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)

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)

I sketch a new constraint on chance, which connects chance ascriptions closely with ascriptions of ability, and more specifically with 'CAN'-claims. This connection between chance and ability has some claim to be a platitude; moreover, it exposes the debate over deterministic chance to the extensive literature on (in)compatibilism about free will. The upshot is that a prima facie case for the tenability of deterministic chance can be made. But the main thrust of the paper is (...) to draw attention to the connection between the truth conditions of sentences involving 'CAN' and 'CHANCE', and argue for the context sensitivity of each term. Awareness of this context sensitivity has consequences for the evaluation of particular philosophical arguments for (in) compatibilism when they are presented in particular contexts. (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)

A new philosophical analysis is provided of the notorious Sleeping Beauty Problem. It is argued that the correct solution is one-third, but not in the way previous philosophers have typically meant this. A modified version of the Problem demonstrates that neither self-locating information nor amnesia is relevant to the core Problem, which is simply to evaluate the conditional chance of heads given an undated Monday-or-Tuesday awakening. Previous commentators have failed to appreciate the significance of the information that Beauty gains (...) upon waking, and which is relevant to the conditional chance of heads: de re acquaintance with the awakening itself and the non-locating knowledge that it is an experimental awakening. David Lewis and company are committed to several unjustifiable and unacceptable probability assessments. Previous commentators have in effect confused the information that Beauty undergoes this particular experimental awakening for the information that she undergoes some experimental awakening or other. Lewis in particular thereby illegitimately tips the scales both in favor of heads and in favor of Monday. The Sleeping Beauty Problem is equivalent to a ball-in-urn word problem in elementary probability theory. (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)

Counterfactual scepticism holds that most ordinary counterfactuals are false. The main argument for this view appeals to a ‘chance undermines would’ principle: if ψ would have some chance of not obtaining had ϕ obtained, then ϕ □→ ψ is false. This principle seems to follow from two fairly weak principles, namely, that ‘chance ensures could’ and that ϕ □→ ψ and ϕ ⋄→ ¬ ψ clash. Despite their initial plausibility, I show that these principles are independently problematic: (...) given some modest closure principles, they entail absurdities. Moreover, on the most promising strategy for saving these principles, they do not, in the relevant sense, entail the chance-undermines-would principle. Instead, they entail a principle that only supports counterfactual indeterminism, the view that most ordinary counterfactuals are chancy, that is, not settled true. I demonstrate this by developing an indeterminist semantics that vindicates the clash and chance-ensures-could principles but not the chance-undermines-would principle. This view, I argue, offers a better account of our credal and linguistic judgements than counterfactual scepticism. (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)

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)

Abstract: The sinking of the RMS Titanic in 1912 remains a poignant historical event that continues to captivate our collective imagination. In this research paper, we delve into the realm of data-driven analysis by applying Artificial Neural Networks (ANNs) to predict the chances of survival for passengers aboard the Titanic. Our study leverages a comprehensive dataset encompassing passenger information, demographics, and cabin class, providing a unique opportunity to explore the complex interplay of factors influencing survival outcomes. Our ANN-based predictive model (...) achieved an accuracy rate of 78%, shedding light on the underlying patterns within the data. However, this paper underscores the multifaceted nature of survival prediction and acknowledges several challenges. These include missing data imputation, feature engineering, and the inherent noise within historical datasets. We further discuss the importance of model evaluation metrics, showcasing not only accuracy but also precision, recall, and F1-score as essential indicators of predictive performance. The research paper meticulously outlines the architecture of the ANN model, emphasizing the key hyperparameters, activation functions, and regularization techniques employed in model development. Additionally, we address ethical considerations related to data handling and potential biases within the dataset. While our achieved accuracy is a notable achievement, this study emphasizes the importance of interpreting the results with due caution. It underscores the need for a holistic perspective that considers the practical implications of false positives and false negatives, especially in the context of a disaster scenario. In conclusion, this research contributes to our understanding of survival prediction in historical events like the Titanic disaster using modern machine learning techniques. It calls for further exploration and refinement of predictive models, with a focus on enhancing the interpretability and generalizability of such models to real-world applications. (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)

A previously unrecognised argument against deterministic chance is introduced. The argument rests on the twin ideas that determined outcomes are settled, while chancy outcomes are unsettled, thus making cases of determined but chancy outcomes impossible. Closer attention to tacit assumptions about settledness makes available some principled lines of resistance to the argument for compatibilists about chance and determinism. Yet the costs of maintaining compatibilism may be higher with respect to this argument than with respect to existing incompatibilist arguments.

