Chapter

Constructibility and Open‐Sentences

Charles S. Chihara

in Constructibility and Mathematical Existence

Published in print June 1991 | ISBN: 9780198239758
Published online November 2003 | e-ISBN: 9780191597190 | DOI: http://dx.doi.org/10.1093/0198239750.003.0003

Series: Clarendon Paperbacks

 Constructibility and Open‐Sentences

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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

Chapter.  6188 words. 

Subjects: Philosophy of Mathematics and Logic

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