Second-Order Arithmetic Sans Sets
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 languageAuthor's Profile
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References found in this work
Foundations without foundationalism: a case for second-order logic.Stewart Shapiro -1991 - New York: Oxford University Press.
From a Logical Point of View.Richard M. Martin -1955 -Philosophy and Phenomenological Research 15 (4):574-575.
To be is to be a value of a variable (or to be some values of some variables).George Boolos -1984 -Journal of Philosophy 81 (8):430-449.
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