Tn this paper I explore and to an extent defend HS. The main philosophical challenges to HS come from philosophical views that say that nomic concepts-laws, chance, and causation-denote features of the world that fail to supervene on non-nomic features. Lewis rejects these views and has labored mightily to construct HS accounts of nomic concepts. His account of laws is fundamental to his program, since his accounts of the other nomic notions rely on it. Recently, a number of philosophers have (...) criticized Lewis's account, and Humean accounts of laws generally, for delivering, at best, a pale imitation ofthe genuine item. These philosophers think that the notion of law needed by science requires laws-if there are any-to be fundamental features of our world that are completely distinct from and not supervenient on the particular facts that they explain. I side with Lewis against these philosophers. Here I will argue that although Lewis-laws don't fulfill all our philosophical expectations, they do play the roles that science needs laws to play. The metaphysics and epistemology of Humean laws, and more specifically, Lewis-laws, are in much better shape than the metaphysics and epistemology of the main anti-Humean alternatives. However, I do have inisgivings about Lewis's account. Both he and his critics assume that the basic properties are so individuated so that the laws are not metaphysically necessary. If this assumption is rejected, then the question of Humean supervenience lapses. I conclude with a brief discussion of this position. (shrink)

_Anthropic Bias_ explores how to reason when you suspect that your evidence is biased by "observation selection effects"--that is, evidence that has been filtered by the precondition that there be some suitably positioned observer to "have" the evidence. This conundrum--sometimes alluded to as "the anthropic principle," "self-locating belief," or "indexical information"--turns out to be a surprisingly perplexing and intellectually stimulating challenge, one abounding with important implications for many areas in science and philosophy. There are the philosophical thought experiments and paradoxes: (...) the Doomsday Argument; Sleeping Beauty; the Presumptuous Philosopher; Adam & Eve; the Absent-Minded Driver; the Shooting Room. And there are the applications in contemporary science: cosmology ; evolutionary theory ; the problem of time's arrow ; quantum physics ; game-theory problems with imperfect recall ; even traffic analysis. _Anthropic Bias_ argues that the same principles are at work across all these domains. And it offers a synthesis: a mathematically explicit theory of observation selection effects that attempts to meet scientific needs while steering clear of philosophical paradox. (shrink)

We think we have lots of substantial knowledge about the future. But contemporary wisdom has it that indeterminism prevails in such a way that just about any proposition about the future has a non-zero objective chance of being false.2, 3 What should one do about this? One, pessimistic, reaction is scepticism about knowledge of the future. We think this should be something of a last resort, especially since this scepticism is likely to infect alleged knowledge of the present and past. (...) One anti-sceptical strategy is to pin our hopes on determinism, conceding that knowledge of the future is unavailable in an indeterministic world. This is not satisfying either: we would rather not be hostage to empirical fortune in the way that this strategy recommends. A final strategy, one that we shall explore in this paper, is one of reconciliation: knowledge of a proposition is compatible with a subject’s belief having a non-zero objective chance of error.4 Following Williamson, we are interested in tying knowledge to the presence or absence of error in close cases, and so we shall explore the connections between knowledge and objective chance within such a framework. We don’t want to get tangled up here in complications involved in attempting to formulate a necessary and sufficient condition for knowledge in terms of safety. Instead, we will assume the following rough and ready necessary condition: a subject knows P only if she could not easily have falsely believed P.5 Assuming that easiness is to be spelt.. (shrink)

Kolmogorov''s axiomatization of probability includes the familiarratio formula for conditional probability: 0).$$ " align="middle" border="0">.

Dr. Evil learns that a duplicate of Dr. Evil has been created. Upon learning this, how seriously should he take the hypothesis that he himself is that duplicate? I answer: very seriously. I defend a principle of indifference for self-locating belief which entails that after Dr. Evil learns that a duplicate has been created, he ought to have exactly the same degree of belief that he is Dr. Evil as that he is the duplicate. More generally, the principle shows that (...) there is a sharp distinction between ordinary skeptical hypotheses, and self-locating skeptical hypotheses. (shrink)

The pragmatic character of the Dutch book argument makes it unsuitable as an "epistemic" justification for the fundamental probabilist dogma that rational partial beliefs must conform to the axioms of probability. To secure an appropriately epistemic justification for this conclusion, one must explain what it means for a system of partial beliefs to accurately represent the state of the world, and then show that partial beliefs that violate the laws of probability are invariably less accurate than they could be otherwise. (...) The first task can be accomplished once we realize that the accuracy of systems of partial beliefs can be measured on a gradational scale that satisfies a small set of formal constraints, each of which has a sound epistemic motivation. When accuracy is measured in this way it can be shown that any system of degrees of belief that violates the axioms of probability can be replaced by an alternative system that obeys the axioms and yet is more accurate in every possible world. Since epistemically rational agents must strive to hold accurate beliefs, this establishes conformity with the axioms of probability as a norm of epistemic rationality whatever its prudential merits or defects might be. (shrink)

