Logical consequence: A defense of Tarski

Ray, Greg

doi:10.1007/bf00265256

Cited by 30 publications

(25 citation statements)

References 18 publications

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“…This judgment, in turn, tends to undermine Etchemendy’s divergence argument, because that argument presupposes that Tarski made the greater error [the mistake of missing the need for domain variation, PM]. (Ray 1996, 630)…”

Section: Sher Corcoran Bach Ray Sagüillomentioning

confidence: 99%

Fixed‐ versus Variable‐domain Interpretations of Tarski’s Account of Logical Consequence

Mancosu

2010

Philosophy Compass

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In this article I describe and evaluate the debate that surrounds the proper interpretation of Tarski’s account of logical consequence given in his classic 1936 article ‘On the concept of logical consequence’. In the late 1980s Etchemendy argued that the familiar model theoretic account of logical consequence is not to be found in Tarski’s original article. Whereas the contemporary account of logical consequence is a variable‐domain conception – in that it calls for a reinterpretation of the domain of variation of the quantifiers when evaluating logical consequence –, no such reinterpretation is found in Tarski’s original account, which was rather based on a ‘fixed‐domain’ conception. Etchemendy’s claims have sparked a debate on Tarski’s conception of logical consequence with important contributions by, among others, Bach, Bays, Corcoran, Gómez‐Torrente, Mancosu, Ray, Sagüillo, and Sher.

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Section: Sher Corcoran Bach Ray Sagüillomentioning

confidence: 99%

Fixed‐ versus Variable‐domain Interpretations of Tarski’s Account of Logical Consequence

Mancosu

2010

Philosophy Compass

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“…(See, e.g., Etchemendy (1988), Bays (2001), Mancosu (2006). For alternative views see Gómez-Torrente (1996) and Ray (1996).) In my view there are in fact differences between Tarski's notion and the current notion (see e.g.…”

mentioning

confidence: 81%

Are There Model‐Theoretic Logical Truths that are not Logically True?

Gómez‐Torrente¹

2008

New Essays on Tarski and Philosophy

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The question in the title is similar to other important unsettled questions prompted by attempted mathematical characterizations of pretheoretical notions, by coextensionality "theses" about them. 1 Church and Turing's thesis that a function is computable iff it is recursive 2 gives rise to the question "are there computable functions that are not recursive?". The thesis, especially associated with Stephen Cook, that a natural problem has a feasible algorithm iff it has a polynomial-time algorithm 3 gives rise to the question "are there natural problems having a feasible algorithm that do not have a polynomial-time algorithm?". 4 But there are remarkable dissimilarities too. A central one is that the notion of "model-theoretic logical truth" is a notion relative to (at least) a choice of a set of formalized languages, of a set of logical constants, of a notion of model, and of a notion of truth in a model, while the notions of recursiveness and of a polynomial-time algorithm are * Parts of this paper were presented in workshops at the University of California at Irvine (2002), the Universidade Nova de Lisboa (2003), the University of Melbourne (2004), and the Universidad de Santiago de Compostela (2006), and as lectures at the Universidad Nacional Autónoma de México (2006) and the Universidade Federal do Rio de Janeiro (2006). I thank the audiences at these events for very helpful comments and criticism. Special thanks to Rodrigo Bacellar, Bill Hanson, Øystein Linnebo, Gila Sher and two anonymous readers. 1 Here by "pretheoretical" of course I don't mean "previous to any theoretical activity"; in this sense there could hardly be pretheoretical notions of computability, of a feasible algorithm, or of logical truth. What I mean is "previous to the theoretical activity of mathematical characterization".

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“…With a firstorder language, the analysis fails unless we add an important modification whose consistency with the original analysis has yet to be explained. 13 Adding this 13 Greg Ray [27] argues that Tarski originally intended to employ varying domains, presumably to prove that the feature is consistent with the original account. But Ray's interpretation is inconsistent with the motivations Tarski gives for the reductive account, with Tarski's explicit description of the account, and with the consequences that he expressly draws from it.…”

Section: Extensional Adequacy Of Tarski's Accountmentioning

confidence: 95%

Reflections on Consequence

Etchemendy¹

2008

New Essays on Tarski and Philosophy

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Logical consequence: A defense of Tarski

Cited by 30 publications

References 18 publications

Fixed‐ versus Variable‐domain Interpretations of Tarski’s Account of Logical Consequence

Fixed‐ versus Variable‐domain Interpretations of Tarski’s Account of Logical Consequence

Are There Model‐Theoretic Logical Truths that are not Logically True?

Reflections on Consequence

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