Indeterminacy, Degree of Belief, and Excluded Middle

Hartry Field

in Truth and the Absence of Fact

Published in print March 2001 | ISBN: 9780199242894
Published online November 2003 | e-ISBN: 9780191597381 | DOI:
 Indeterminacy, Degree of Belief, and Excluded Middle

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Discusses the question of how to reconcile the acceptance of indeterminacy in one's own language with the acceptance of a minimal notion of truth. Argues that regarding a sentence of one's own language as indeterminate involves adopting non‐standard laws of thought for it: not necessarily a non‐standard logic, but non‐standard degrees of belief that do not obey the laws of classical probability. (A postscript gives an alternative, somewhat similar in spirit, where the laws of logic are revised as well.) The view is compared to a recent suggestion by Stephen Leeds, that we not recognize any indeterminacy in our own language other than indeterminacy as to how to translate it into a privileged sub‐part of the language, the vocabulary we take seriously even in our most serious theorizing.

Keywords: continuum hypothesis; degree of belief; excluded middle; indeterminacy; Stephen Leeds; probability; supervaluation; vagueness

Chapter.  19095 words. 

Subjects: Philosophy

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