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The Construction of Logical Space$
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Agustín Rayo

Print publication date: 2013

Print ISBN-13: 9780199662623

Published to Oxford Scholarship Online: September 2013

DOI: 10.1093/acprof:oso/9780199662623.001.0001

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(p.171) 7 Paraphrase
The Construction of Logical Space

Agustín Rayo

Oxford University Press

This chapter examines the expressive resources that would be needed to supply nominalistic paraphrases for the language of arithmetic. The upshot is that characterizing a suitable paraphrase-method is not as straightforward as one might have thought. One option is to avail oneself of potentially controversial logical resources, such as variables of very high type or infinitary operations. Another option is to make use of intensional operators. Intensional paraphrase-functions need to be treated with care, however, since they might be thought to shed more light on the truth-conditions of arithmetical sentences than they actually succeed in shedding.

Keywords:   arithmetic, paraphrase, nominalism, Higher-order logic, type theory, infinitary languages

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