## Philosophy Dictionary of ArgumentsHome | |||

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Hilary Putnam on Loewenheim - Dictionary of Arguments V 54 ff Loewenheim/Reference/PutnamVsTradition: 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." - Reinterpretation with cherries and trees so that 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: by the reinterpretation cat will be enhanced to cat* - 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 even can 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: be S a language with predicates F1,F2,...Fk. Be I an interpretation in the sense that each predicate if 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: Be W1, W2, all possible worlds in a well-ordering, be Ui the set of possible individuals existing in world Wi - be Ri 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) - Be J 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 worlds Wj. - in other words: the extension of Fi in every world Wj under interpretation J is defined 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 ambigue: e.g. "pure": pain, E.g. "impure": 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 - then 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 - contradiction. - But this is not the real antinomy - Solution: (1) "tells us" that S is non-countable only, if the quantifier (ER) is interpreted such 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 be "in reality" countable - ...+ descending ... Skolem shows, that the whole use fo our language (i.e. theoretical and operational conditions) will not determine the "uniquely intended interpretation". - Solution: Platonism: postulates "magical reference". - Realism: has no solution. I (d) 105 At 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 [Author1]Vs[Author2] or [Author]Vs[term] 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 InVon 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) InVon 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 InVon 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. InVon 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. InVon einem realistischen Standpunkt, Vincent C. Müller, Reinbek 1993 Putnam I (e) Hilary Putnam Reference and Truth InVon 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 InVon 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) InVon 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 InVon einem realistischen Standpunkt, Vincent C. Müller, Reinbek 1993 Putnam I (i) Hilary Putnam Realism with a Human Face, Cambridge/MA 1990 InVon 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 InVon 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 InKünstliche 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 InTruth 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 InTheories of Truth, Paul Horwich, Aldershot 1994 SocPut I Robert D. Putnam Bowling Alone: The Collapse and Revival of American Community New York 2000 |

> Counter arguments against **Putnam**

> Counter arguments in relation to **Loewenheim**

Ed. Martin Schulz, access date 2021-09-25