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The author or concept searched is found in the following 6 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Models | Putnam | I (d) 107 Definition ω model/Putnam: a ω model is a model for a set theory in which the natural numbers are ordered "as it should be", that means, the sequence of "the natural numbers" of the model ω-sequence. I (d) 109f Countable/over-countable/uncountable/infinity/Loeweheim/Putnam: e.g. an instrument that will detect the presence of a particle within a volume, will at most give countable measurements. But if the instrument is shifted by r centimeters and r can be any real number, then there are over-countable many measurements. N.B.: then operational conditions cannot be identified with the totality of facts that can be observed, but only with the actual observed. If the shifted intervals are then rational, there are only a countable number of facts. Loewenheim: then, a model can be constructed that matches with all facts. >Löwenheim sentence. Counterfactual Conditional: a model with a predicate "makes subjunctive necessary" for not occurred cases can be constructed that induces an interpretation of counterfactual speech that makes precisely those counterfactual conditionals true that are according to some completion to our theory true. This means, the appeal to counterfactual observations cannot exclude models. Wittgenstein: the question of what God could calculate, is a matter within the math and cannot determine the interpretation of mathematics (PU §§ 193,352,426). --- II 112 There are possible set theories with and without the axiom of choice. Skolem: we should assign a truth value only as a part of a previously accepted theory. >Truth value, >Set theory, >Selection axiom. |
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 |
| Properties | Stalnaker | I 9 Def property/Stalnaker: a) Def thin/economic definition: a property is a way in which individuals can be grouped b) Def richer/Stalnaker: (more robust): a property is something in relation to which the individuals are grouped. To do this, we identify intrinsic properties with regions of a property-space. >Intrinsicness. Important argument: since the elements of the sets are not identical with the individuals that instantiate the property, this represents the independence of properties from their instantiation. ((s) So Stalnaker believes that properties also exist if they are not instantiated). >Instantiation, >Individuals, >Individuation. I 75 Modal Logic/ML/semantics/extensional/Stalnaker: e.g. property: a property is represented as a singular propositional function which takes an individual as an argument and delivers a proposition as a value. >Propositional functions. Equivalent to this: property: a property is a function that takes a possible world as an argument and delivers a set of individuals as a value. It is therefore intuitively a selection rule for a class of individuals, given the facts and vice versa: a selection selective procedure for a class of individuals is a property of the selected individuals. Cf. >Selection axiom, >Sets, >Set theory. Problem: there is no extensional equivalent to the distinction between referential and purely qualitative properties - unlike with the distinction between essential and accidental ones. >Essential properties, >Accidental properties. Def Referential properties: referential properties are defined in terms of the individuals that they have. Wrong solution: to stipulate that only accidental propositions may be selected for atomic predicates. This does not prevent that essential attributions could be true. It prevents only that they can be expressed. Anti-essentialism/solution: the property must be defined independently of the possible worlds and the individuals. >Essentialism. I 78 Intrinsic Property/bare particular/theory: to identify an intrinsic property we must distinguish possible world-indexed, time-indexed and referential properties from them. These do not correspond to any particular regions in the logical space. >Intrinsicness, >Bare particulars. E.g. having the same weight as Babe Ruth. - This is how we can represent anti-essentialism. I 79 Kripke, early: Babe Ruth could have been a billiard ball. Kripke, later: there is a fallacy in that. Stalnaker: one cannot assume that he is actually a billiard ball, because then one could not refer to him as we already did. That is not what it is about (see below). This confuses the limits of what could actually be with the limitations of assumptions about what could counterfactually have been. >Conceivability. Essential property/Kripke/Stalnaker: e.g. Kripke: thesis: names for natural species (natural kind terms) express essential properties. >Natural kinds, >Essence. Names for species are referential terms. Referential: referential means that they are determined by a causal connection. >Causal theory of reference. Natural kinds: natural kinds are not purely linguistic, but restrict the movement in the logical space. Bare particulars: if one allows Babe Ruth to be a billiard ball, then one must also allow it for any other thing - then this solution is uninteresting. I 81 Property/narrow/wide/propositional function: the distinction between 1) narrow P and 2) propositional functions: a propositional function in general is analogous to the distinction between possible individuals and concepts of individuals in general. >Narrow/wide, >Propositional functions. I 94f Physical non-property: a physical non-property is a complex combination of physical properties and relations (see below, e.g. golden mountain). Strong supervenience/Stalnaker: strong supervenience allows complex (composite) physical attributes to be physical properties. >Supervenience. Attribute: an attribute is an easy way of picking out. >Attributes. I 103 Def Property/Stalnaker: properties are simply a way to group individuals. Basic property/Stalnaker: basic properties must provide distinctions between individuals that could otherwise not be explained. Problem: then basic properties cannot supervene on something else. |
Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
| Reduction | Quine | XII 92 Definition Reduction Sentence/Carnap/Quine: weaker than definition: provides no equivalent sentences without the term in question, but only implications. XII 93 No full explanation but only partial explanation. Implication here: the reduction sentences name a few sentences that are implied by sentences with this term and imply some other sentences, that imply sentences with this term. - This does not provide a genuine reduction, but a fictional story of language acquisition. ((s) > "Rylean Ancestors"). VII (a) 19 Conceptual Scheme/Reduction/Quine: we want to see how far a physicalist scheme can be reduced to a phenomenalist one. The latter has epistemological priority. The choice between conceptual schemes is guided by purposes and interests. XI 143 Reduction/Ontology/Quine/Lauener: for ontological reduction, it is not extensional equality that is decisive, but the preservation of the relevant structure. For example Frege's, v. Neumann's and Zermelo's definitions do not produce equivalent predicates, but are nevertheless suitable for reduction, because all three represent a structure-preserving model of arithmetic. Extensional Equality(s): ensures the uniformity of the quantities considered. The reduction then takes place at the description level. It would not reduce the ontology. XI 146 Reduction/Theory/Quine/Lauener: by the condition that an n-tuple of arguments applies to a predicate exactly when the open sentence is fulfilled by the corresponding n-tuple of values, we avert an impending trivialization. We can do this by determining the proxy function. If the truth values of the closed sentences are preserved, we can actually speak of a reduction to the natural numbers. (Ways of Paradox, p. 203). XI 145 Def Proxy Function/Quine/Lauener: is a function that assigns each object of the original theory a function of the new theory. Example "The Goedel number of". This need not be expressed in one theory or another. It is sufficient if we have the necessary means of expression at the meta level. Reduction: from one theory to another: so we need a special function for this XI 146 whose arguments are from the old theory and whose values are from the new theory. Proxy Function/Quine/Lauener: does not need to be unique at all. Example: Characterization of persons on the basis of their income: here different values are assigned to an argument. For this we need a background theory: We map the universe U in V in such a way that both the objects of U and their proxies are contained in V. If V forms a subset of U, U itself can be defined as background theory, within which its own ontological reduction is described. XI 147 VsQuine: this is not a reduction at all, because then the objects must exist. QuineVsVs: this is comparable to a reductio ad absurdum: if we want to show that a part of U is superfluous, we may presuppose this for the duration of argument U (>Ontology). Lauener: that brings us to >ontological relativity. Löwenheim/Ontology/Reduction/Quine/Lauener: if a theory of its own requires a super-countable range, we can no longer present a proxy function that would allow a reduction to a countable range. This would require a much stronger framework theory, which could no longer be discussed away absurdly as reductio ad absurdum according to Quine's proposal. XII 60 Specification/Reduction/Quine: we cannot find a clear difference between specifying one item area and reducing that area to another. We have not discovered a clear difference between the clarification of the concept of "expression" and its replacement by that of number. ((s) > Goedel Numbers). And now, if we are to say what numbers actually are, we are forced to reveal them and instead assign a new, e.g. set-theoretical model to arithmetic. XII 73 Reduction/Ontology/Quine: an ontology can always be reduced to another if we know of a reversibly unique deputy function f. Reason: for each predicate P of the old system, there is a predicate of the new system that takes over the role of P there. We interpret this new predicate in such a way that it applies exactly to the values f(x) of the old objects x to which P applied. Example: Suppose f(x): is the Goedel number of x, Old system: is a syntactical system, Predicate in the old system: "... is a section of___" an x New system: the corresponding predicate would have the same extension (coextensive) as the words "...is the Gödel number of a section whose Goedel number is___". (Not in this wording but as a purely arithmetic condition.) XII 74 Reduction/ontological relativity/Quine: it may sound contradictory that the objects discarded in the reduction must exist. Solution: this has the same form as a reduction ad absurdum: here we assume a wrong sentence to refute it. As we show here, the subject area U is excessively large. XII 75 Löwenheim/Skolem/strong form/selection axiom/ontology/reduction/onthological relativity/Quine: (early form): thesis: If a theory is true and has a supernumerable range of objects, then everything but a countable part is superfluous, in the sense that it can be eliminated from the range of variables without any sentence becoming false. This means that all acceptable theories can be reduced to countable ontologies. And this in turn can be reduced to a special ontology of natural numbers. For this purpose, the enumeration, as far as it is explicitly known, is used as a proxy function. And even if the enumeration is not known, it exists. Therefore, we can regard all our items as natural numbers, even if the enumeration number ((s) of the name) is not always known. Ontology: could we not define once and for all a Pythagorean general purpose ontology? Pythagorean Ontology/Terminology/Quine: consists either of numbers only, or of bodies only, or of quantities only, etc. Problem: suppose, we have such an ontology and someone would offer us something that would have been presented as an ontological reduction before our decision for Pythagorean ontology, namely a procedure according to which in future theories all things of a certain type A are superfluous, but the remaining range would still be infinite. XII 76 In the new Pythagorean framework, his discovery would nevertheless still retain its essential content, although it could no longer be called a reduction, it would only be a manoeuvre in which some numbers would lose a number property corresponding to A. We do not even know which numbers would lose a number property corresponding to A. VsPythagoreism: this shows that an all-encompassing Pythagoreanism is not attractive, because it only offers new and opaque versions of old methods and problems. >Proxy function. |
