Notre Dame Journal of Formal Logic

Field on the Notion of Consistency

Ken Akiba

Abstract

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.

Article information

Source
Notre Dame J. Formal Logic Volume 37, Number 4 (1996), 625-630.

Dates
First available: 16 December 2002

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1040046146

Mathematical Reviews number (MathSciNet)
MR1446233

Digital Object Identifier
doi:10.1305/ndjfl/1040046146

Zentralblatt MATH identifier
0883.03002

Subjects
Primary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30}
Secondary: 00A30: Philosophy of mathematics [See also 03A05]

Citation

Akiba, Ken. Field on the Notion of Consistency. Notre Dame Journal of Formal Logic 37 (1996), no. 4, 625--630. doi:10.1305/ndjfl/1040046146. http://projecteuclid.org/euclid.ndjfl/1040046146.


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References

  • [1] Akiba, K., ``Nominalistic metalogic," Journal of Philosophical Logic, vol. 26 (1997), in press.
  • [2] Etchemendy, J., The Concept of Logical Consequence, Harvard University Press, Cambridge, 1990.
  • [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.
  • [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.
  • [7] Shapiro, S., ``Modality and ontology,'' Mind, vol. 102 (1993), pp. 455--81.