An objective Bayesian account of confirmation
This paper revisits Carnap's theory of degree of confirmation, identifies certain shortcomings, and argues that a new approach based on objective Bayesian epistemology can overcome these shortcomings.Rudolf Carnap can be thought of as one of the progenitors of Bayesian confirmation theory (§1). Bayesian confirmation theory is construed in §2 as a four-step process, the third step of which results in the identification of the degree to which e confirms h, c(h, e), with the probability of h conditional on e in the total absence of further evidence, P ø(h|e). The fourth step of this process involves isolating an appropriate candidate for P ø; Carnap rejected the most natural construal of P ø on the grounds that it leads to a confirmation function c † that fails to adequately capture the phenomenon of learning from experience (§3). This led him, and subsequent confirmation theorists, to more elaborate interpretations of P ø, resulting in certain continua of confirmation functions (§§4, 5). I argue in §§5, 6 that this was a wrong move: the original construal of P ø is in fact required in order that degree of confirmation can capture the phenomenon of partial entailment. There remains the problem of learning from experience. I argue that this problem is best solved by revisiting the third—rather than the fourth— step of the four-step Bayesian scheme (§7) and that objective Bayesianism, which is outlined in §8, offers the crucial insight as to how this step can be rectified. This leads to an objective Bayesian confirmation theory that can capture both partial entailment and learning from experience (§9).
Williamson, J. (2011)., An objective Bayesian account of confirmation, in D. Dieks, S. Hartmann, T. Uebel, M. Weber & W. J. González (eds.), Explanation, prediction, and confirmation, Dordrecht, Springer, pp. 53-81.
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