Some remarks on Hartry Field's notion of “logical consistency”

Krzysztof Wójtowicz

DOI: http://dx.doi.org/10.12775/LLP.2001.013

Abstract


In this article the notion of “logical consistency” in the sense introduced by Field in [Field 1991] is discussed. Field argues, that it is possible to introduce the notion of “logical consistency” as a primitive metalogical notion, which is independent from model-theoretical and proof-theoretical notions. In this article I want to indicate some difficulties of this standpoint, and to identify some hidden presuppositions. I also would like to show, that introducing this concept (at least in the form considered by Field) does not really support Field’s argumentation against realism. I confine myself to the analysis of Field’s standpoint, and will not discuss the more general issue, whether it is possible to treat the notion of “logical consequence” as a primitive notion.

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References


Field, H., 1980, Science Without Numbers, Oxford: Basil Blackwell.

Field, H., 1991, “Metalogic and Modality”, Philosophical Studies 62, 1–22.

Kreisel, G. 1969, “Informal rigour and completeness proofs”, in: J. Hinitkka (ed.) The Philosophy of Mathematics, Oxford University Press, 78–94.

Shapiro, S., 1987, “Principles of reflection and second-order logic”, Journal of Philosophical Logic 16, 309–333.

Shapiro, S., 1993, “Modality and Ontology”, Mind 102, 455–481.








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