David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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History and Philosophy of Logic 32 (4):359 - 374 (2011)
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
|Keywords||ALFRED TARSKI LOGICAL CONSEQUENCE UNIVERSE OF DISCOURSE BERTAND RUSSELL MODEL THEORY ALONZO CHURCH FIXED INTERPRETATION INDIVIDUALS RANGE OF VARIABLE Kurt Gödel|
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References found in this work BETA
George Boolos, John Burgess, Richard P. & C. Jeffrey (2007). Computability and Logic. Cambridge University Press.
W. V. Quine (1986). Philosophy of Logic. Harvard University Press.
Alfred Tarski (1956). Logic, Semantics, Metamathematics. Oxford, Clarendon Press.
John Etchemendy (1990). The Concept of Logical Consequence. Harvard University Press.
Citations of this work BETA
Georg Schiemer (2013). Carnap's Early Semantics. Erkenntnis 78 (3):487-522.
John Corcoran & Hassan Masoud (2014). Existential Import Today: New Metatheorems; Historical, Philosophical, and Pedagogical Misconceptions. History and Philosophy of Logic 36 (1):39-61.
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