Kant's notion of ‘discipline’ has received considerable attention from scholars of his philosophy of education, but its role in his theoretical philosophy has been largely ignored. This omission is surprising since his discussion of discipline in the first Critique is not only more extensive and expansive in scope than his other discussions but also predates them. The goal of this essay is to provide a comprehensive reading of the Discipline that emphasizes its systematic importance in the first Critique. I argue (...) that its goal is to establish a set of rules for the use of pure reason that, if followed, will mitigate and perhaps even eliminate our tendency to make judgments about supersensible objects. Since Kant's justification for these rules relies crucially on claims he has defended in the Doctrine of Elements, I argue further that, far from being a dispensable part of the Critique as commentators have tended to claim, the Discipline is, in fact, the culmination of Kant's critique of metaphysics. (shrink)

Hume’s account of causation is often regarded a challenge Kant must overcome if the Critical philosophy is to be successful. But from Kant’s time to the present, Hume’s denial of our ability to cognize supersensible objects, a denial that relies heavily on his account of causation, has also been regarded as a forerunner to Kant’s critique of metaphysics. After identifying reasons for rejecting Wayne Waxman’s recent account of Kant’s debt to Hume, I present my own, more modest account of this (...) debt, an account that seeks to unite the two very different pictures of Kant’s relationship to Hume sketched above. (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)

Lewis’s Principal Principle says that one should usually align one’s credences with the known chances. In this paper I develop a version of the Principal Principle that deals well with some exceptional cases related to the distinction between metaphysical and epistemic modal­ity. I explain how this principle gives a unified account of the Sleeping Beauty problem and chance-­based principles of anthropic reasoning. In doing so, I defuse the Doomsday Argument that the end of the world is likely to be (...) nigh. GPI Working Paper No. 8-2021. (shrink)

Every metaphysical system must take something as fundamental and unanalyzed, something to which everything else ultimately reduces. Most philosophers today prefer to conceive fundamental reality as non-mental and categorical. This leaves them seeking to reduce the mental to the non-mental and the dispositional to the categorical. Pelczar proposes to invert this picture, putting experience and chance at the foundation and attempting to explain the non-mental and categorical features of our world in their terms. The resulting view, which he calls (...) phenomenalism, takes physical objects to be possibilities (or tendencies) for experience. (shrink)

A principle endorsed by many theories of objective chance, and practically forced on us by the standard interpretation of the Kolmogorov semantics for chance, is the principle that when a proposition P has a chance, any proposition Q that is necessarily equivalent to P will have the same chance as P. Call this principle SUB (for the substitution of necessary equivalents into chance ascriptions). I will present some problems for a theory of chance, (...) and will argue that the best way to resolve these problems is to reject SUB, and similar principles e.g. for the chances of outcomes or the chances of events. Objective chance, it turns out, carves things more finely than necessary equivalence does. (shrink)

We offer a new argument for the claim that there can be non-degenerate objective chance (“true randomness”) in a deterministic world. Using a formal model of the relationship between different levels of description of a system, we show how objective chance at a higher level can coexist with its absence at a lower level. Unlike previous arguments for the level-specificity of chance, our argument shows, in a precise sense, that higher-level chance does not collapse (...) into epistemic probability, despite higher-level properties supervening on lower-level ones. We show that the distinction between objective chance and epistemic probability can be drawn, and operationalized, at every level of description. There is, therefore, not a single distinction between objective and epistemic probability, but a family of such distinctions. (shrink)

I argue that there are non-trivial objective chances (that is, objective chances other than 0 and 1) even in deterministic worlds. The argument is straightforward. I observe that there are probabilistic special scientific laws even in deterministic worlds. These laws project non-trivial probabilities for the events that they concern. And these probabilities play the chance role and so should be regarded as chances as opposed, for example, to epistemic probabilities or credences. The supposition of non-trivial deterministic chances (...) might seem to land us in contradiction. The fundamental laws of deterministic worlds project trivial probabilities for the very same events that are assigned non-trivial probabilities by the special scientific laws. I argue that any appearance of tension is dissolved by recognition of the level-relativity of chances. There is therefore no obstacle to accepting non-trivial chance-role-playing deterministic probabilities as genuine chances. (shrink)

