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 -