The fundamental constants that are involved in the laws of physics which describe our universe are finely-tuned for life, in the sense that if some of the constants had slightly different values life could not exist. Some people hold that this provides evidence for the existence of God. I will present a probabilistic version of this fine-tuning argument which is stronger than all other versions in the literature. Nevertheless, I will show that one can have reasonable opinions such that the (...) fine-tuning argument doesn’t lead to an increase in one’s probability for the existence of God. (shrink)

I maintain, in defending “thirdism,” that Sleeping Beauty should do Bayesian updating after assigning the “preliminary probability” 1/4 to the statement S: “Today is Tuesday and the coin flip is heads.” (This preliminary probability obtains relative to a specific proper subset I of her available information.) Pust objects that her preliminary probability for S is really zero, because she could not be in an epistemic situation in which S is true. I reply that the impossibility of being in such an (...) epistemic situation is irrelevant, because relative to I, statement S nonetheless has degree of evidential support 1/4. (shrink)

In the 1970’s, a controversy arose about a probability problem posed by Irving Copi. One side argued that a common spontaneous intuition about the problem is correct; the other side argued that this intuition is mistaken. Here, I argue (1) that the naïve intuition yields the correct answer, but accidentally and for a wrong reason; (2) that a more reflective intuition yields a wrong answer, and hence, is also mistaken; and (3) that an even more reflective intuition yields the correct (...) answer for a correct reason. This warrants what I call optimistic fallibilism concerning intuitions about probability: although intuition is certainly prone to error in this domain, intuition has the capacity for self-correction. A naïve intuition that is mistaken can be replaced by a distinct, reflective intuition; and a reflective intuition that is mistaken can be replaced by another reflective intuition – with the process ultimately yielding a sound intuition. (shrink)

We present a new argument for the claim that in the Sleeping Beauty problem, the probability that the coin comes up heads is 1/3. Our argument depends on a principle for the updating of probabilities that we call ‘generalized conditionalization’, and on a species of generalized conditionalization we call ‘synchronic conditionalization on old information’. We set forth a rationale for the legitimacy of generalized conditionalization, and we explain why our new argument for thirdism is immune to two attacks that Pust (...) (Synthese 160:97–101, 2008) has leveled at other arguments for thirdism. (shrink)

Bayesian confirmation theory is our best formal framework for describing inductive reasoning. The problem of old evidence is a particularly difficult one for confirmation theory, because it suggests that this framework fails to account for central and important cases of inductive reasoning and scientific inference. I show that we can appeal to the fragmentation of doxastic states to solve this problem for confirmation theory. This fragmentation solution is independently well-motivated because of the success of fragmentation in solving other problems. I (...) also argue that the fragmentation solution is preferable to other solutions to the problem of old evidence. These other solutions are already committed to something like fragmentation, but suffer from difficulties due to their additional commitments. If these arguments are successful, Bayesian confirmation theory is saved from the problem of old evidence, and the argument for fragmentation is bolstered by its ability to solve yet another problem. (shrink)

Predictivism asserts that novel confirmations carry special probative weight. Epistemic pluralism asserts that the judgments of agents (about, e.g., the probabilities of theories) carry epistemic import. In this paper, I propose a new theory of predictivism that is tailored to pluralistic evaluators of theories. I replace the orthodox notion of use-novelty with a notion of endorsement-novelty, and argue that the intuition that predictivism is true has two roots. I provide a detailed Bayesian rendering of this theory and argue that pluralistic (...) theory evaluation pervades scientific practice. I compare my account of predictivism with those of Maher and Worrall. Introduction Why construction is a red herring for pluralist evaluators The unvirtuous accommodator Virtuous endorsers and the two roots of predictivism The two roots in Bayesian terms: the priors and background beliefs of endorsers Who are the pluralist evaluators? Two contemporary theories of predictivism 7.1 Maher: Reliable methods of theory construction 7.2 Worrall: The confirmation of core ideas Conclusion. (shrink)

It seems improbable that life would exist in a naturalistic universe. But if the universe were spatially infinite, then seemingly improbable events would be expected to happen; life would be expected to exist. It follows that the existence of life provides evidence that the universe is spatially infinite.