "King of France". Quine: actually unnecessary, but enlightening. Russell tends commingle existing entities and expressions. Also on the occasion of his remarks on Propositions: (P.M.): propositions are always expressions, but then he speaks in a manner that does not match this attitude of the "unity of the propositions" (p.50) and of the impossibility of infinite propositions (p.145) II 105 Russell: The proposition is nothing more than a symbol, even later, instead: Apparently, propositions are nothing..." the assumption that there are a huge number of false propositions running around in the real, natural world is outrageous." Quine: this revocation is astounding. What is now being offered to us instead of existence is nothingness. Basically Russell has ceased to speak of existence. What had once been regarded as existing is now accommodated in one of three ways a) equated with the expression, b) utterly rejected c) elevated to the status of proper existence. II 107 Russell/later: "All there is in the world I call a fact." QuineVsRussell: Russell's preference for an ontology of facts depends on his confusion of meaning with reference. Otherwise he would probably have finished the facts off quickly. What the reader of "Philosophy of logical atomism" notices would have deterred Russell himself, namely how much the analysis of facts is based on the analysis of language. Russell does not recognize the facts as fundamental in any case. Atomic facts are as atomic as facts can be. Atomic Facts/Quine: but they are composite objects! Russell's atoms are not atomic facts, but sense data! II 183 ff Russell: Pure mathematics is the class of all sentences of the form "p implies q" where p and q are sentences with one or more variables, and in both sets the same. "We never know what is being discussed, nor if what we say is true." II 184 This misinterpretation of mathematics was a response to non-Euclidean geometry. Numbers: how about elementary arithmetic? Pure numbers, etc. should be regarded as uninterpreted. Then the application to apples is an accumulation. Numbers/QuineVsRussell: I find this attitude completely wrong. The words "five" and "twelve" are nowhere uninterpreted, they are as much essential components of our interpreted language as apples. >Numbers. They denote two intangible objects, numbers that are the sizes of quantities of apples and the like. The "plus" in addition is also interpreted from start to finish, but it has nothing to do with the accumulation of things. Five plus twelve is: how many apples there are in two separate piles. However, without pouring them together. The numbers "five" and "twelve" differ from apples in that they do not denote a body, that has nothing to do with misinterpretation. The same could be said of "nation" or "species". The ordinary interpreted scientific speech is determined to abstract objects as it is determined to apples and bodies. All these things appear in our world system as values of variables. II 185 It even has nothing to do with purity (e.g. of the set theory). Purity is something other than uninterpretedness. XII 60 Expression/Numbers/Knowledge/Explication/Explanation/Quine: our knowledge of expressions is alone in their laws of interlinking. Therefore, every structure that fulfills these laws can be an explication. XII 61 Knowledge of numbers: consists alone in the laws of arithmetic. Then any lawful construction is an explication of the numbers. RussellVs: (early): Thesis: arithmetic laws are not sufficient for understanding numbers. We also need to know applications (use) or their embedding in the talk about other things. Number/Russell: is the key concept here: "there are n such and suches". Number/Definition/QuineVsRussell: we can define "there are n such and suches" without ever deciding what numbers are beyond their fulfillment of arithmetic addition. Application/Use/QuineVsRussell: wherever there is structure, the applications set in. E.g. expressions and Gödel numbers: even the mention of an inscription was no definitive proof that we are talking about expressions and not about Gödel numbers. We can always say that our ostension was shifted. VII (e) 80 Principia Mathematica(1)/PM/Russell/Whitehead/Quine: shows that the whole of mathematics can be translated into logic. Only three concepts need to be clarified: Mathematics, translation and logic. VII (e) 81 QuineVsRussell: the concept of the propositional function is unclear and obscures the entire PM. VII (e) 93 QuineVsRussell: PM must be complemented by the axiom of infinity if certain mathematical principles are to be derived. VII (e) 93/94 Axiom of infinity: ensures the existence of a class with infinitely many elements. Quine: New Foundations instead makes do with the universal class: θ or x^ (x = x). 