This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible (...) to randomly pick out a point on a continuum, for instance using a roulette wheel or by flipping a countable infinity of fair coins, it follows, given the axioms of ZFC, that there are many different cardinalities between countable infinity and the cardinality of the continuum. (shrink)

The most familiar philosophical conception of objective chance renders determinism incompatible with non-trivial chances. This conception – associated in particular with the work of David Lewis – is not a good fit with our use of the word ‘chance’ and its cognates in ordinary discourse. In this paper we show how a generalized framework for chance can reconcile determinism with non-trivial chances, and provide for a more charitable interpretation of ordinary chance-talk. According to our proposal, (...) variation in an admissible ‘evidence base’ generates a spectrum of different chance functions. Successive coarse-grainings of the evidence base generates a partial ordering of chance functions, with finer trumping coarser if known. We suggest that chance-attributions in ordinary discourse express different chance functions in different contexts, and we sketch a potential contextual mechanism for making particular chance functions salient. The mechanism involves the idea that admissible evidence is available evidence: propositions that could be known. A consequence is that attributions of objective chances inherit the relatively familiar context-sensitivity associated with the modal ‘could’. We show how this context-dependency undermines certain arguments for the incompatibility of chance with determinism. (shrink)

What explains the outcomes of chance processes? We claim that their setups do. Chances, we think, mediate these explanations of outcome by setup but do not feature in them. Facts about chances do feature in explanations of a different kind: higher-order explanations, which explain how and why setups explain their outcomes. In this paper, we elucidate this 'mediator view' of chancy explanation and defend it from a series of objections. We then show how it changes the playing field in (...) four metaphysical disputes concerning chance. First, it makes it more plausible that even low chances can have explanatory power. Second, it undercuts a circularity objection against reductionist theories of chance. Third, it redirects the debate about a prominent argument against epistemic theories of chance. Finally, it sheds light on potential chancy explanations of the Universe's origin. (shrink)

Are mandatory lockdown measures, which place restrictions on one’s freedom to move and assemble, justifiable? Offhand, such measures appear to compromise important rights to secure goals of public health. Proponents of such measures think the trade-off is worth it; opponents think it isn’t. However, one might think that casting the debate in these terms concedes too much to the opponents. Mandatory lockdown measures don’t infringe important rights because no one has a right to impose a risk of grievous harm on (...) others—and, in the context of a pandemic, participating in the prohibited activities (e.g., going out to the bar) does just that. -/- This chapter explores whether this defense of mandatory lockdown measures holds up. It, first, considers whether we have a right against risk imposition—and, if so, how such a right is best understood. It then considers the objection that, even if there is such a right, people who voluntarily choose to engage in the prohibited activities—at least if fully appraised of the risks involved—effectively waive it. The chapter argues that this objection fails. (shrink)

This chapter focuses on the relations between objective probabilities in physical theories at different levels. In general philosophy of probability, it is frequently assumed that a fundamental deterministic theory cannot support probabilistic phenomena at any higher level, or more generally that there cannot be non-trivial probabilities in higher-level theories that are not encoded in probabilities at the lower level. These assumptions face significant challenges from some well-understood physical theories – I focus on statistical mechanics and Bohmian mechanics – where (...) a deterministic description at some lower level gives rise to an effectively probabilistic theory at some higher level; in each case, constraints arising from an objective physical limitation on the acquisition of evidence concerning the lower level plays a crucial role in supporting the higher-level probabilities. (shrink)

The scarcity of livers available for transplants forces tough choices upon us. Lives for those not receiving a transplant are likely to be short. One large group of potential recipients needs a new liver because of alcohol consumption, while others suffer for reasons unrelated to their own behaviour. Should the former group receive lower priority when scarce livers are allocated? This discussion connects with one of the most pertinent issues in contemporary political philosophy; the role of personal responsibility in distributive (...) justice. One prominent theory of distributive justice, luck egalitarianism, assesses distributions as just if, and only if, people's relative positions reflect their exercises of responsibility. There is a principled luck egalitarian case for giving lower priority to those who are responsible for their need. Compared to the existing literature favouring such differentiation, luck egalitarianism provides a clearer rationale of fairness, acknowledges the need for individual assessments of responsibility, and requires initiatives both inside and outside of the allocation systems aimed at mitigating the influence from social circumstances. Furthermore, the concrete policies that luck egalitarians can recommend are neither too harsh on those who make imprudent choices nor excessively intrusive towards those whose exercises of responsibility are assessed. (shrink)

There is widespread excitement in the literature about the method of arbitrary functions: many take it to show that it is from the dynamics of systems that the objectivity of probabilities emerge. In this paper, I differentiate three ways in which a probability function might be objective, and I argue that the method of arbitrary functions cannot help us show that dynamics objectivise probabilities in any of these senses.

