Recent work has focussed on tensions between the Principle of Indifference and imprecise probabilities (Rinard 2014 White 2010) and self-locating beliefs (Marcoci 2020). Present-day proponents simply accept that uncertain inference depends on the choice of an appropriate state space (Paris 2014 Halpern and Koller 2004 Novack 2010 Williamson 2010) and point out that the principle is consistent under uniform refinements of the underlying state space (Paris 2006). One often-voiced criticism of the Principle of Indifference is that it results in contradictions when the underlying state space is changed (Seidenfeld 1987 Norton 2019). This result is surprising because it suggests that the Principal Principle requires an objective Bayesian framework (in which degrees of belief are highly constrained in the absence of relevant evidence) rather than the usual subjective Bayesian framework, and because the Principle of Indifference is much more controversial than the Principal Principle. ( 2017), which shows that, given certain auxiliary conditions about the admissibility of additional information, the Principal Principle implies a version of the Principle of Indifference: it implies that a contingent atomic proposition should be believed to degree 12, in the absence of evidence that bears on that proposition. In this paper, we pick up on the argument of Hawthorne et al. A number of other chance-credence calibration principles have been proposed (Hall 1994 Vranas 2004). Further topics of interest have included the notion of admissibility (Meacham 2010) and the relation between the Principal Principle and Humeanism (Black 1998). Some researchers have identified problems with the principle: for example, it has been argued that the Principal Principle conflicts with the requirement to have accurate degrees of belief (Easwaran and Fitelson 2012) and that it creates tensions with the claim that conditional beliefs are conditional probabilities (Wallmann and Hawthorne 2018 Wallmann and Williamson 2020). There has been a lot of interesting work on the Principal Principle in recent years. The most prominent of these principles, David Lewis’ Principal Principle, says that one ought to believe a proposition A, conditional on the chance of A being x and other admissible information, to degree x. Bayesian epistemology captures such claims by means of principles of rationality that link degrees of belief to objective probabilities (often called chances). For example, if a coin will be tossed and the coin is a fair coin, according to our evidence, then we ought to be equally confident that it will land heads as tails. Our personal beliefs should be responsive to our evidence.
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