The best arguments for the 1/3 answer to the Sleeping Beauty problem all require that when Beauty awakes on Monday she should be uncertain what day it is. I argue that this claim should be rejected, thereby clearing the way to accept the 1/2 solution.

Statistical evidence—say, that 95% of your co-workers badmouth each other—can never render resenting your colleague appropriate, in the way that other evidence (say, the testimony of a reliable friend) can. The problem of statistical resentment is to explain why. We put the problem of statistical resentment in several wider contexts: The context of the problem of statistical evidence in legal theory; the epistemological context—with problems like the lottery paradox for knowledge, epistemic impurism and doxastic wrongdoing; and the context of a (...) wider set of examples of responses and attitudes that seem not to be appropriately groundable in statistical evidence. Regrettably, we do not come up with a fully general, fully adequate, fully unified account of all the phenomena discussed. But we give reasons to believe that no such account is forthcoming, and we sketch a somewhat messier account that may be the best that can be had here. (shrink)

The principle of epistemic closure is the claim that what is known to follow from knowledge is known to be true. This intuitively plausible idea is endorsed by a vast majority of knowledge theorists. There are significant problems, however, that have to be addressed if epistemic closure – closed knowledge – is endorsed. The present essay locates the problem for closed knowledge in the separation it imposes between knowledge and evidence. Although it might appear that all that stands between knowing (...) the truth of the premises of a valid inference and knowledge of its conclusion is inferring it from the premises, the evidence for each of the premises may jointly count against the conclusion. The intuitive view regarding inferred knowledge says one thing, the evidence says another. One epistemological framework that seems to have the resources to resolve this tension endorses the view that knowledge always requires conclusive evidence. A second framework resolves the tension by limiting the scope of the closure principle. Only inferences drawn directly from propositions contained in the scope of a single knowledge operator are considered closed. The aim of the present essay is to revive the unpopular third option, the idea that knowledge is open. The essay proceeds by arguing that in different ways the two former frameworks only succeed in relocating the problem, not in resolving it. The first framework, the infallibilist view, relocates the problem to a sharp separation between knowledge of the occurrences of events from knowledge of their chance of occurring, a separation leading to several significant additional problems. The fallibilist view, the second framework, in endorsing closure neglects to take into full account the ways in which evidence fails to be transitive. For instance, evidence can count in favor of a conjunction while counting against each of its conjuncts. This fact, which is argued for in the essay on probabilistic as well as non-probabilistic grounds, is used as the foundation of an argument against closed knowledge that can be used as a way to understand several of the most fundamental challenges of epistemology. Not only can an open knowledge view that is based on open evidence resolve all these problems in a simple and natural way, it can also respond to formidable challenges that significantly hinder other open knowledge views. There are good reasons, then, to view both knowledge and evidence as open. (shrink)

The Sleeping Beauty problem remains controversial with disagreement between so-called Halfers and Thirders, although the Thirders appear to be leading these days. I analyze three popular arguments for the Thirder position, including the long-run frequency argument, Egla’s ‘symmetry’ argument, and new-information arguments, and find problems with each. The long-run frequency argument is almost unequivocally thought to strongly support Thirders, but in formalizing the argument for an arbitrary number of repetitions, I show that the expected proportion of Heads-Awakenings for a single-trial (...) experiment is unambiguously 1/2. My criticisms of Elga’s symmetry argument and the new-information arguments point to subtle misalignments between the narrative/causal description of thought-experiments and the mathematical probability expressions and theory we use to describe these narratives. I end with distinguishing two varieties of possibility—a dynamic forward type and static historical type—that help clarify the Sleeping Beauty problem, nullify the main criticism against Lewis’s Halfer argument, and have applicability to probability theory in general. (shrink)

People are often offended by beliefs, expect apologies for beliefs, apologize for their own beliefs. In many mundane cases, people are morally criticized for their beliefs. Intuitively, then, beliefs seem to sometimes wrong people. Recently, the philosophical literature has picked up on this theme, and has started to discuss it under the heading of doxastic wrongdoing. In this paper we argue that despite the strength of such initial intuitions, at the end of the day they have to be rejected. If (...) it can be ever truthfully asserted that beliefs wrong, this is always derivative – beliefs wrong only in virtue of other things (like evidence-gathering actions) wronging. We distinguish between modest and ambitious doxastic wrongdoing theories (the former deny, while the latter accept, the possibility of a morally wrong yet epistemically permissible belief); we argue that each of these options faces insurmountable problems; and we offer partly debunking explanations of the intuitions purportedly supporting doxastic wrongdoing. (shrink)

A large number of essays address the Sleeping Beauty problem, which undermines the validity of Bayesian inference and Bas Van Fraassen's 'Reflection Principle'. In this study a straightforward analysis of the problem based on probability theory is presented. The key difference from previous works is that apart from the random experiment imposed by the problem's description, a different one is also considered, in order to negate the confusion on the involved conditional probabilities. The results of the analysis indicate that no (...) inconsistency takes place, whereas both Bayesian inference and 'Reflection Principle' are valid. (shrink)