Methodological Practice and Complementary Concepts of Logical Consequence: Tarski's Model-Theoretic Consequence and Corcoran's Information-Theoretic Consequence

Sagüillo, José Miguel

doi:10.1080/01445340802113531

Cited by 9 publications

(5 citation statements)

References 26 publications

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“…True in the fixed-domain universe over which all individual variables (and the higher-order variables) range. This is also the solution proposed by Sagüillo (1997) who provides a reading of Tarski as having upheld a fixed-domain viewpoint in 1936.…”

Section: Sher Corcoran Bach Ray Sagüillomentioning

confidence: 93%

“…This is the notion that relates the premises and the conclusion of a logically valid argument. When we try to spell out this notion informally we have recourse to various turns of phrase that include, among others, modal notions (possibility, necessity) or the notion of information (see Sagüillo 2009). Thus, we might say that C follows logically from premises P 1 , …, P n if and only if it is not possible for P 1 , …, P n and ¬C to be jointly true; or, using the notion of information, that C follows logically from premises P 1 , …, P n if and only if all the information provided by P 1 , …, P n already contains the information provided by C. In elementary courses in logic, most of the work is devoted to setting up derivational systems and semantic interpretations of the derivational systems that aim at capturing the informal notion(s) of logical consequence referred to above.…”

Section: Logical Consequence and Model‐theoretic Semanticsmentioning

confidence: 99%

“…In addition, fixed-domain conceptions of consequence were not rare at the time of Tarski's writing and were in fact upheld by logicians with logicist leanings (Carnap, Ramsey, Russell, Lewis, Langford, etc.) who worked with type theories with a fixed domain of individuals given at the outset (explicit references to such authors are also found, among others, in Gómez-Torrente 1996 andCorcoran andSagüillo 2009). Thus, the fixed-domain conception is not 'nonstandard' after all.…”

Section: Counter-reactions and New Evidence (Bays Mancosu)mentioning

confidence: 99%

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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: 93%

Section: Logical Consequence and Model‐theoretic Semanticsmentioning

confidence: 99%

Section: Counter-reactions and New Evidence (Bays Mancosu)mentioning

confidence: 99%

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

Mancosu

2010

Philosophy Compass

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“…In neither edition of Principia mathematica does metalogic play any explicit role; yet shortly before preparing the second edition Russell had achieved one of his finest philosophical insights when, in retort to Wittgenstein on showing and saying, he proposed 'that every language has, as Mr. Wittgenstein says, a structure concerning which, in the language, nothing can be said, but that there may be another language dealing with the structure of the first language, and having itself a new structure, and that to this hierarchy of languages there may be no limit' [181, xxii]. However, he did not recognise its importance; in particular, 26 See [183]; and also [57], who questions aspects of the version of pluralism expounded in [9], where the inference version of logics is adopted. 27 The differences between paraconsistent logic and the primacy of metatheorising was aired in my reply [76] to [164], to which [166] was the response.…”

Section: Monism and Pluralism In Logics: The Need For Metalogicsmentioning

confidence: 97%

Omnipresence, Multipresence and Ubiquity: Kinds of Generality in and Around Mathematics and Logics

Grattan‐Guinness

2011

Log. Univers.

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A prized property of theories of all kinds is that of generality, of applicability or least relevance to a wide range of circumstances and situations. The purpose of this article is to present a pair of distinctions that suggest that three kinds of generality are to be found in mathematics and logics, not only at some particular period but especially in developments that take place over time: 'omnipresent' and 'multipresent' theories, and 'ubiquitous' notions that form dependent parts, or moments, of theories. The category of 'facets' is also introduced, primarily to assess the roles of diagrams and notations in these two disciplines. Various consequences are explored, starting with means of developing applied mathematics, and then reconsidering several established ways of elaborating or appraising theories, such as analogising, revolutions, abstraction, unification, reduction and axiomatisation. The influence of theories already in place upon theory-building is emphasised. The roles in both mathematics and logics of set theory, abstract algebras, metamathematics, and model theory are assessed, along with the different relationships between the two disciplines adopted in algebraic logic and in mathematical logic. Finally, the issue of monism versus pluralism in these two disciplines is rehearsed, and some suggestions are made about the special character of mathematical and logical knowledge, and also the differences between them. Since the article is basically an exercise in historiography, historical examples and case studies are described or noted throughout. Mathematics Subject Classification (2000). Primary 00A30, 01A55, 01A60, 01A85, 03-03, 03-99; Secondary 00A35, 00A69, 00A71, 00A79, 03B10, 03C55, 03G05, 30-03, 31-03.Keywords. History and philosophy of pure and applied mathematics, history and philosophy of symbolic logics, parts and moments, generality of theories, theory change, monism and pluralism, sets and multisets, abstract algebras, metamathematics, model theory.

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“…Likewise, . 18 See Sagüillo 2009, but compare with Sagüillo 1997 John Corcoran and José Miguel Sagüillo Chapter 2 of Simons 1992 brought the issue up in reconsidering the criterion for logicality sketched in the still monistic setting of .…”

Section: The Place Of the Monistic-pluralistic Distinctionmentioning

confidence: 99%

The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper

Corcoran¹,

Sagüillo²

2018

Studies in Universal Logic

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Methodological Practice and Complementary Concepts of Logical Consequence: Tarski's Model-Theoretic Consequence and Corcoran's Information-Theoretic Consequence

Cited by 9 publications

References 26 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

Omnipresence, Multipresence and Ubiquity: Kinds of Generality in and Around Mathematics and Logics

The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper

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