The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper (2011)
Corcorana, John (Author)
Sagüillob, José Miguel (Author)
History and Philosophy of Logic
Volume: 32, no. 4
Issue: 4
Pages: 359-374
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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