By Dogeu D. (ed.), Lucaks E. (ed.), Rohatgi V.K. (ed.)
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Extra resources for Analytical Methods in Probability Theory: Proceedings
E. II. III Credences Although the classical idea that probabilities measure possibilities applies naturally to chances and epistemic probabilities, it does not apply at all to credences. To see why not, suppose that a coin toss is fair and known to be fair. That is, its chance of landing heads is known to be 1/2 and, relative to this evidence, B, the epistemic probability of the proposition A, that the toss will in fact land heads, is also 1/2. So if B is all I know about the coin toss, and if my belief in A comes by probabilistic degrees, then its degree – my credence in A – should also be 1/2.
For as I hinted at the end of chapter 2, frequentists cannot credibly claim that all frequencies are chances. Take the fact that six of the 38 FREQUENCIES nine major planets have orbits that are further from the sun than is the earth’s. No one will infer from this that major planets have a 2/3 chance of being further from the sun than we are. Frequentists must therefore distinguish frequencies that are chances from frequencies that are not. II, a Humean view of the statistical laws they occur in may well provide frequentists with the distinction they need.
This kind of possibility I shall call metaphysical and take to be measured by A’s chance of being true. The other reading of the claim that A may or may not be true is, in our example, that because we do not know how the coin toss lands, we do not know whether A is true. It is this epistemic kind of possibility that A’s epistemic probability, given whatever we do know, measures. This distinction, between metaphysical and epistemic possibilities, will be familiar to philosophers from other contexts.