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You’ve Come a Long Way, Bayesians

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Notes

  1. This is one area where the founding editor-in-chief of this journal did influential work: [82].

  2. They gave this result a very different, pragmatic interpretation though.

  3. Joyce asserts that the restriction to a partition can be dropped, but does not prove this in the paper.

  4. I would add that an opponent of Probabilism might well reject the Principal Principle as standardly formulated. She might prefer to explicate the dictum that one’s credences should reflect known chances other than by just having one’s credences line up with those chances numerically.

  5. See [6, 7, 18, 21] for other criticisms of Joyce’s overall approach.

  6. This happens when the available evidence doesn’t point to any individual possibility specifically, even though it perhaps points to pairs of them, triples, etc.

  7. Authors who base their Bayesianism on representation theorems may have other motivations for embracing imprecise credences [33, 35].

  8. Other proposals are on offer. Elga groups these under various rubrics and argues that each group only escapes his argument at unacceptable cost. Chandler [9] replies that one proposal, the Γ-maximin rule, satisfies an appealing standard that is slightly weaker than the one Elga’s argument assumes. Bradley & Steele [2] argue that Γ-maximin nevertheless faces other problems raised in [74] and [79].

  9. See [85] for more on this dialectic.

  10. Consider what Elga’s argument would prove about an agent only capable of on/off beliefs, whose evidence justified neither believing nor rejecting H.

  11. See [32, §9] for a fuller catalogue of motivations.

  12. That is, a proposition’s unconditional probability can lie outside the span of its conditional probabilities across a partition.

  13. See [32] for a different argument in this “arms-race” style.

  14. See [22] for some additional benefits for our definition of independence.

  15. Pryor [68] highlights some assumptions tacit in this argument.

  16. The bootstrapping problem first arose as a challenge for reliabilist theories of knowledge [26, 86], but as we see here it is generalizable into a paradox that makes trouble much more broadly [55, 93, 94].

  17. See Douven [13] for a general study of the intransitivity of probabilistic support.

  18. Another promising approach we haven’t space to explore: you ought to believe P if (roughly) doing so maximizes expected epistemic utility [25, 38, 44, 46, 49].

  19. Cf. also Weatherson [89] and Ross & Schroeder [70], though Weatherson argues that a decision table should only be shaped by beliefs constituting knowledge.

  20. See [5] for a very different, novel view of the respective roles of full and partial belief.

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  1. Department of Philosophy, University of Toronto, Toronto, Canada

    Jonathan Weisberg

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Correspondence to Jonathan Weisberg.

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This article is dedicated to the memory of Herbert Weisberg, for whom the last forty years were dedicated to family. Thanks to Kristen Aspevig, Kenny Easwaran, Franz Huber, and Alexander Pruss for much helpful discussion.

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Weisberg, J. You’ve Come a Long Way, Bayesians. J Philos Logic 44, 817–834 (2015). https://doi.org/10.1007/s10992-015-9363-9

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