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. VII (f) 122 Propositional Functions/QuineVsRussell: ambiguous: a) open sentences b) properties. Russell no classes theory uses propositional functions as properties as value-bound variables. IX 15 QuineVsRussell: inexact terminology. "Propositional function", he used this expression both when referring to attributes (real properties) and when referring to statements or predicates. In truth, he only reduced the theory of classes to an unreduced theory of attributes. IX 93 Rational Numbers/QuineVsRussell: I differ in one point: for me, rational numbers are themselves real numbers, not so for Russell and Whitehead. Russell: rational numbers are pairwise disjoint for them like those of Peano. (See Chapter 17), while their real numbers are nested. ((s) pairwise disjoint, contrast: nested) Natural Numbers/Quine: for me as for most authors: no rational integers. Rational Numbers/Russell: accordingly, no rational real numbers. They are only "imitated" by the rational real numbers. Rational Numbers/QuineVsRussell: for me, however, the rational numbers are real numbers. This is because I have constructed the real numbers according to Russell's version b) without using the name and the designation of rational numbers. Therefore, I was able to retain name and designation for the rational real numbers IX 181 Type Theory/TT/QuineVsRussell: in the present form our theory is too weak to prove some sentences of classical mathematics. E.g. proof that every limited class of real numbers has a least upper boundary (LUB). IX 182 Suppose the real numbers were developed in Russell's theory similar to Section VI, however, attributes were now to take the place of classes and the alocation to attributes replaces the element relation to classes. LUB: (Capters 18, 19) of a limited class of real numbers: the class Uz or {x:Ey(x ε y ε z)}. Attribute: in parallel, we might thus expect that the LUB of a limited attribute φ of real numbers in Russell's system is equal to the Attribute Eψ(φψ u ψ^x). Problem: under Russell's order doctrine is this LUB ψ is of a higher order than that of the real numbers ψ which fall under the attribute φ whose LUB is sought. Boundary/LUB/QuineVsRussell: You need LUB for the entire classic technique of calculus, which is based on continuity. However, LUB have no value for these purposes if they are not available as values of the same variables whose value range already includes those numbers whose upper boundary is wanted. An upper boundary (i.e. LUB) of higher order cannot be the value of such variables, and thus misses its purpose. Solution/Russell: Axiom of Reducibility: Def Axiom of Reducibility/RA/Russell/Quine: every propositional function has the same extension as a certain predicative one. I.e. Ey∀x(ψ!x φx), Eψ∀x∀y[ψ!(x,y) φ(x,y)], etc. IX 184 VsConstruktivism/Construction/QuineVsRussell: we have seen Russell's constructivist approach to the real numbers fail (LUB, see above). He gave up on constructivism and took refuge in the RA. IX 184/185 The way he gave it up had something perverse to it: Axiom of Reducibility/QuineVsRussell: the RA implies that all the distinctions that gave rise to its creation are superfluous! (... + ...) IX 185 Propositional Function/PF/Attribute/Predicate/TT/QuineVsRussell: overlooked the following difference and its analogs: a) "propositional functions": as attributes (or intentional relations) and b) proposition functions: as expressions, i.e. predicates (and open statements: e.g. "x is mortal") Accordingly: a) attributes b) open statements As expressions they differ visibly in the order if the order is to be assessed on the basis of the indices of bound variables within the expression. For Russell everything is "AF". Since Russell failed to distinguish between formula and object (word/object, mention/use), he did not remember the trick of allowing that an expression of higher order refers straight to an attribute or a relation of lower order. X 95 Context Definition/Properties/Stage 2 Logic/Quine: if you prefer properties as sets, you can introduce quantification over properties, and then introduce quantification over sets through a schematic context definition. Russell: has taken this path. Quine: but the definition has to ensure that the principle of extensionality applies to sets, but not to properties. That is precisely the difference. Russell/QuineVsRussell: why did he want properties? X 96 He did not notice at which point the unproblematic talk of predicates capsized to speaking about properties. ((s) object language/meta language/mention/use). Propositional Function/PF: Russell took it over from Frege. QuineVsRussell: he sometimes used PF to refer to predicates, sometimes to properties. |
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 Chisholm I R. Chisholm The First Person. Theory of Reference and Intentionality, Minneapolis 1981 German Edition: Die erste Person Frankfurt 1992 Chisholm III Roderick M. Chisholm Theory of knowledge, Englewood Cliffs 1989 German Edition: Erkenntnistheorie Graz 2004 |
