Quine's conjecture on many-sorted logic
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Quine's conjecture on many-sorted logic. / Barrett, Thomas William; Halvorson, Hans.
I: Synthese, Bind 194, 2017, s. 3563-3582.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Quine's conjecture on many-sorted logic
AU - Barrett, Thomas William
AU - Halvorson, Hans
PY - 2017
Y1 - 2017
N2 - 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 is 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.
AB - 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 is 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.
KW - Theoretical equivalence
KW - Definitional equivalence
KW - Morita equivalence
KW - Quine
KW - Model theory
KW - Many-sorted logic
U2 - 10.1007/s11229-016-1107-z
DO - 10.1007/s11229-016-1107-z
M3 - Journal article
VL - 194
SP - 3563
EP - 3582
JO - Synthese
JF - Synthese
SN - 0039-7857
ER -
ID: 289118337