Quine’s conjecture on many-sorted logic

Thomas William Barrett, Hans Halvorson

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)3563-3582
Number of pages20
Issue number9
StatePublished - Sep 1 2017

All Science Journal Classification (ASJC) codes

  • Philosophy
  • General Social Sciences


  • Definitional equivalence
  • Many-sorted logic
  • Model theory
  • Morita equivalence
  • Quine
  • Theoretical equivalence


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