| Russell, B. | Hintikka Vs Russell, B. | II 165 On Denoting/Russell/Hintikka: (Russell 1905) Problem: with phrases that stand for genuine constituents of propositions. Problem/Frege: failure of substitutivity of identity (SI) in intensional contexts. Informative Identity/Frege: the fact that identity can even sometimes be informative is connected to this. EG/Existential Generalization/Russell: it, too, may fail in in intensional contexts, (problem of empty terms). HintikkaVsRussell: he does not recognize the depth of the problem and rather circumvents the problems of denoting terms. E.g. The bald king of France/Russell: Problem: we cannot prove by existential generalization that there is a present king of France. HintikkaVsRussell: But there are also other problems. (see below for ambiguity of cross world identificaiton). Description/Russell/Hintikka: Def Primary Description: the substitutivity of identity applies to them (SI) Def secondary description: for them, substitutivity of identity (SI) fails. II 166 Existential Generalization/Russell: two readings: (1) George IV did not know whether Scott was the author of Waverley. Description/Logical Form/Russell/Hintikka: "the author of Waverley": (ix)A(x) primarily: the description has the following power: (2) (Ex)[A(x) & (y) A(y) > y = x) & ~ George IV knew that (Scott = x)]. ((s) notation: quantifier here always normal existential quantifier, mirrored E). I.e. the quantifier has the maximum range in the primary identification. The second reading is more likely, however: Secondary: (3) ~George IV knew that (Ex)[A(x) & (y)(A(y) > y = x & (Scott = x)]. ((s) narrow range): Range/HintikkaVsRussell: he did not know that there is also a third option for the range of a quantifier ((s) >"medium range"/Kripke). (4) ~(Ex)[A(x) & (y)(A(y) > y = x ) & George IV knew that (Scott = x)]. II 166 Existential Generalization/HintikkaVsRussell: he did not see that there was a reason for the failure of the existential generalization, which is not caused by the non-existence of the object. E.g. (5) George IV knew that the author of Waverley is the author of Waverley. a) trivial Interpretation: I 167 (6) George IV knew that (Ex)(A(x) & (y)(A(y) > y = x)) everyday language translation: he knew that one and only one person wrote Waverley. I 166 b) non-trivial interpretation: (7) (Ex)(A(x) & (y)(A(y) > y = x) & George IV knew that (A(x) & (y)(A(y) > y = x))). ((s) no quantifier after "knew that everyday language translation: George knew of the only person who actually wrote Waverley, that they did. Because knowledge implies truth, (7) is equivalent to (8) (Ex) George IV knew that (Ez)(A(z) & (y)(A(y) > y = z) & x = z). this is equivalent to. (9) (Ex) George IV knew that (the author of Waverley = x) Here, the description has secondary (narrow) range. Everyday language translation: George knew who the author of Waverley is. I 167 Knowledge/Who/What/Where/HintikkaVsRussell: Russell cannot explicitly analyze structures of the form knows + W-sentence. General: (10) a knows, who (Ex x) is so that A(x) becomes (11) (Ex) a knows that A(x). Hintikka: this is only possible if we modify Russell’s approach: Problem: the existential generalization now collapses in a way that cannot be attributed to non-existence, and which cannot be analyzed by Russell’s Theory of Descriptions (ThoD). Problem: for every person, there are a lot of people whose names they know and of whose existence they know, but of who they do not know who they are. II 168 E.g. Charles Dodgson was for Queen Victoria someone of whom she had heard, but whom she did not know. Problem: if we assume that (11) is the correct analysis of (10), the following applies. (12) ~(Ex) Victoria knew that Dodgson = x) But that’s trivially false, even according to Russell. Because the following is certainly true: (13) Victoria knew that Dodgson = Dodgson) Existential Generalization/EG: then yields (14) (Ex) Victoria knew that Dodgson = x) So exactly the negation of (12) contradiction. II 168 Descriptions/Hintikka: are not involved here. Therefore, Russell’s description theory cannot help here, either. E.g. we can also assume that Victoria knew of the existence of Dodgson. Empty Terms/Empty Names: are therefore not the problem, either. Ontology/Hintikka: so our problem gets an ontological aspect. Existential Generalization/EG/Being/Quine/Ontology/Hintikka: the question of whether existential generalization may be applied on a singular term "b", E.g. in a context "F(b)", is the same as whether b may be value of a bound variable. Existential Generalization/Hintikka: does not fail here because of non-existence. II 169 We are dealing with the following problems here: Manifestation used by a) no SI Frege, Russell b) no EG (i) due to non-existence Russell (ii) because of ambiguity Hintikka Ambiguity/Solution/Hintikka: possible worlds semantics. E.g. (12) - (14) the problem is not that Dodgson did not exist in the actual world or not in one of Victoria’s worlds of knowledge, but that the name Dodgson singles out different individuals in different possible worlds. Hence (14) does not follow from (13). II 170 Existential Generalization/EG/Ambiguity/Clarity/Russell/Hintikka: Which way