Limits in the Revision Theory
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We present a new proposal for what to do at limits in the revision theory. The usual criterion for a limit stage is that it should agree with any definite verdicts that have been brought about before that stage. We suggest that one should not only consider definite verdicts that have been brought about but also more general properties; in fact any closed property can be considered. This more general framework is required if we move to considering revision theories for concepts that are concerned with real numbers, but also has consequences for more traditional revision theories such as the revision theory of truth.
KeywordsRevision theory Self-reference Circular definitions Taking limits Probability
I would like to thank Hannes Leitgeb, Johannes Stern, Seamus Bradley and Leon Horsten and for their helpful discussions and comments on versions of this paper. I am also very grateful to the organisers and participants at a number of conferences, including: Predicate Approaches to Modality, Munich; 45th meeting of the Society for Exact Philosophy, Caltech, Pasadena; Bristol-Leuven conference, Bristol; Logic Seminar, Cambridge; Bristol-München Conference on Truth and Rationality, Bristol.
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