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What's in a function?

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Abstract

In this paper we argue that Revision Rules, introduced by Anil Gupta and Nuel Belnap as a tool for the analysis of the concept of truth, also provide a useful tool for defining computable functions. This also makes good on Gupta's and Belnap's claim that Revision Rules provide a general theory of definition, a claim for which they supply only the example of truth. In particular we show how Revision Rules arise naturally from relaxing and generalizing a classical construction due to Kleene, and indicate how they can be employed to reconstruct the class of the general recursive functions. We also point at how Revision Rules can be employed to access non-minimal fixed points of partially defined computing procedures.

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Authors and Affiliations

  1. Department of Philosophy, Yale University, P.O. Box 208306, 06520-8306, New Haven, CT

    Gian Aldo Antonelli

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  1. Gian Aldo Antonelli
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Additional information

I thank Nuel Belnap, Rich Thomason, Ken Manders, and Jamie Tappenden for much helpful advice given while I was trying to get clear on the ideas presented here. I also thank two anonymous referees for helpful comments and criticisms on an earlier version of this paper.

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Antonelli, G.A. What's in a function?. Synthese 107, 167–204 (1996). https://doi.org/10.1007/BF00413605

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