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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 Purely Modal Strategy

A Purely Modal Strategy

Chapter:
(p.124) B A Purely Modal Strategy
Source:
A Subject With No Object
Author(s):

John P. Burgess (Contributor Webpage)

Gideon Rosen (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0198250126.003.0004

Begins with an extended discussion of the analogy between mood and tense, bringing out how in ordinary language one often engages in cross‐comparison between, so to speak, how something that is is and how something that isn’t, but could have been, would have been if it had been, just as one often engages in cross‐comparison between how something that is is and how something that isn’t, but once was, was when it was. Then outlines a strategy for interpreting statements about the relations between physical objects and abstract numbers (e.g. ‘number X measures the mass in grams that the object x has’) by suitable cross‐comparisons with concrete numerals (‘numeral X would have marked how massive in grams the object x is’). Existing formal systems of modal logic, when enriched with operators for actuality and related notions, are just barely adequate to the task of representing all this formally. In all this, nominalistically unacceptable talk of so‐called possible worlds is rigorously avoided, and only ordinary‐language modal locutions are used.

Keywords:   abstract numbers, actuality, concrete numerals, modal logic, mood, nominalism, ordinary language, possible worlds, tense

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