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

History and Philosophy of Logic 32 (4):359 - 374 (2011)
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Abstract
This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple universes of discourse serving as different ranges of the individual variables in different interpretations?as in post-WWII model theory. In the early 1960s, many logicians?mistakenly, as we show?held the ?contrary alternative? that Tarski 1936 had already adopted a Gödel-type, pluralistic, multiple-universe framework. We explain that Tarski had not yet shifted out of the monistic, Frege?Russell, fixed-universe paradigm. We further argue that between his Principia-influenced pre-WWII Warsaw period and his model-theoretic post-WWII Berkeley period, Tarski's philosophy underwent many other radical changes
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References found in this work BETA
Computability and Logic.Boolos, George; Burgess, John; P., Richard & Jeffrey, C.
Philosophy of Logic.Quine, W. V. O.
What Are Logical Notions?Corcoran, John & Tarski, Alfred
Collected Papers.McGinn, Colin & Evans, Gareth

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Existential-Import Mathematics.Corcoran, John & Masoud, Hassan

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2011-09-10

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