Abstract
We have reasons to want an epistemology of simple belief in addition to the Bayesian notion of belief which admits of degree. Accounts of simple belief which attempt to reduce it to the notion of credence all face difficulties. We argue that each conception captures an important aspect of our pre-theoretic thinking about epistemology; the differences between the two accounts of belief stem from two different conceptions of unlikelihood. On the one hand there is unlikelihood in the sense of improbability, on the other hand there is unlikelihood in the sense of far-fetchedness. A non-reductive account of simple belief is outlined. Belief aims not just at truth, but at attaining the status of knowledge, and knowledge should satisfy the weak modal principle: If S knows that p then S is certain that there is no possibility very close to actuality at which p is false. The account faces a difficulty in dealing with statistical inductive cases. We sketch a speculative strategy for dealing with such cases, based on the pragmatic considerations that lead to an agent’s partition of the space of possibilities and a nonprobabilistic notion of the “estimated distance” of elements of such a partition from actuality.
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Notes
Leitgeb is a notable exception to the rule mentioned above. He does not assume that belief in the AGM sense requires Probability 1 and in Leitgeb (2017) develops a correspondence between AGM revision and Bayesian credence in which the former is allowed to model simple belief. He holds on to (i), (iii), and (iv) here. However Leitgeb violates assumption (ii): that the AGM ordering should be one of comparative far-fetchedness rather than something that captures likelihood in probabilistic terms. This can be seen most clearly from his “Outclassing Condition” p. 108 which states that for a proposition A to be P-stable, the least probable way for A to be true must be more probable than the negation of A. Since the nested P-stable propositions are precisely the ordered AGM fallback positions, this yields a probabilistic notion of comparative likelihood.
This example was suggested by an anonymous referee.
I am indebted here to an anonymous referee who pointed out an error in an earlier version of this reformulation of the Principle.
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Early versions of this material were presented as the Jerrold Katz Memorial Lecture at the CUNY Graduate Center on February 7, 2007, at the Synthese Annual Conference “Between Logic and Intuition: David Lewis and the Future of Formal Methods in Philosophy”, the Carlsberg Academy, Copenhagen, October 3, 2007, at “Another World is Possible: a Conference on the Work of David Lewis” at the University of Urbino, June 16–18, 2011, and at a Columbia Philosophy Work-in-Progess Seminar on March 6, 2014. My thanks to the audiences on those occasions and to two anonymous referees for this journal for insightful comments and criticism.
For the Synthese special issue on “The Legacy of David Lewis” edited by Marianna Antonutti and Pierluigi Graziani. Final version of February 9th, 2018.
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Collins, J. Simple belief. Synthese 197, 4867–4885 (2020). https://doi.org/10.1007/s11229-018-1746-3
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DOI: https://doi.org/10.1007/s11229-018-1746-3