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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Author Profiles

John Corcoran
PhD: Johns Hopkins University; Last affiliation: University at Buffalo

References found in this work

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Principles of mathematics.Bertrand Russell - 1931 - New York,: W.W. Norton & Company.
Logic, semantics, metamathematics.Alfred Tarski - 1956 - Oxford,: Clarendon Press. Edited by John Corcoran & J. H. Woodger.
Introduction to mathematical logic.Alonzo Church - 1944 - Princeton,: Princeton University Press. Edited by C. Truesdell.
Introduction to mathematical logic..Alonzo Church - 1944 - Princeton,: Princeton university press: London, H. Milford, Oxford university press. Edited by C. Truesdell.

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