, Volume 27, Issue 1, pp 35-47

Nominalistic metalogic

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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.