According to Humean theories of objective chance, the chances reduce to patterns in the history of occurrent events, such as frequencies. According to non-Humean accounts, the chances are metaphysically fundamental, existing independently of the "Humean Mosaic" of actually-occurring events. It is therefore possible, by the lights of non-Humeanism, for the chances and the frequencies to diverge wildly. Humeans often allege that this undermines the ability of non-Humean accounts of chance to rationalize adherence to David Lewis' Principal Principle (...) (PP), which states that an agent's degrees of belief should match what they take to be the objective chances. In this paper, I propose two approaches to justifying (PP) for non-Humean chance, hence defusing the Humean objection. The first approach justifies (PP) via the role it plays in informing outright beliefs about long-run frequencies. The second approach justifies (PP) by showing that adherence to (PP), even for non-Humean chance, maximizes expected epistemic utility according to the actual objective chance function. I then address an objection to this approach, concerning the alleged circularity of the derivations. (shrink)

An intuitive objection to modal realism is that merely possible worlds and their inhabitants seem to be irrelevant to an analysis of modality. Kripke originally phrased the objection in terms of being concerned about one’s modal properties without being concerned about the properties one’s other-worldly counterparts have. The author assesses this objection in a variety of forms, and then provides his own formulation that does not beg the question against the modal realist. Finally, the author considers two potential answers to (...) the objection so understood and concludes that only one of them has a chance of succeeding. (shrink)

Though almost forty years have elapsed since its first publication, it is a testament to the philosophical acumen of its author that 'The Matter of Chance' contains much that is of continued interest to the philosopher of science. Mellor advances a sophisticated propensity theory of chance, arguing that this theory makes better sense than its rivals (in particular subjectivist, frequentist, logical and classical theories) of ‘what professional usage shows to be thought true of chance’ (p. xi) – (...) in particular ‘that chance is objective, empirical and not relational, and that it applies to the single case’ (ibid.). The book is short and dense, with the serious philosophical content delivered thick and fast. There is little by way of road-mapping or summarising to assist the reader: the introduction is hardly expansive and the concluding paragraph positively perfunctory. The result is that the book is often difficult going, and the reader is made to work hard to ensure correct understanding of the views expressed. On the other hand, the author’s avoidance of unnecessary use of formalism and jargon ensures that the book is still reasonably accessible. In the following, I shall first summarise the key features of Mellor’s propensity theory, and then offer a few critical remarks. (shrink)

The journalistic device of applying military imagery to describe business strategies is appropriate insofar as businesses implicitly base their strategies on a military model whose origins lie in Social Darwinism. What this involves is an unexamined understanding that any means may be adopted to achieve corporate objectives. Recent workforce reductions are manifestations of this understanding; but so are practices associated with mergers and acquisitions and with government-effectuated takings. Regulation, rather than being overbroad, cannot contain these corporate excesses; and social pressure (...) is an underdeveloped counterforce. Business ethics will remain futile, unfortunately, so long as its practitioners assume a peacetime state of affairs and businesses assume a state of war. (shrink)

This paper asks how Kant’s mature theory of freedom handles an objection pertaining to chance. This question is significant given that Kant raises this criticism against libertarianism in his early writings on freedom before coming to adopt a libertarian view of freedom in the Critical period. After motivating the problem of how Kant can hold that the free actions of human beings lack determining grounds while at the same maintain that these are not the result of ‘blind chance,’ (...) I argue that Kant’s Critical doctrine of transcendental idealism, while creating the conceptual space’ for libertarian freedom, is not intended to provide an answer to the problem of chance with respect to our free agency. I go on to show how the resources for a refutation of chance only come about in the practical philosophy. In the 2nd Critique, Kant famously argues for the reality of freedom on the basis of our consciousness of the moral law as the law of a free will. However, Kant also comes to build into his account of the will a genuine power of choice, which involves the capacity to deviate from the moral law. I conclude by showing that this apparent tension can be resolved by turning to his argument for the impossibility of a diabolical will. This involves a consideration of the distinct kind of grounding relationship that practical laws have to the human will, as well as the way that transcendental idealism makes this possible. (shrink)

