Second-Order Arithmetic Sans Sets

Philosophia Mathematica 21 (3):339-350 (2013)
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Abstract

This paper examines the ontological commitments of the second-order language of arithmetic and argues that they do not extend beyond the first-order language. Then, building on an argument by George Boolos, we develop a Tarski-style definition of a truth predicate for the second-order language of arithmetic that does not involve the assignment of sets to second-order variables but rather uses the same class of assignments standardly used in a definition for the first-order language

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10.1093/philmat/nkt016

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Lon Berk
Massachusetts Institute of Technology

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From a Logical Point of View.Willard Van Orman Quine - 1953 - Cambridge: Harvard University Press.
From a Logical Point of View.Richard M. Martin - 1955 - Philosophy and Phenomenological Research 15 (4):574-575.
Philosophy of Logic.W. V. O. Quine - 2005-01-01 - In José Medina & David Wood (eds.), Truth. Blackwell.

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