Quine’s conjecture on many-sorted logic

Synthese 194 (9):3563-3582 (2017)

Authors
Hans Halvorson
Princeton University
Thomas William Barrett
University of California at Santa Barbara
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 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
Keywords Theoretical equivalence  Definitional equivalence  Morita equivalence  Quine  Model theory  Many-sorted logic
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Reprint years 2017
DOI 10.1007/s11229-016-1107-z
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References found in this work BETA

Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.
Glymour and Quine on Theoretical Equivalence.Thomas William Barrett & Hans Halvorson - 2016 - Journal of Philosophical Logic 45 (5):467-483.
What Scientific Theories Could Not Be.Hans Halvorson - 2012 - Philosophy of Science 79 (2):183-206.
Ontological Pluralism.Jason Turner - 2010 - Journal of Philosophy 107 (1):5-34.

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Citations of this work BETA

Morita Equivalence.Thomas William Barrett & Hans Halvorson - 2016 - Review of Symbolic Logic 9 (3):556-582.
What Do Symmetries Tell Us About Structure?Thomas William Barrett - 2017 - Philosophy of Science (4):617-639.
Equivalent and Inequivalent Formulations of Classical Mechanics.Thomas William Barrett - forthcoming - British Journal for the Philosophy of Science:axy017.

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