Affiliation:
1. Department of Philosophy , University of California, Davis, Davis, CA 95616, USA
Abstract
Abstract
In this paper, I argue against the thesis that the meaning of ‘computability’ is logic-dependent. I do this from a category-theoretic perspective. Applying a method due to Mortensen and Lavers [26], I show that we can dualize the internal logic of the effective topos, in order to obtain a model of paraconsistent computability theory. Since the dualization leaves the structural properties of universal constructions in the topos unchanged, in particular the properties of the natural numbers object, I conclude that, at least in this case, changing the logic does not change our characterization of computability.
Publisher
Oxford University Press (OUP)
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