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 |
| Set Theory | Set Theory: set theory is the system of rules and axioms, which regulates the formation of sets. The elements are exclusively numbers. Sets contain individual objects, that is, numbers as elements. Furthermore, sets contain sub-sets, that is, again sets of elements. The set of all sub-sets of a set is called the power set. Each set contains the empty set as a subset, but not as an element. The size of sets is called the cardinality. Sets containing the same elements are identical. See also comprehension, comprehension axiom, selection axiom, infinity axiom, couple set axiom, extensionality principle. |
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| Set Theory | Basieux | Basieux I 86 Axioms of the Set Theory/Halmos(1)/Basieux: 1) extensionality axiom: two sets are only equal iff they have the same elements >Extensionality. 2) selection axiom: for every set A and every condition (or property) E(x) there is a set B, whose elements are exactly every x of A, for which E(x) applies >Selection axiom 3) pairing axiom: for every two sets there is always one set that contains those two as elements 4) combination axiom: for every set system there is a set that contains all elements that belong to at least one set of the given system 5) power set axiom: for every quantity there is a set system that contains all the subsets of the given set among its elements >Power set. 6) infinity axiom: there is a set that contains the empty set and with each of its elements also its successor >Infinity axiom 7) choice axiom: the Cartesian product of a (non-empty) system of non-empty sets is non-empty 8) replacement axiom: S(a,b) be a statement of the kind that for each element a of a set A the set {b I S (a,b)} can be formed. Then there is a function F with domain A such that F(a) = {b I S(a,b)} for every a in A. >Axioms. 1. Halmos, Paul (1974). Naive set theory, Santa Clara University. |
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| Set Theory | Lewis | Schwarz I 75 Set theory/Mereology/Lewis: (Parts of Classes, 1991)(1): are sets simply mereological sums? Set theory proves to be mereologically extended arithmetic, with successor relation, a set relation between thing A and its unit set {A}. Through a structural analysis of this relationship Lewis finally leads the whole mathematics back to the assumption that there are many things. >Mereology/Lewis. Schwarz I 78 Classical set theory/Schwarz: sets form a hierarchical structure (cumulative or iterative). lowest level: things that are not sets "individuals", "primal elements". pure set theory: here the lowest level is empty (no individuals, nothing outside sets, nothing is not a set!) >Individual/Lewis. Omega/ω/Set theory/Schwarz: on ω all sets are located whose elements occur on one of the finite levels. On ω+1 there are sets whose elements are on ω or below etc. up to ω + ω (=ω * ω) followed by ω * 2 + 1 etc. A set that contains itself/Russell's paradox/Schwarz: is excluded by the hierarchy: it must already have occurred at a level below the level at which it occurs for the first time. Then there are also no quantities of all quantities that do not contain themselves, because that would be nothing other than the quantity of all quantities. Cf. >Russellean paradox. Schwarz I 79f Non-naive set theory/Schwarz: here things only form a set if they are not too many, i.e. if they do not correspond one-to-one with all sets. This motivates the selection axiom and the replacement axiom. Schwarz I 79ff Classical Set Theory: set and element (member) are undefined. Schwarz I 80 Set theory/Mereology/Lewis: (Parts of Classes(1), Part 1): Thesis: sets and classes are mereological sums. But the parts are not elements but subsets. >Mereological sum/Lewis. Main thesis: (MT): x is subclass of y, gdw. y is a class and x is part of y. (1991(1),§1,3) Schwarz I 93 Set theory/Properties/VsLewis/Schwarz: Lewis has a similar problem: according to his set-theoretical structuralism, an expression like "{A,B,C}" does not refer to a particular thing, the class of A, B, and C. Classes are relative to single set relations and single set relations are very numerous. According to Lewis, statements about classes - and thus also about properties - are actually plural quantifications about single set relationships (2002a(4), §5, (1986e(2), 52 Fn 39). Quantification via properties would then be plural quantification via ED. For example that a thing is red: that it is one of the red things. Schwarz I 94 SchwarzVsLewis: does not say how this should work for relations. V 346 "Nominalistic Set Theory" (1970d)(3) Nominalistic set theory/Lewis: if one assumes the individual calculus and a relation of the neighborhood between atoms as basic concepts, it is possible to define a pseudo element relation between individuals. 1. David Lewis [1991]: Parts of Classes. Oxford: Blackwell 2. David Lewis [1986e]: On the Plurality of Worlds. Malden (Mass.): Blackwell 3. David Lewis [1970d]: “Nominalistic Set Theory”. Nous, 4. 4. David Lewis [2002a]: “Tensing the Copula”. Mind, 111: 1–13 |
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 Schw I W. Schwarz David Lewis Bielefeld 2005 |
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