On the question of whether gambling behavior can be changed as result of teaching gamblers the mathematics of gambling, past studies have yielded contradictory results, and a clear conclusion has not yet been drawn. In this paper, I bring some criticisms to the empirical studies that tended to answer no to this hypothesis, regarding the sampling and laboratory testing, and I argue that an optimal mathematical scholastic intervention with the objective of preventing problem gambling is possible, by providing the (...) principles that would optimize the structure and content of the teaching module. Given the ethical aspects of the exposure of mathematical facts behind games of chance, and starting from the slots case – where the parametric design is missing, we have to draw a line between ethical and optional information with respect to the mathematical content provided by a scholastic intervention. Arguing for the role of mathematics in problem-gambling prevention and treatment, interdisciplinary research directions are drawn toward implementing an optimal mathematical module in cognitive therapies. (shrink)

A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but Howson is speaking (...) of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

A probability distribution is regular if it does not assign probability zero to any possible event. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson and Benci et al. have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s “isomorphic” events are not in fact isomorphic, but Howson is speaking (...) of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

This article aims to highlight the extent to which Kant’s account of belief draws on the views of his contemporaries. Situating the non-evidentialist features of Crusius’s account of belief within his broader account, I argue that they include antecedents to both Kant’s distinction between pragmatic and moral belief and his conception of a postulate of pure practical reason. While moving us closer to Kant’s arguments for the first postulate, however, both Crusius’s and Meier’s arguments for the immortality of the soul (...) fail to anticipate the most important aspect of their Kantian counterparts. Developing the non-evidentialist features of Basedow’s account of belief, I distinguish it from its Pascalian and Jamesian relatives and argue that it is the clearest antecedent to Kant’s arguments for the first and second postulates. Finally, I consider the development of Kant’s account of belief after the first Critique in light of the foregoing, and discuss the broader implications of my analysis. (shrink)

Kant's response to scepticism in the Critique of Pure Reason is complex and remarkably nuanced, although it is rarely recognized as such. In this paper, I argue that recent attempts to flesh out the details of this response by Paul Guyer and Michael Forster do not go far enough. Although they are right to draw a distinction between Humean and Pyrrhonian scepticism and locate Kant's response to the latter in the Transcendental Dialectic, their accounts fail to capture two important aspects (...) of this response. The first is that Kant's response to Pyrrhonian scepticism is also a response to Hume. The second is that aspects of this response are decidedly positive. In particular, I argue (1) that Kant believed Hume's scepticism manifested important elements of Pyrrhonian scepticism and (2) that both Pyrrhonian scepticism and Hume had a significant positive influence on the development of the Transcendental Dialectic. (shrink)

Eric Watkins has argued on philosophical, textual, and historical grounds that Kant’s account of causation in the first Critique should not be read as an attempt to refute Hume’s account of causation. In this paper, I challenge the arguments for Watkins’ claim. Specifically, I argue (1) that Kant’s philosophical commitments, even on Watkins’ reading, are not obvious obstacles to refuting Hume, (2) that textual evidence from the “Disciple of Pure Reason” suggests Kant conceived of his account of causation as such (...) a refutation, and (3) that none of Hume’s early German critics provided responses to this account that would have satisfied Kant. Watkins’ reading of Kant’s account of causation is thus more compatible with traditional views about Kant’s relationship to Hume than Watkins believes. (shrink)

Peter van Inwagen famously offers a version of the luck objection to libertarianism called the ‘Rollback Argument.’ It involves a thought experiment in which God repeatedly rolls time backward to provide an agent with many opportunities to act in the same circumstance. Because the agent has the kind of freedom that affords her alternative possibilities at the moment of choice, she performs different actions in some of these opportunities. The upshot is that whichever action she performs in the actual-sequence is (...) intuitively a matter of mere chance. I explore a new response to the Rollback Argument. If there are true counterfactuals of libertarian freedom, then the agent performs the same action each time she is placed in the same circumstance, because that is what she would freely do in that circumstance. This response appears to negate the chancy intuition. Ultimately, however, I argue that this new response is unsuccessful, because there is a variant of the Rollback Argument that presents the same basic challenge to the libertarian on the assumption that there are true counterfactuals of libertarian freedom. Thus, true counterfactuals of libertarian freedom do not provide the libertarian with a solution to the Rollback Argument. (shrink)

