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

Ken Akiba
Virginia Commonwealth University
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
Keywords Philosophy
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Reprint years 2004
DOI 10.1023/A:1004201013891
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References found in this work BETA

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Mathematics Without Foundations.Hilary Putnam - 1967 - Journal of Philosophy 64 (1):5-22.
Modality and Ontology.Stewart Shapiro - 1993 - Mind 102 (407):455-481.

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Field on the Notion of Consistency.Ken Akiba - 1996 - Notre Dame Journal of Formal Logic 37 (4):625-630.

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