Do not claim too much: Second-order logic and first-order logic

Philosophia Mathematica 7 (1):42-64 (1999)
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Abstract

The purpose of this article is to delimit what can and cannot be claimed on behalf of second-order logic. The starting point is some of the discussions surrounding my Foundations without Foundationalism: A Case for Secondorder Logic.

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10.1093/philmat/7.1.42

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Stewart Shapiro
Ohio State University

Citations of this work

Speaking with Shadows: A Study of Neo‐Logicism.Fraser MacBride - 2003 - British Journal for the Philosophy of Science 54 (1):103-163.
Speaking with Shadows: A Study of Neo‐Logicism.Fraser MacBride - 2003 - British Journal for the Philosophy of Science 54 (1):103-163.
Higher-Order Logic or Set Theory: A False Dilemma.S. Shapiro - 2012 - Philosophia Mathematica 20 (3):305-323.
Second-order Logic and the Power Set.Ethan Brauer - 2018 - Journal of Philosophical Logic 47 (1):123-142.

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References found in this work

Introduction to mathematical logic.Alonzo Church - 1944 - Princeton,: Princeton University Press. Edited by C. Truesdell.
Philosophy of Logic.W. V. O. Quine - 2005-01-01 - In José Medina & David Wood (eds.), Truth. Blackwell.
Logicism and the ontological commitments of arithmetic.Harold T. Hodes - 1984 - Journal of Philosophy 81 (3):123-149.

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