Higher-order logic or set theory: a false dilemma

Stewart Shapiro

doi:10.1093/philmat/nks002

Higher-order logic or set theory: a false dilemma

Stewart Shapiro

School of Philosophical, Anthropological and Film Studies

Research output: Contribution to journal › Article › peer-review

Abstract

The purpose of this article is show that second-order logic, as understood through standard semantics, is intimately bound up with set theory, or some other general theory of interpretations, structures, or whatever. Contra Quine, this does not disqualify second-order logic from its role in foundational studies. To wax Quinean, why should there be a sharp border separating mathematics from logic, especially the logic of mathematics?

Original language	English
Pages (from-to)	305-323
Journal	Philosophia Mathematica
Volume	20
Issue number	3
Early online date	9 Feb 2012
DOIs	https://doi.org/10.1093/philmat/nks002
Publication status	Published - Oct 2012

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10.1093/philmat/nks002

FOUNDATIONS OF LOGICAL CONSEQUENCE: Foundations of Logical Consequence
Read, S. (PI), Priest, G. G. (CoI), Shapiro, S. (CoI) & Celani, L. (Student)
Arts and Humanities Research Council
1/01/09 → 30/06/12
Project: Standard

Cite this

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Higher-order logic or set theory: a false dilemma

Abstract

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FOUNDATIONS OF LOGICAL CONSEQUENCE: Foundations of Logical Consequence

Cite this