would have been open to Russell?. Knowing-Who/Russell/Hintikka: Russell himself very often speaks of the equivalence of knowledge, who did something with the existence of another individual, which is known to have done... + ... II 173 Denotation/Russell/Hintikka: Important argument: an ingenious feature of Russell’s theory of denotation from 1905 is that it is the quantifiers that denote! Theory of Denotation/Russell: (end of "On Denoting") includes the reduction of descriptions to objects of acquaintance. II 174 Hintikka: this relation is amazing, it also seems to be circular to allow only objects of acquaintance. Solution: We need to see what successfully denoting expressions (phrases) actually denote: they precisely denote objects of acquaintance. Ambiguity/Clarity/Hintikka: it is precisely ambiguity that leads to the failure of the existential generalization. Existential Generalization/Waverley/Russell/Hintikka: his own example shows that only objects of acquaintance are allowed: "the author of Waverley" in (1) is in fact a primary incident i.e. his example (2). "Whether"/Russell/Hintikka: only difference: wanted to know "if" instead of "did not know". (secondary?). Secondary Description/Russell: can also be expressed like this: that George wanted to know of the man who actually wrote Waverley whether he was Scott. II 175 That would be the case if George IV had seen Scott (in the distance) and had asked "Is that Scott?". HintikkaVsRussell: why does Russell select an example with a perceptually known individual? Do we not usually deal with beings of flesh and blood whose identity is known to us, instead of only with objects of perception?. Knowing Who/Knowing What/Perception Object/Russell/Hintikka: precisely with perception objects it seems as if the kind of clarity that we need for a knowing-who, is not just given. Identifcation/Possible Worlds Semantics/HintikkaVsRussell/Hintikka: in my approach Dodgson is a bona fide individual iff. he is one and the same individual in all worlds of knowledge of Victoria. I.e. identifiable iff. (15) (E.g.) in all relevant possible worlds it is true that (Dodgson = x). Problem: What are the relevant possible worlds?. II 178 Quantifier/Quantification/HintikkaVsRussell: Russell systematically confuses two types of quantifiers. (a) of acquaintance, b) of description). Problem: Russell has not realized that the difference cannot be defined solely in terms of the actual world!. Solution/Hintikka: we need a relativization to sets of possible worlds that change with the different propositional attitudes. II 179 RussellVsHintikka: he would not have accepted my representation of his position like this. HintikkaVsRussell: but the reason for this merely lies in a further error of Russell’s: I have not attributed to him what he believed, but what he should have believed. Quantification/Russell/Hintikka: he should have reduced to objects of acquaintance. Russell believed, however, it was sufficient to eliminate expressions that seemingly denote objects that are not such of acquaintance. Important argument: in that his quantifiers do not enter any ontological commitment. Only denoting expressions do that. Variable/Russell/Hintikka: are only notational patterns in Russell. Ontological Commitment/Quine/HintikkaVsRussell: Russell did not recognize the ontological commitment that 1st order languages bring with them. Being/Ontology/Quine: "Being means being value of a bound variable". HintikkaVsRussell: he has realized that. II 180 Elimination/Eliminability/HintikkaVsRussell/Hintikka: in order to eliminate merely seemingly denoting descriptions one must assume that the quantifiers and bound variables go over individuals that are identified by way of description. ((s) Object of the >Description). Otherwise, the real Bismarck would not be a permissible value of the variables with which we express that there is an individual of a certain species. Problem: then these quantifiers may not be constituents of propositions, because their value ranges do not only consist of objects of acquaintance. Therefore, Russell’s mistake was twofold. Quantifier/Variable/Russell/Hintikka, 1905, he had already stopped thinking that quantifiers and bound variables are real constituents of propositions. Def Pseudo Variable/Russell/Hintikka: = bound variable. Acquaintance/Russell: values of the variable should only be objects of acquaintance. (HintikkaVsRussell). Quantifiers/HintikkaVsRussell: now we can see why Russell did not differentiate between different quantifiers (acquaintance/description): For him quantifiers were only notational patterns, and for them the range of possible Interpretations need not be determined, therefore it makes no difference if the rage changes!. Quantification/Russell: for him, it was implicitly objectional (referential), and in any event not substitutional. Peacocke I 190 Possible Worlds/Quantification/HintikkaVsRussell: R. is unable to explain the cases in which we quantify in belief contexts (!) where (according to