Nominalistic metalogic
Journal of Philosophical Logic 27 (1):35-47 (1998)
| 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 | |||||||||
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