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Kolmogorov’s Axiomatization and Its Discontents

In Alan Hájek & Christopher Hitchcock (eds.), The Oxford Handbook of Probability and Philosophy. Oxford: Oxford University Press (2016)

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  1. Bertrand’s Paradox and the Principle of Indifference.Nicholas Shackel - 2024 - Abingdon: Routledge.
    Events between which we have no epistemic reason to discriminate have equal epistemic probabilities. Bertrand’s chord paradox, however, appears to show this to be false, and thereby poses a general threat to probabilities for continuum sized state spaces. Articulating the nature of such spaces involves some deep mathematics and that is perhaps why the recent literature on Bertrand’s Paradox has been almost entirely from mathematicians and physicists, who have often deployed elegant mathematics of considerable sophistication. At the same time, the (...)
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  • Accuracy and infinity: a dilemma for subjective Bayesians.Mikayla Kelley & Sven Neth - 2023 - Synthese 201 (12):1-14.
    We argue that subjective Bayesians face a dilemma: they must offend against the spirit of their permissivism about rational credence or reject the principle that one should avoid accuracy dominance.
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  • Why Perceptual Experiences cannot be Probabilistic.Matteo Colombo & Nir Fresco - forthcoming - Philosophical Quarterly.
    Perceptual Confidence is the thesis that perceptual experiences can be probabilistic. This thesis has been defended and criticised based on a variety of phenomenological, epistemological, and explanatory arguments. One gap in these arguments is that they neglect the question of whether perceptual experiences satisfy the formal conditions that define the notion of probability to which Perceptual Confidence is committed. Here, we focus on this underexplored question and argue that perceptual experiences do not satisfy such conditions. But if they do not, (...)
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