The importance of the pure concepts of the understanding (i.e. the categories) within Kant’s system of philosophy is undeniable. As I hope to make clear in this essay, however, the categories are also an essential part of Kant’s critique of Christian Wolff. In particular, I argue that Kant’s development of the categories represents a decisive break with the Wolffian conception of the understanding and that this break is central to understanding the task of the Transcendental Analytic. This break, however, is (...) not merely that Kant affirms while Wolff and his followers deny a sharp distinction between sensibility and the understanding, which is the aspect of Kant’s rejection of Wolff that scholars most frequently note. Rather, this break concerns differences in their views about the understanding itself. For while Wolff conceives of the understanding as a mental capacity to extract and make distinct content already present in the senses, Kant conceives of the understanding in its “real use” as a capacity to produce purely intellectual content. (shrink)

This paper attempts to shed light on three sets of issues that bear directly on our understanding of Locke and Kant. The first is whether Kant believes Locke merely anticipates his distinction between analytic and synthetic judgments or also believes Locke anticipates his notion of synthetic a priori cognition. The second is what should we as readers of Kant and Locke should think about Kant’s view whatever it turns out to be, and the third is the nature of Kant’s justification (...) for the comparison he draws between his philosophy and Locke’s. I argue (1) that Kant believes Locke anticipates both the analytic-synthetic distinction and Kant’s notion of synthetic a priori cognition, (2) that the best justification for Kant’s claim draws on Locke’s distinction between trifling and instructive knowledge, (3) that the arguments against this claim developed by Carson, Allison, and Newman fail to undermine it, and (4) that Kant’s own justification for his claim is quite different from what many commentators have thought it was (or should have been). (shrink)

It is often claimed that the structure of the Transcendental Logic is modeled on the Wolffian division of logic textbooks into sections on concepts, judgments, and inferences. While it is undeniable that the Transcendental Logic contains elements that are similar to the content of these sections, I believe these similarities are largely incidental to the structure of the Transcendental Logic. In this essay, I offer an alternative and, I believe, more plausible account of Wolff’s influence on the structure of the (...) Transcendental Logic, one that puts the focus on his empirical psychology rather than his logic. In particular, I argue that the structure of the Transcendental Logic is deeply indebted to a conception of purity that Wolff introduces in his empirical psychology and that this conception sheds more light on the overall structure of the Transcendental Logic than the accepted view. In section one, I outline two conceptions of purity found in Kant and trace them to similar views in Wolff. In section two, I turn to Kant’s views about logic as they are expressed in the Critique and argue that it is best to interpret Kant’s taxonomy of logic on its own terms rather than reading it through its terminological similarities to aspects of the Wolffian tradition. In section three, I argue that the second of the two conceptions of purity identified in section one is central to the structure of the Transcendental Logic. In doing so, I argue against the widespread view that this section of the Critique is modeled solely on what Kant calls pure general logic as opposed to both pure and applied general logic. I then conclude by briefly reviewing my account and considering some of its broader implications for our understanding of Kant. (shrink)

Memory evolved to supply useful, timely information to the organism’s decision-making systems. Therefore, decision rules, multiple memory systems, and the search engines that link them should have coevolved to mesh in a coadapted, functionally interlocking way. This adaptationist perspective suggested the scope hypothesis: When a generalization is retrieved from semantic memory, episodic memories that are inconsistent with it should be retrieved in tandem to place boundary conditions on the scope of the generalization. Using a priming paradigm and a decision task (...) involving person memory, the authors tested and confirmed this hypothesis. The results support the view that priming is an evolved adaptation. They further show that dissociations between memory systems are not—and should not be—absolute: Independence exists for some tasks but not others. (shrink)

It is widely thought that chance should be understood in reductionist terms: claims about chance should be understood as claims that certain patterns of events are instantiated. There are many possible reductionist theories of chance, differing as to which possible pattern of events they take to be chance-making. It is also widely taken to be a norm of rationality that credence should defer to chance: special cases aside, rationality requires that one's credence function, when conditionalized (...) on the chance-making facts, should coincide with the objective chance function. It is a shortcoming of a theory of chance if implies that this norm of rationality is unsatisfiable. The primary goal of this paper is to show, on the basis of considerations concerning computability and inductive learning, that this shortcoming is more common than one would have hoped. (shrink)

