The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. _Philosophical Theories of Probability_ is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.

Objective Bayesianism is a methodological theory that is currently applied in statistics, philosophy, artificial intelligence, physics and other sciences. This book develops the formal and philosophical foundations of the theory, at a level accessible to a graduate student with some familiarity with mathematical notation.

:A normative Bayesian theory of deliberation and judgement requires a procedure for merging the evidence of a collection of agents. In order to provide such a procedure, one needs to ask what the evidence is that grounds Bayesian probabilities. After finding fault with several views on the nature of evidence, it is argued that evidence is whatever is rationally taken for granted. This view is shown to have consequences for an account of merging evidence, and it is argued that standard (...) axioms for merging need to be altered somewhat. (shrink)

We are prone to gross error, even in favorable circumstances of extended reflection, about our own ongoing conscious experience, our current phenomenology. Even in this apparently privileged domain, our self-knowledge is faulty and untrustworthy. We are not simply fallible at the margins but broadly inept. Examples highlighted in this essay include: emotional experience (for example, is it entirely bodily; does joy have a common, distinctive phenomenological core?), peripheral vision (how broad and stable is the region of visual clarity?), and the (...) phenomenology of thought (does it have a distinctive phenomenology, beyond just imagery and feelings?). Cartesian skeptical scenarios undermine knowledge of ongoing conscious experience as well as knowledge of the outside world. Infallible judgments about ongoing mental states are simply banal cases of self-fulfillment. Philosophical foundationalism supposing that we infer an external world from secure knowledge of our own consciousness is almost exactly backward. (shrink)

To believe is to possess a wide variety of dispositions pertinent to the proposition believed. Among those dispositions are self-ascriptive dispositions. Consequently, being disposed to self-ascribe belief that P is partly constitutive of believing that P. Such self-ascriptive dispositions can be underwritten by any of a variety of mechanisms, acting co-operatively or competitively. But since self-ascriptive dispositions are only partly constitutive of belief, there can be cases in which the self-ascriptive dispositions splinter away from the remaining dispositions. It is then (...) an empirical question how often our self-ascriptive dispositions diverge from the remaining dispositions constitutive of belief. The dispositions will tend to align reliably when possession of the belief in question is normatively neutral, straightforwardly connected to behavior, and most centrally manifested in explicit assertions or judgments. When these three conditions are not met, self-ascription, self-conscious avowal, sincere utterance, and explicit judgment will often diverge from the various other dispositions constitutive of belief. Even self-knowledge of explicit judgment can be problematic when we are attracted to half-empty forms of words or when we are not entirely persuaded of what we are saying. (shrink)

For any proposition P, it may sometimes occur that a person is not quite accurately describable as believing that P, nor quite accurately describable as failing to believe that P. Such a person, I will say, is in an "in-between state of belief." This paper argues for the prevalence of in-between states of believing and asserts the need for an account of belief that allows us intelligibly to talk about in-between believing. It is suggested that Bayesian and representationalist approaches are (...) inadequate to the task and that a Rylean dispositional account of belief might do the trick. (shrink)

This paper describes and defends in detail a novel account of belief, an account inspired by Ryle's dispositional characterization of belief, but emphasizing irreducibly phenomenal and cognitive dispositions as well as behavioral dispositions. Potential externalist and functionalist objections are considered, as well as concerns motivated by the inevitably ceteris paribus nature of the relevant dispositional attributions. It is argued that a dispositional account of belief is particularly well-suited to handle what might be called "in-between" cases of believing - cases in (...) which it is neither quite right to describe a person as having a particular belief nor quite right to describe her as lacking it. (shrink)

Is it possible to give an explicit definition of belief in terms of subjective probability, such that believed propositions are guaranteed to have a sufficiently high probability, and yet it is neither the case that belief is stripped of any of its usual logical properties, nor is it the case that believed propositions are bound to have probability 1? We prove the answer is ‘yes’, and that given some plausible logical postulates on belief that involve a contextual “cautiousness” threshold, there (...) is but one way of determining the extension of the concept of belief that does the job. The qualitative concept of belief is not to be eliminated from scientific or philosophical discourse, rather, by reducing qualitative belief to assignments of resiliently high degrees of belief and a “cautiousness” threshold, qualitative and quantitative belief turn out to be governed by one unified theory that offers the prospects of a huge range of applications. Within that theory, logic and probability theory are not opposed to each other but go hand in hand. (shrink)

I introduce and argue for the importance of a cognitive state that I call alief. An alief is, to a reasonable approximation, an innate or habitual propensity to respond to an apparent stimulus in a particular way. Recognizing the role that alief plays in our cognitive repertoire provides a framework for understanding reactions that are governed by nonconscious or automatic mechanisms, which in turn brings into proper relief the role played by reactions that are subject to conscious regulation and deliberate (...) control. (shrink)

Forthcoming, Journal of Philosophy [pdf manuscript].

Probabilism is committed to two theses: 1) Opinion comes in degrees—call them degrees of belief, or credences. 2) The degrees of belief of a rational agent obey the probability calculus. Correspondingly, a natural way to argue for probabilism is: i) to give an account of what degrees of belief are, and then ii) to show that those things should be probabilities, on pain of irrationality. Most of the action in the literature concerns stage ii). Assuming that stage i) has been (...) adequately discharged, various authors move on to stage ii) with varied and ingenious arguments. But an unsatisfactory response at stage i) clearly undermines any gains that might be accrued at stage ii) as far as probabilism is concerned: if those things are not degrees of belief, then it is irrelevant to probabilism whether they should be probabilities or not. In this paper we scrutinize the state of play regarding stage i). We critically examine several of the leading accounts of degrees of belief: reducing them to corresponding betting behavior (de Finetti); measuring them by that behavior (Jeffrey); and analyzing them in terms of preferences and their role in decision-making more generally (Ramsey, Lewis, Maher). We argue that the accounts fail, and so they are unfit to subserve arguments for probabilism. We conclude more positively: ‘degree of belief’ should be taken as a primitive concept that forms the basis of our best theory of rational belief and decision: probabilism. (shrink)

"This is an important new Cummins work.

