Philosophy Dictionary of ArgumentsHome
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| Leopold Löwenheim: Leopold Löwenheim (1878-1957) was a German mathematician who worked on mathematical logic. He is best known for the Löwenheim-Skolem theorem, which states that every first-order theory with an infinite model also has a countable model. See also Models, Model theory, Satisfaction, Satisfiability, Infinity, Countability, Real numbers, Numbers, Word meaning, Reference, Ambiguity._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. | |||
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H. Putnam on Loewenheim - Dictionary of Arguments
V 54 ff Loewenheim/reference/PutnamVsTradition: Loewenheim tries to fix the intension und extension of single expressions via the determination of the truth values for whole sentences. V 56f PutnamVsOperationalism: e.g. (1) "E and a cat is on the mat." If we re-interpret this with cherries and trees, all truth values remain unchanged. Cat* to mat*: a) some cats on some mats and some cherries on some trees, b) ditto, but no cherry on a tree, c) none of these cases. Definition cat*: x is a cat* iff. a) and x = cherry, or b) and x = cat or c) and x = cherry. Definition mat*: x = mat* iff. a) and x = tree or b) and x = mat or c) and x = quark. Ad c) Here all respective sentences become false ((s) "cat* to mat*" is the more comprehensive (disjunctive) statement and therefore true in all worlds a) or b)). Putnam: cat will be enhanced to cat* by reinterpretation. Then there might be infinitely many reinterpretations of predicates that will always attribute the right truth value. Then we might even hold "impression" constant as the only expression. The reference will be undetermined because of the truth conditions for whole sentences (>Gavagai). V 58 We can even reinterpret "sees" (as sees*) so that the sentence "Otto sees a cat" and "Otto sees* a cat" have the same truth values in every world. V 61 Which properties are intrinsic or extrinsic is relative to the decision, which predicates we use as basic concepts, cat or cat*. Properties are not in themselves extrinsic/intrinsic. V 286ff Loewenheim/Putnam: theorem: S be a language with predicates F1, F2, ...Fk. I be an interpretation in the sense that each predicate S gets an intension. Then, there will be a second interpretation J that is not concordant with I but will make the same sentences true in every possible world that are made true by I. Proof: W1, W2, ... all be possible worlds in a well-ordering, Ui be the set of possible individuals existing in world Wi. Ri be the set, forming the extension of the predicate Fi in the possible world Wj. The structure [Uj;Rij(i=1,2...k)] is the "intended Model" of S in world Wj relative to I (i.e. Uj is the domain of S in world Wj, and Rij is (with i = 1, 2, ...k) the extension of the predicate Fi in Wj). J be the interpretation of S which attributes to predicate Fi (i=1, 2, ...k) the following intension: the function fi(W), which has the value Pj(Rij) in every possible world Wj. In other words: the extension of Fi in every world Wj under interpretation J is defined as such, that it is Pj(Rij). Because [Uj;Pj(Rij)(i=1,2...k)] is a model for the same set of sentences as [Uj;Rij(i=1,2...k)] (because of the isomorphism), in every possible world the same sentences are true under J as under I. J is distinguished from I in every world, in which at least one predicate has got a non-trivial extension. V 66 Loewenheim/intention/meaning/Putnam: this is no solution, because to have intentions presupposes the ability to refer to things. Intention/mind State: is ambiguous: "pure": is e.g. pain, "impure": means e.g. whether I know that snow is white does not depend on me like pain (> twin earth). Non-bracketed belief presupposes that there really is water (twin earth). Intentions are no mental events that evoke the reference. V 70 Reference/Loewenheim/PutnamVsField: a rule like "x prefers to y iff. x is in relation R to y" does not help: even when we know that it is true, could relation R be any kind of a relation (while Field assumes that it is physical). --- I (d) 102ff E.g. the sentence: (1) ~(ER)(R is 1:1. The domain is R < N. The range of R is S). Problem: when we replace S by the set of real numbers (in our favourite set theory), then (1) will be a theorem. In the following our set theory will say that a certain set ("S") is not countable. Then S must in all models of our set theory (e.g. Zermelo-Fraenkel, ZF) be non-countable. Loewenheim: his sentence now tells us, that there is no theory with only uncountable models. This is a contradiction. But this is not the real antinomy. Solution: (1) "tells us" that S is non-countable only, if the quantifier (ER) is interpreted in such a way that is goes over all relations of N x S. I (d) 103 But if we choose a countable model for the language of our set theory, then "(ER)" will not go over all relations but only over the relations in the model. Then (1) tells us only, that S is uncountable in a relative sense of uncountable. "Finite"/"Infinite" are then relative within an axiomatic set theory. Problem: "unintended" models, that should be uncountable will "in reality" be countable. Skolem shows, that the whole use of our language (i.e. theoretical and operational conditions) will not determine the "uniquely intended interpretation". Solution: platonism: postulates "magical reference". Realism: offers no solution. I (d) 105 In the end the sentences of set theory have no fixed truth value. I (d) 116 Solution: thesis: we have to define interpretation in another way than by models._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
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 |
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> Counter arguments against Putnam
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Ed. Martin Schulz, access date 2024-04-18