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Quine's Conjecture on Many-Sorted Logic

Barrett, Thomas William and Halvorson, Hans (2015) Quine's Conjecture on Many-Sorted Logic. [Preprint]

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Abstract

Quine often argued for a simple, untyped system of logic rather than the typed systems that were championed by Russell and Carnap, among others. He claimed that nothing important would be lost by eliminating sorts, and the result would be additional simplicity and elegance. In support of this claim, Quine conjectured that every many-sorted theory is equivalent to a single-sorted theory. We make this conjecture precise, and prove that it's true, at least according to one reasonable notion of theoretical equivalence. Our clarification of Quine's conjecture, however, exposes the shortcomings of his argument against many-sorted logic.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Barrett, Thomas Williamthomaswb@princeton.edu
Halvorson, Hanshhalvors@princeton.edu
Keywords: theoretical equivalence, definitional equivalence, Morita equivalence, Quine, Carnap, model theory, many-sorted logic
Subjects: Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Methodology
General Issues > History of Philosophy of Science
General Issues > Logical Positivism/Logical Empiricism
Specific Sciences > Mathematics
General Issues > Philosophers of Science
General Issues > Structure of Theories
Depositing User: Thomas Barrett
Date Deposited: 29 Jan 2016 03:34
Last Modified: 07 May 2017 16:36
Item ID: 11887
Subjects: Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Methodology
General Issues > History of Philosophy of Science
General Issues > Logical Positivism/Logical Empiricism
Specific Sciences > Mathematics
General Issues > Philosophers of Science
General Issues > Structure of Theories
Date: 5 September 2015
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/11887

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