It is well known that classical, aka ‘sharp’, Bayesian decision theory, which models belief states as single probability functions, faces a number of serious difficulties with respect to its handling of agnosticism. These difficulties have led to the increasing popularity of so-called ‘imprecise’ models of decision-making, which represent belief states as sets of probability functions. In a recent paper, however, Adam Elga has argued in favour of a putative normative principle of sequential choice that he claims to be borne out (...) by the sharp model but not by any promising incarnation of its imprecise counterpart. After first pointing out that Elga has fallen short of establishing that his principle is indeed uniquely borne out by the sharp model, I cast aspersions on its plausibility. I show that a slight weakening of the principle is satisfied by at least one, but interestingly not all, varieties of the imprecise model and point out that Elga has failed to motivate his stronger commitment. (shrink)

When a doctor tells you there’s a one percent chance that an operation will result in your death, or a scientist claims that his theory is probably true, what exactly does that mean? Understanding probability is clearly very important, if we are to make good theoretical and practical choices. In this engaging and highly accessible introduction to the philosophy of probability, Darrell Rowbottom takes the reader on a journey through all the major interpretations of probability, with reference to real–world situations. (...) In lucid prose, he explores the many fallacies of probabilistic reasoning, such as the ‘gambler’s fallacy’ and the ‘inverse fallacy’, and shows how we can avoid falling into these traps by using the interpretations presented. He also illustrates the relevance of the interpretation of probability across disciplinary boundaries, by examining which interpretations of probability are appropriate in diverse areas such as quantum mechanics, game theory, and genetics. Using entertaining dialogues to draw out the key issues at stake, this unique book will appeal to students and scholars across philosophy, the social sciences, and the natural sciences. (shrink)

Why does one theory "succeed" while another, possibly clearer interpretation, fails? By exploring two observationally equivalent yet conceptually incompatible views of quantum mechanics, James T. Cushing shows how historical contingency can be crucial to determining a theory's construction and its position among competing views. Since the late 1920s, the theory formulated by Niels Bohr and his colleagues at Copenhagen has been the dominant interpretation of quantum mechanics. Yet an alternative interpretation, rooted in the work of Louis de Broglie in the (...) early 1920s and reformulated and extended by David Bohm in the 1950s, equally well explains the observational data. Through a detailed historical and sociological study of the physicists who developed different theories of quantum mechanics, the debates within and between opposing camps, and the receptions given to each theory, Cushing shows that despite the preeminence of the Copenhagen view, the Bohm interpretation cannot be ignored. Cushing contends that the Copenhagen interpretation became widely accepted not because it is a better explanation of subatomic phenomena than is Bohm's, but because it happened to appear first. Focusing on the philosophical, social, and cultural forces that shaped one of the most important developments in modern physics, this provocative book examines the role that timing can play in the establishment of theory and explanation. (shrink)

In this paper, I argue that the method of transparency --determining whether I believe that p by considering whether p -- does not explain our privileged access to our own beliefs. Looking outward to determine whether one believes that p leads to the formation of a judgment about whether p, which one can then self-attribute. But use of this process does not constitute genuine privileged access to whether one judges that p. And looking outward will not provide for access to (...) dispositional beliefs, which are arguably more central examples of belief than occurrent judgments. First, one’s dispositional beliefs as to whether p may diverge from the occurrent judgments generated by the method of transparency. Second, even in cases where these are reliably linked — e.g., in which one’s judgment that p derives from one’s dispositional belief that p — using the judgment to self-attribute the dispositional belief requires an ‘inward’ gaze. (shrink)

When a doctor tells you there’s a one percent chance that an operation will result in your death, or a scientist claims that his theory is probably true, what exactly does that mean? Understanding probability is clearly very important, if we are to make good theoretical and practical choices. In this engaging and highly accessible introduction to the philosophy of probability, Darrell Rowbottom takes the reader on a journey through all the major interpretations of probability, with reference to real–world situations. (...) In lucid prose, he explores the many fallacies of probabilistic reasoning, such as the ‘gambler’s fallacy’ and the ‘inverse fallacy’, and shows how we can avoid falling into these traps by using the interpretations presented. He also illustrates the relevance of the interpretation of probability across disciplinary boundaries, by examining which interpretations of probability are appropriate in diverse areas such as quantum mechanics, game theory, and genetics. Using entertaining dialogues to draw out the key issues at stake, this unique book will appeal to students and scholars across philosophy, the social sciences, and the natural sciences. (shrink)

Neo-Cartesian approaches to belief place greater evidential weight on a subject's introspective judgments than do neo-behaviorist accounts. As a result, the two views differ on whether our absent-minded and weak-willed actions are guided by belief. I argue that simulationist accounts of the concept of belief are committed to neo-Cartesianism, and, though the conceptual and empirical issues that arise are inextricably intertwined, I discuss experimental results that should point theory-theorists in that direction as well. Belief is even less closely connected to (...) behaviour than most contemporary functionalists allow. (shrink)