Author: Akiba, K.
Source: Journal of Philosophical Logic, Volume 27, Number 1, February 1998 , pp. 35-47(13)
Abstract:This paper offers a novel method for nominalizing metalogic without transcending first-order reasoning about physical tokens (inscriptions, etc.) of proofs. A kind of double-negation scheme is presented which helps construct, for any platonistic statement in metalogic, a nominalistic statement which has the same assertability condition as the former. For instance, to the platonistic statement “there is a (platonistic) proof of A in deductive system D” corresponds the nominalistic statement “there is no (metalogical) proof token in (possibly informal) set theory for the claim that there is no proof of A in D.” And it is argued that the nominalist can use all the platonistic results by transforming them into such nominalistic correlates.
Document Type: Regular Paper
Affiliations: Division of Humanities, University of Minnesota, Morris, Morris, MN 56267, USA (Current address: Department of Philosophy Faculty of Letters Kumamoto University Kumamoto 860, Japan)
Publication date: February 1, 1998