Hintikka) the quantifier over "publicly descriptively identified" particulars is sufficient. Hintikka: compares with a "roman à clef". Peacocke: it is not clear that (whether) this could not be explained by Russell as cases of general ideas, so that the person with such and such characteristics is so and so. Universals/Acquaintance/Russell/Peacocke: we are familiar with universals and they are constituents of our thoughts. HintikkaVsRussell: this is a desperate remedy to save the principle of acquaintance. PeacockeVsRussell: his arguments are also very weak. Russell: E.g. we cannot understand the transitivity of "before" if we are not acquainted with "before", and even less what it means that one thing is before another. While the judgment depends on a consciousness of a complex, whose analysis we do not understand if we do not understand the terms used. I 191 PeacockeVsRussell: what kind of relationship should exist between subject and universal?. Solution: the reformulated PB: Here we can see to which conditions a term is subject, similar to the principle of sensitivity in relational givenness. I 192 HintikkaVsRussell: ("On denoting what?", 1981, p.167 ff): the elimination of objects with which the subject is not familiar from the singular term position is not sufficient for the irreducibility of acquaintance that Russell had in mind. Quantification/Hintikka: the quantifiers will still reach over objects with which the subject is not familiar. But such quantifiers cannot be constituents of propositions, if that is to be compatible with the PB. Because they would certainly occur through their value range Occur and these do not consist of particulars with which one is familiar. |
Hintikka I Jaakko Hintikka Merrill B. Hintikka Investigating Wittgenstein German Edition: Untersuchungen zu Wittgenstein Frankfurt 1996 Hintikka II Jaakko Hintikka Merrill B. Hintikka The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989 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 |
| Schlick, M. | Verschiedene Vs Schlick, M. | Hempel I 102 Basic Sentences/Schlick: Vs complete renunciation of a system of unchangeable basic sentences: leads to relativism. VsSchlick: nowhere in science can one find an absolutely indisputable criterion. I 103 Confirmation/Schlick: in contrast to ordinary empirical statements, they are understood and verified in one act, namely by comparison with the facts. Thus he returns to the material way of speaking. Unlike statements, they cannot be recorded and are only valid in one moment. Thiel I 41 ThielVsSchlick: can the problem really be solved that way? Schlick's language is not the everyday language, it is already strictly regulated. Our interpretations always give the signs additional meaning. Why are some sign systems transferable to reality and others are not? I 42 Russell (1903) when "empirical constants" are used for variables, it must be examined each time whether the formulas are fulfilled. Math would then only be transferable if it is "isomorphic" (structurally equal) to the world of experience. |
Hempel I Carl Hempel "On the Logical Positivist’s Theory of Truth" in: Analysis 2, pp. 49-59 In Wahrheitstheorien, Gunnar Skirbekk Frankfurt/M. 1977 Hempel II Carl Hempel Problems and Changes in the Empirist Criterion of Meaning, in: Revue Internationale de Philosophie 11, 1950 German Edition: Probleme und Modifikationen des empiristischen Sinnkriteriums In Philosophie der idealen Sprache, J. Sinnreich München 1982 Hempel II (b) Carl Hempel The Concept of Cognitive Significance: A Reconsideration, in: Proceedings of the American Academy of Arts and Sciences 80, 1951 German Edition: Der Begriff der kognitiven Signifikanz: eine erneute Betrachtung In Philosophie der idealen Sprache, J. Sinnreich München 1982 T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |
| substit. Quantific. | Hintikka Vs substit. Quantific. | II 171 Substitutional Quantification/SQ/HintikkaVsSQ/HintikkaVsSubstitutional Quantification/Hintikka: is a mock paradise, at maximum of formal interest, there has never been a satisfactory explanation for them. Ad (i)/Russell/Hintikka: implied the equivalence of (120) and (11) in the period 1905-14). Description/Knowledge/Russell. Knowledge by description: E.g. we do not know Bismarck. We do wish that the object itself were a constituent of our proposition, but that is not possible. But we know that there is an object called Bismarck (existence). Russell: We also know about this Bismarck that he is a skillful diplomat. ((s) attribution of properties, predication, to individuation, property that goes beyond the mere naming). Solution/Russell: then we can describe the proposition that we want to assert, namely: "B was a skillful diplomat" with B being the object that Bismarck is. (logical form). Logical Form/Hintikka: (15) (Eb)(b = Bismarck & we judge that b was a skillful diplomat) "b": this variable then has current objects (objects from the real world) as values. Russell/Hintikka: this shows that he has not chosen the