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Constructibility and Mathematical Existence$
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Charles S. Chihara

Print publication date: 1991

Print ISBN-13: 9780198239758

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198239750.001.0001

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Constructibility and Open‐Sentences

Constructibility and Open‐Sentences

(p.40) 3 Constructibility and Open‐Sentences
Constructibility and Mathematical Existence

Charles S. Chihara (Contributor Webpage)

Oxford University Press

Since the constructibility quantifiers, used in the mathematical system to be developed, will all assert the constructibility of open sentences, an explanation is given of the kinds of open sentences that will be asserted to be constructible. Each of these open sentences will be assigned to a specific ‘level’, depending on the kind of objects or open sentences that can satisfy it, thus providing the basis for the Simple Type Theoretical characteristic of the system to be developed. The satisfaction relation under discussion will be taken to be a primitive of the system. The relevance of Quine's objections to modality for this system is taken up.

Keywords:   modality, open sentence, Quine, Simple Type Theory

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