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Field on the notion of consistency. (English) Zbl 0883.03002
Summary: Field’s claim that we have a notion of consistency which is neither model-theoretic nor proof-theoretic but primitive, is examined and criticized. His argument is compared to similar examinations by Kreisel and Etchemendy, and Etchemendy’s distinction between interpretational and representational semantics is employed to reveal the flaw in Field’s argument.
MSC:
03A05 Philosophical and critical aspects of logic and foundations
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[1] Akiba, K., “Nominalistic metalogic,” Journal of Philosophical Logic , vol. 26 (1997), · Zbl 0894.03006
[2] Etchemendy, J., The Concept of Logical Consequence , Harvard University Press, Cambridge, 1990. · Zbl 0743.03002
[3] Field, H., “Is mathematical knowledge just logical knowledge?,” Philosophical Review , vol. 93 (1984), pp. 509–52. Reprinted, with substantial changes, pp. 79–124 in his Realism, Mathematics and Modality , Basil Blackwell, Oxford, 1989.
[4] Field, H., “Metalogic and modality,” Philosophical Studies , vol. 62 (1991), pp. 1–22.
[5] Hintikka, J., ed., Philosophy of Mathematics , Oxford University Press, London, 1969. · Zbl 0181.29501
[6] Kreisel, G., “Informal rigor and completeness proofs,” pp. 138–71 in Problems in the Philosophy of Mathematics , edited by I. Lakatos, North-Holland, Amsterdam, 1967. Reprinted, in part, in Hintikka [?], pp. 78–94.
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