solution (i). However, Russell says on another occasion, admittedly: II 172 Description/Knowledge/Russell/Hintikka: knowledge by description: Here we know propositions about the "so-and-so" without knowing who or what the so-and-so is. Ad (ii): E.g. description: instead of Bismarck: "the first chancellor of the German Reich". HintikkaVs (ii) that sweeps the problem under the carpet. Problem: The use of descriptions must ultimately lead to the descriptions being re-translated into names, and that is not possible here! Furthermore: Reduction/Description/Name/Hintikka: not all individuals of which we speak with descriptions have identities that are known to everyone. The Interpretation of Russell does precisely not exclude that many different entities act as legitimate values of the variables that can, in principle, also be denoted with names. Ad (iii) Russell/Hintikka: that was Russell’s implicit solution: he redefined the domain of the individual variables so that they are limited to individuals who we know by acquaintance. Existential Generalization/EG/Russell/Hintikka: applies only to names of individuals with whom we are familiar. Hidden Description/Russell/Hintikka: existential generalization fails for individuals whose names must be regarded as hidden descriptions ((s) because we only know them by description). |
Hintikka I Jaakko Hintikka Merrill B. Hintikka Investigating Wittgenstein German Edition: Untersuchungen zu Wittgenstein Frankfurt 1996 Hintikka II Jaakko Hintikka Merrill B. Hintikka The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989 |
| Tarski, A. | Brendel Vs Tarski, A. | I 49 Truth-Def/Tarski/Brendel: contains no object constants and only one relation expression for class inclusion. Testimony/Property/Name/Model Theory/Brendel: compared to Tarski we need some changes: 1. Statements no longer result from the fact that free variable n AF are bound by universal quantification, but e.g. that object constants are assigned property or relation expressions. Example "Hans loves Paula". 2. Property/Model Theory: here you also have to specify for each property what it means that I 50 a sequence of objects satisfies this property or relation. 3. Naming/Model Theory: a semantic relation of the naming of objects by object constants must be formulated. Interpretation/Model Theory/Brendel: (instead of fulfillment) new: now the constants as well as the variables and the property and relation expressions can be used as descriptive signs. This is done by a function of assignment. (Assignment function). variables/Model Theory: new: now also variables are interpreted semantically. Therefore also formulas with free variables are truthful statements. Truth-Def/Modell Theory/BrendelVsTarski: new: now also a recursive truth definition about the structure of statements is possible. Example for the language L with countable infinite property and relation expressions ...+.... I 51 Model Theory/T-Def/BrendelVsTarski: this model theoretical truth definition is more general than Tarski's definition, since it cannot only make statements about set-theoretical entities. Semantic: but it is also because "truth" is defined by "Interpretation in an area of objects", i.e. a function is described that connects linguistic entities with non-linguistic ones. I 58 Semantic Truth/T-Concept/Brendel: should be ontologically neutral in relation to truth value-bearers. VsRealism: should the T-concept force a realistic position, it could not function as minimal consensus of all knowledge conceptions. VsTarski: he is often accused of his T-concept being based on an uncritical realism. (Because of the existence of state of affairs as truth makers.) TarskiVsVs: no realism is implied, but only that if a statement is rejected, then also the assertion of the truth of this statement. (Tarski 1944, 169). I 59 JenningsVsTarski: his T-term is ambivalent: a) semantic, as relation between statements and the state of affairs b) that only an equivalence of two statements (e.g. "snow is white" and, "sn..."is true") (Jennings 1987). I.e. the assertiveness conditions are the same. But then the semantic dimension is abandoned! Brendel: Thesis: we should keep the semantic T-concept, which however is not ontologically neutral. |
Bre I E. Brendel Wahrheit und Wissen Paderborn 1999 |
| Various Authors | Schiffer Vs Various Authors | I 283 Quaddition/John Carroll: that goes without non-standard interpretations: one would only have to redefine Quaddition like this: that if numbers are> = # in the game, delivers x + y = zt + 1. ((s) then you cannot notice this at incredibly large numbers.) SchifferVsCarroll: if you understand general propositions about addition, one will also appreciate that the sum of two numbers can never be equal to this sum plus 1! ((s) So if you look at the general shape notated with variables. But for this z would at first has to be written as a sum and then + 1!). |
Schi I St. Schiffer Remnants of Meaning Cambridge 1987 |
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