We show that five important elements of the ‘nomological package’— laws, counterfactuals, chances, dispositions, and counterfactuals—needn’t be a problem for the Growing-Block view. We begin with the framework given in Briggs and Forbes (in The real truth about the unreal future. Oxford studies in metaphysics. Oxford University Press, Oxford, 2012 ), and, taking laws as primitive, we show that the Growing-Block view has the resources to provide an account of possibility, and a natural semantics for non-backtracking causal counterfactuals. We show (...) how objective chances might ground a more fine-grained concept of feasibility, and furnished a places in the structure where causation and dispositions might fit. The Growing-Block view, thus understood, provides the resources to explain the close link between modality and tense, so that it predicts modal change as time passes. This account lets us capture not only what the future might hold for us, and also what might have been. (shrink)

A thesis (“weak BCP”) nearly universally held among philosophers of probability connects the concepts of objective chance and metaphysical modality: Any prospect (outcome) that has a positive chance of obtaining is metaphysically possible—(nearly) equivalently, any metaphysically impossible prospect has zero chance. Particular counterexamples are provided utilizing the monotonicity of chance, one of them related to the four world paradox. Explanations are offered for the persistent feeling that there cannot be chancy metaphysical necessities or chancy metaphysical (...) impossibilities. Chance is objective but contrary to popular opinion it is also largely epistemic. Chancy necessities are analogous to necessary a posteriori truths. Philosophy and Phenomenological Research, Volume 99, Issue 3, Page 644-662, November 2019. (shrink)

Causalists and Evidentialists can agree about the right course of action in an (apparent) Newcomb problem, if the causal facts are not as initially they seem. If declining $1,000 causes the Predictor to have placed $1m in the opaque box, CDT agrees with EDT that one-boxing is rational. This creates a difficulty for Causalists. We explain the problem with reference to Dummett's work on backward causation and Lewis's on chance and crystal balls. We show that the possibility that the (...) causal facts might be properly judged to be non-standard in Newcomb problems leads to a dilemma for Causalism. One horn embraces a subjectivist understanding of causation, in a sense analogous to Lewis's own subjectivist conception of objective chance. In this case the analogy with chance reveals a terminological choice point, such that either (i) CDT is completely reconciled with EDT, or (ii) EDT takes precedence in the cases in which the two theories give different recommendations. The other horn of the dilemma rejects subjectivism, but now the analogy with chance suggests that it is simply mysterious why causation so construed should constrain rational action. (shrink)

One of our most sophisticated accounts of objective chance in quantum mechanics involves the Deutsch-Wallace theorem, which uses state-space symmetries to justify agents’ use of the Born rule when the quantum state is known. But Wallace argues that this theorem requires an Everettian approach to measurement. I find that this argument is unsound. I demonstrate a counter-example by applying the Deutsch-Wallace theorem to the de Broglie-Bohm pilot-wave theory.

I propose an account of probability in the Everett interpretation of quantum mechanics. According to the account, probabilities are objective chances of centered propositions. As I show, the account solves a number of problems concerning the role of probability in the Everett interpretation. It also challenges an implicit assumption, concerning the aim and scope of fundamental physical theories, that is made throughout the philosophy of physics literature.

The question I am addressing in this paper is the following: how is it possible to empirically test, or confirm, counterfactuals? After motivating this question in Section 1, I will look at two approaches to counterfactuals, and at how counterfactuals can be empirically tested, or confirmed, if at all, on these accounts in Section 2. I will then digress into the philosophy of probability in Section 3. The reason for this digression is that I want to use the way observable (...) absolute and relative frequencies, two empirical notions, are used to empirically test, or confirm, hypotheses about objective chances, a metaphysical notion, as a role-model. Specifically, I want to use this probabilistic account of the testing of chance hypotheses as a role-model for the account of the testing of counterfactuals, another metaphysical notion, that I will present in Sections 4 to 8. I will conclude by comparing my proposal to one non-probabilistic and one probabilistic alternative in Section 9. (shrink)

