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Properties and the Interpretation of Second-Order Logic (2013)

Hale, B.

Oxford University Press

In: Philosophia Mathematica

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Publication Date: 2013-06-11

Description: This paper defends a deflationary conception of properties, according to which a property exists if and only if there could be a predicate with appropriate satisfaction conditions. I argue that purely general properties and relations necessarily exist and discuss the bearing of this conception of properties on the interpretation of higher-order logic and on Quine's charge that higher-order logic is ‘set theory in sheep's clothing’. On my approach, the usual semantics involves a false assimilation of the logic to set theory. I conclude with remarks about implications for the programme of founding mathematical theories in higher-order logic plus abstraction principles.

Print ISSN: 0031-8019

Electronic ISSN: 1744-6406

Topics: Mathematics , Philosophy

Published by Oxford University Press

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