Chapter

A Common Framework for Strategies

John P. Burgess and Gideon Rosen

in A Subject With No Object

Published in print December 1999 | ISBN: 9780198250128
Published online November 2003 | e-ISBN: 9780191597138 | DOI: http://dx.doi.org/10.1093/0198250126.003.0002
 A Common Framework for Strategies

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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

Chapter.  11742 words.  Illustrated.

Subjects: Philosophy of Mathematics and Logic

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