Reductionist accounts of objective chance rely on a notion of fit, which ties the chances at a world to the frequencies at that world. Here, I criticize extant measures of the fit of a chance system and draw on recent literature in epistemic utility theory to propose a new model: chances fit a world insofar as they are accurate at that world. I show how this model of fit does a better job of explaining the normative features (...) of chance, its role in the laws of nature, and its status as an expert function than do previous accounts. (shrink)

Stalnaker's Thesis about indicative conditionals is, roughly, that the probability one ought to assign to an indicative conditional equals the probability that one ought to assign to its consequent conditional on its antecedent. The thesis seems right. If you draw a card from a standard 52-card deck, how confident are you that the card is a diamond if it's a red card? To answer this, you calculate the proportion of red cards that are diamonds -- that is, you calculate the (...) probability of drawing a diamond conditional on drawing a red card. Skyrms' Thesis about counterfactual conditionals is, roughly, that the probability that one ought to assign to a counterfactual equals one's rational expectation of the chance, at a relevant past time, of its consequent conditional on its antecedent. This thesis also seems right. If you decide not to enter a 100-ticket lottery, how confident are you that you would have won had you bought a ticket? To answer this, you calculate the prior chance--that is, the chance just before your decision not to buy a ticket---of winning conditional on entering the lottery. The central project of this article is to develop a new uniform theory of conditionals that allows us to derive a version of Skyrms' Thesis from a version of Stalnaker's Thesis, together with a chance-deference norm relating rational credence to beliefs about objective chance. (shrink)

A mental state is luminous if, whenever an agent is in that state, they are in a position to know that they are. Following Timothy Williamson’s Knowledge and Its Limits, a wave of recent work has explored whether there are any non-trivial luminous mental states. A version of Williamson’s anti-luminosity appeals to a safety- theoretic principle connecting knowledge and confidence: if an agent knows p, then p is true in any nearby scenario where she has a similar level of confidence (...) in p. However, the relevant notion of confidence is relatively underexplored. This paper develops a precise theory of confidence: an agent’s degree of confidence in p is the objective chance they will rely on p in practical reasoning. This theory of confidence is then used to critically evaluate the anti-luminosity argument, leading to the surprising conclusion that although there are strong reasons for thinking that luminosity does not obtain, they are quite different from those the existing literature has considered. In particular, we show that once the notion of confidence is properly understood, the failure of luminosity follows from the assumption that knowledge requires high confidence, and does not require any kind of safety principle as a premise. (shrink)

Why should we refrain from doing things that, taken collectively, are environmentally destructive, if our individual acts seem almost certain to make no difference? According to the expected consequences approach, we should refrain from doing these things because our individual acts have small risks of causing great harm, which outweigh the expected benefits of performing them. Several authors have argued convincingly that this provides a plausible account of our moral reasons to do things like vote for policies that will reduce (...) our countries’ greenhouse gas emissions, adopt plant-based diets, and otherwise reduce our individual emissions. But this approach has recently been challenged by authors like Bernward Gesang and Julia Nefsky. Gesang contends that it may be genuinely impossible for our individual emissions to make a morally relevant difference. Nefsky argues more generally that the expected consequences approach cannot adequately explain our reasons not to do things if there is no precise fact of the matter about whether their outcomes are harmful. -/- In the following chapter, author Howard Nye defends the expected consequences approach against these objections. Nye contends that Gesang has shown at most that our emissions could have metaphysically indeterministic effects that lack precise objective chances. He argues, moreover, that the expected consequences approach can draw upon existing extensions to cases of indeterminism and imprecise probabilities to deliver the result that we have the same moral reasons to reduce our emissions in Gesang’s scenario as in deterministic scenarios. Nye also shows how the expected consequences approach can draw upon these extensions to handle Nefsky’s concern about the absence of precise facts concerning whether the outcomes of certain acts are harmful. The author concludes that the expected consequences approach provides a fully adequate account of our moral reasons to take both political and personal action to reduce our ecological footprints. (shrink)

