Combining Philosophers

Ideas for Kurt Vonnegut, G. Aldo Antonelli and Hilary Putnam

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2 ideas

5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms

14207	If cats equal cherries, model theory allows reinterpretation of the whole language preserving truth [Putnam]
	Full Idea: If the number of cats happens to equal the cherries, then it follows from the theory of models that there is a reinterpretation of the entire language that leaves all sentences unchanged in truth value while permuting the extensions of 'cat' and 'cherry'.
	From: Hilary Putnam (Reason, Truth and History [1981], Ch.2)
	A reaction: This horrifying result seems to come simply from the fact that there is an isomorphism between two models, which in turn seems to rest largely on the cardinality of the models. There seems to be something wrong with model theory here (?).

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

9913	The Löwenheim-Skolem Theorem is close to an antinomy in philosophy of language [Putnam]
	Full Idea: The Löwenheim-Skolem Theorem says that a satisfiable first-order theory (in a countable language) has a countable model. ..I argue that this is not a logical antinomy, but close to one in philosophy of language.
	From: Hilary Putnam (Models and Reality [1977], p.421)
	A reaction: See the rest of this paper for where he takes us on this.