Our evidence can be about different subject matters. In fact, necessarily equivalent pieces of evidence can be about different subject matters. Does the hyperintensionality of ‘aboutness’ engender any hyperintensionality at the level of rational credence? In this paper, I present a case which seems to suggest that the answer is ‘yes’. In particular, I argue that our intuitive notions of independent evidence and inadmissible evidence are sensitive to aboutness in a hyperintensional way. We are thus left with a paradox. While (...) there is strong reason to think that rational credence cannot make such hyperintensional distinctions, our intuitive judgements about certain cases seem to demand that it does. (shrink)

Karl Raimund Poppers (1902-1994) Hauptwerk, die Logik der Forschung (1934), gilt als Grundlagenwerk des kritischen Rationalismus. Der kritische Rationalismus zeigt, warum unser Wissen fehlbar ist und versteht den Erkenntnisfortschritt als Resultat von Hypothesenbildung und -widerlegung. Der Sammelband orientiert sich an der Gliederung der Logik der Forschung. Seine Beiträge kommentieren die jeweiligen Themen nach aktueller Forschungslage.

We develop a Bayesian framework for thinking about the way evidence about the here and now can bear on hypotheses about the qualitative character of the world as a whole, including hypotheses according to which the total population of the world is infinite. We show how this framework makes sense of the practice cosmologists have recently adopted in their reasoning about such hypotheses.

The standard treatment of conditional probability leaves conditional probability undefined when the conditioning proposition has zero probability. Nonetheless, some find the option of extending the scope of conditional probability to include zero-probability conditions attractive or even compelling. This article reviews some of the pitfalls associated with this move, and concludes that, for the most part, probabilities conditional on zero-probability propositions are more trouble than they are worth.

It is well known that de se (or ‘self-locating’) propositions complicate the standard picture of how we should respond to evidence. This has given rise to a substantial literature centered around puzzles like Sleeping Beauty, Dr. Evil, and Doomsday—and it has also sparked controversy over a style of argument that has recently been adopted by theoretical cosmologists. These discussions often dwell on intuitions about a single kind of case, but it’s worth seeking a rule that can unify our treatment of (...) all evidence, whether de dicto or de se. -/- This paper is about three candidates for such a rule, presented as replacements for the standard updating rule. Each rule stems from the idea that we should treat ourselves as a random sample, a heuristic that underlies many of the intuitions that have been pumped in treatments of the standard puzzles. But each rule also yields some strange results when applied across the board. This leaves us with some difficult options. We can seek another way to refine the random-sample heuristic, e.g. by restricting one of our rules. We can try to live with the strange results, perhaps granting that useful principles can fail at the margins. Or we can reject the random-sample heuristic as fatally flawed—which means rethinking its influence in even the simplest cases. (shrink)

_Anthropic Bias_ explores how to reason when you suspect that your evidence is biased by "observation selection effects"--that is, evidence that has been filtered by the precondition that there be some suitably positioned observer to "have" the evidence. This conundrum--sometimes alluded to as "the anthropic principle," "self-locating belief," or "indexical information"--turns out to be a surprisingly perplexing and intellectually stimulating challenge, one abounding with important implications for many areas in science and philosophy. There are the philosophical thought experiments and paradoxes: (...) the Doomsday Argument; Sleeping Beauty; the Presumptuous Philosopher; Adam & Eve; the Absent-Minded Driver; the Shooting Room. And there are the applications in contemporary science: cosmology ; evolutionary theory ; the problem of time's arrow ; quantum physics ; game-theory problems with imperfect recall ; even traffic analysis. _Anthropic Bias_ argues that the same principles are at work across all these domains. And it offers a synthesis: a mathematically explicit theory of observation selection effects that attempts to meet scientific needs while steering clear of philosophical paradox. (shrink)

Let κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti and Dubins, subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-­additive has conditional probabilities that fail to be conglomerable in a partition of cardinality no greater than κ. This generalizes our result, where we established that each finite but not countably additive probability has (...) conditional probabilities that fail to be conglomerable in some countable partition. (shrink)

We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as 'Trumped' (Arntzenius and McCarthy 1997), 'Rouble trouble' (Arntzenius and Barrett 1999), 'The airtight Dutch book' (McGee 1999), and 'The two envelopes puzzle' (Broome 1995). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably (...) additive. The resolution also shows that when infinitely many decisions are involved, the difference between making the decisions simultaneously and making them sequentially can be the difference between riches and ruin. Finally, the resolution reveals a new way in which the ability to make binding commitments can save perfectly rational agents from sure losses. (shrink)

The Eternal Coin is a fair coin has existed forever, and will exist forever, in a region causally isolated from you. It is tossed every day. How confident should you be that the Coin lands heads today, conditional on (i) the hypothesis that it has landed Heads on every past day, or (ii) the hypothesis that it will land Heads on every future day? I argue for the extremely counterintuitive claim that the correct answer to both questions is 1.