In decision-theory, the notion of regret enters into the minimax decision-rule and has a determinate usage in this context. However, there are many alternative ways of conceiving of regret. The chapter constructs the einmalist- nicht-keinmal ('once is not never') game, in which a single sampling radically changes the expected value of the game in a way that is quite counterintuitive, as the basis for studying regret after a loss following the choice of an uncertain action. Crucially, the very loss affects (...) the posterior expectation of the game and the posterior credence about the objective chances of a win. Our taxonomy of regret contains regret over the action chosen and regret over the outcome obtained as its main categories, and is mirrored by a taxonomy of joy after a win following the choice of an uncertain action, and is used to critique of Krähmer and Stone's analysis of risk aversion for uncertain actions. (shrink)

According to the orthodox treatment of risk preferences in decision theory, they are to be explained in terms of the agent's desires about concrete outcomes. The orthodoxy has been criticised both for conflating two types of attitudes and for committing agents to attitudes that do not seem rationally required. To avoid these problems, it has been suggested that an agent's attitudes to risk should be captured by a risk function that is independent of her utility and probability functions. The main (...) problem with that approach is that it suggests that attitudes to risk are wholly distinct from people's (non-instrumental) desires. To overcome this problem, we develop a framework where an agent's utility function is defined over chance propositions (i.e., propositions describing objective probability distributions) as well as ordinary (non-chance) ones, and argue that one should explain different risk attitudes in terms of different forms of the utility function over such propositions. (shrink)

In a recent article, Gordon Belot uses the so-called undermining phenomenon to try to raise a new difficulty for reductive accounts of objective probability, such as Humean Best System accounts. In this paper I will give a critical discussion of Belot’s paper and argue that, in fact, there is no new difficulty here for chance reductionists to address.

Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of this analysis (...) for Bayesian reasoning with idealized models in science. (shrink)

In A Metaphysics for Freedom, Helen Steward proposes and defends a novel version of the libertarian account of free action. Amongst several objections that she considers to her view, one that looms particularly large is the Challenge from Chance: ‘the most powerful, widely-promulgated and important line of anti-libertarian reasoning’. This paper begins by arguing that Steward’s response to the Challenge is not fully convincing. It then goes on to explore a further possible libertarian line of defence against the Challenge, (...) arguing that it, too, ultimately fails. The conclusion is that the Challenge remains an important source of dialectical advantage for the compatibilist. (shrink)

I distinguish three primary notions of objectivity that may be applied to the sciences. There is an ontological sense of objectivity which relates to the way in which the natural world exists independently of human thought. There is a semantic form of objectivity which relates to the nature of truth. There is an epistemic notion of objectivity which relates to the methodological norms and procedures which are employed in the sciences, and the epistemic justification of beliefs and theories which are (...) licensed by those norms and procedures. These three forms of objectivity may be brought into conjunction. It is because we employ methods of scientific inquiry which function to exclude subjective factors and to incorporate only genuinely epistemic factors that the results and theories of the sciences should be accepted. They should be accepted because by employing such methods we have the best chance of arriving at true beliefs about the nature of reality. In short, it is the epistemic objectivity of the methods of science that leads us to the objective truth about the objective world. (shrink)

John Broome has proposed a theory of fairness according to which fairness requires that agents’ claims to goods be satisfied in proportion to the relative strength of those claims. In the case of competing claims for a single indivisible good, Broome argues that what fairness requires is the use of a weighted lottery as a surrogate to satisfying the competing claims: the relative chance of each claimant's winning the lottery should be set to the relative strength of each claimant's (...) claim. In this journal, James Kirkpatrick and Nick Eastwood have objected that the use of weighted lotteries in the case of indivisible goods is unacceptable. In this article, I explain why Kirkpatrick and Eastwood's objection misses its mark. (shrink)

Affirmative action is standardly pursued in relation to admissions to prestigious universities, in hiring for prestigious jobs, and when it comes to being elected to parliament. Central to these forms of affirmative action is that they have to do with competitive goods. A good is competitive when, if we improve A’s chances of getting the good, we reduce B’s chances of obtaining the good. I call this Competitive Affirmative Action. I distinguish this from Non-competitive Affirmative Action. The latter has to (...) do with non-competitive goods, e.g., being granted early parole or freedom from arbitrary arrest. I argue that some of the most prominent objections against affirmative action—in particular, the reverse discrimination objection and the merit objection—speak less against Non-competitive Affirmative Action. And that some of the most prominent arguments in favor of affirmative action, insofar as they justify Competitive Affirmative Action, also justify Non-competitive Affirmative Action. (shrink)