- Ken Akiba
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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.
- Chihara, C.: A Simple Type Theory Without Platonistic Domains, Journal of Philosophical Logic 13 (1984), 249–283.
- Detlefsen, M.: Hilbert's Program, Reidel, Dordrecht, 1986.
- Field, H.: Science Without Numbers, Princeton University Press, Princeton, NJ, 1980.
- Field, H.: Is Mathematical Knowledge Just Logical Knowledge?, Philosophical Review 93 (1984), 509–552. Reprinted, with substantial changes, in Field, Realism, Mathematics and Modality, 79–124. Basil Blackwell, Oxford, 1989.
- Field, H.: Metalogic and Modality, Philosophical Studies 62 (1991), 1-22.
- Putnam, H.: The Thesis That Mathematics Is Logic, in R. Schoenman (ed.), Bertrand Russell: Philosopher of the Century, 273–303. Allen & Unwin, London, 1967a. Reprinted in Putnam, 1979, 12–42.
- Putnam, H.: Mathematics Without Foundations, Journal of Philosophy 64 (1967b), 5–22. Reprinted in Putnam, 1979, 43–78.
- Putnam, H.: Mathematics, Matter and Method: Philosophical Papers, vol. 1. 2nd edn. Cambridge University Press, Cambridge, England, 1979.
- Resnik, M.: Review of Field, 1980, Noûs 17 (1983), 514-519.
- Shapiro, S.: Modality and Ontology, Mind 102 (1993), 455–481.
- Nominalistic metalogic
Journal of Philosophical Logic
Volume 27, Issue 1 , pp 35-47
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- Kluwer Academic Publishers
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- Ken Akiba (1)
- Author Affiliations
- 1. Division of Humanities, University of Minnesota, 56267, USA