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A Subject With No ObjectStrategies for Nominalistic Interpretation of Mathematics$
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John P. Burgess and Gideon Rosen

Print publication date: 1999

Print ISBN-13: 9780198250128

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198250126.001.0001

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A Common Framework for Strategies

A Common Framework for Strategies

(p.67) B A Common Framework for Strategies
A Subject With No Object

John P. Burgess (Contributor Webpage)

Gideon Rosen (Contributor Webpage)

Oxford University Press

Sets up a schematic framework for the formal representation of current scientific theories and nominalistic alternatives thereto, presupposing only some previous acquaintance with first‐order logic. The framework is a two‐sorted first‐order language with one style of variable for physical entities, and another for mathematical entities. An examination of just which mathematical entities are needed in current theories leads to the conclusion that real numbers are enough, so it is over these that the second style of variable will be taken to range. Then contrasts contextual reduction, which aims to replace statements about real numbers by statements about physical objects or pairs or triples of physical objects that somehow represent numbers, with other, technically easier but philosophically less significant reductions making use of the Löwenheim–Skolem Theorem or Craig's Lemma.

Keywords:   Craig's Lemma, first‐order logic, Löwenheim–Skolem Theorem, nominalism

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