Humean accounts of chance have a problem with undermining futures: they have to accept that some series of events are physically possible and have a nonzero chance but are inconsistent with the chances being what they are. This contradicts basic platitudes about chances (such as those given by Bigelow et al. (1993) and Schaffer (2007)) and leads to inconsistency between plausible constraints on credences. We show how Humeans can avoid these contradictions by drawing on metaphysically impossible worlds that (...) are, nevertheless, scientifically possible. One major advantage of our approach is that one single move deals with these both problems, whereas previous Humean approaches to undermining (such as that given by Lewis (1994), Thau (1994), and Hall (1994)) have only addressed the connection between credence and chance. Furthermore, our approach connects more closely with the way we employ stochastic scientific theories. And it’s part of a unified solution to other challenges that the Humean faces. (shrink)

In recent work, Callender and Cohen (2009) and Hoefer (2007) have proposed variants of the account of chance proposed by Lewis (1994). One of the ways in which these accounts diverge from Lewis’s is that they allow special sciences and the macroscopic realm to have chances that are autonomous from those of physics and the microscopic realm. A worry for these proposals is that autonomous chances may place incompatible constraints on rational belief. I examine this worry, and attempt to (...) determine (i) what kinds of conflicts would be problematic, and (ii) whether these proposals lead to problematic conflicts. After working through a pair of cases, I conclude that these proposals do give rise to problematic conflicts. (shrink)

The modern synthesis in evolutionary biology is taken to be that period in which a consensus developed among biologists about the major causes of evolution, a consensus that informed research in evolutionary biology for at least a half century. As such, it is a particularly fruitful period to consider when reflecting on the meaning and role of chance in evolutionary explanation. Biologists of this period make reference to “chance” and loose cognates of “chance,” such as: “random,” “contingent,” (...) “accidental,” “haphazard,” or “stochastic.” Of course, what an author might mean by “chance” in any specific context varies. -/- In the following, we first offer a historiographical note on the synthesis. Second, we introduce five ways in which synthesis authors spoke about chance. We do not take these to be an exhaustive taxonomy of all possible ways in which chance meaningfully figures in explanations in evolutionary biology. These are simply five common uses of the term by biologists at this period. They will serve to organize our summary of the collected references to chance and the analysis and discussion of the following questions: • What did synthesis authors understand by chance? • How did these authors see chance operating in evolution? • Did their appeals to chance increase or decrease over time during the synthesis? That is, was there a “hardening” of the synthesis, as Gould claimed (1983)? (shrink)

Scepticism concerning the idea of causation being linked to contingent chance-raising is articulated in Beebee’s challenging chapter. She suggests that none of these approaches will avoid the consequence that spraying defoliant on a weed is a cause of the weed’s subsequent health. We will always be able to abstract away enough of the healthy plant processes so all that’s left is the causal chain involving defoliation and health. In those circumstances, there will be contingent chance-raising. Beebee’s conclusion is (...) that we should reject the idea of contingent chance-raising and just accept that all causation involves chance-raising. This involves the reclassification of some intuitive cases of causation as causal processes without causation but rather hindering (a distinctive kind of process). It seems clear from this discussion and from the brief earlier remarks about the status of prevention that the classification of types of causal processes and the characterization of their link to causation are matters of some importance. (shrink)

When philosophers of physics explore the nature of chance, they usually look to quantum mechanics. When philosophers of biology explore the nature of chance, they usually look to microevolutionary phenomena, such as mutation or random drift. What has been largely overlooked is the role of chance in macroevolution. The stochastic models of paleobiology employ conceptions of chance that are similar to those at the microevolutionary level, yet different from the conceptions of chance often associated with (...) quantum mechanics and Laplacean determinism. (shrink)

The sample space of the chance distribution at a given time is a class of possible worlds. Thanks to this connection between chance and modality, one’s views about modal space can have significant consequences in the theory of chance and can be evaluated in part by how plausible these implications are. I apply this methodology to evaluate certain forms of modal contingentism, the thesis that some facts about what is possible are contingent. Any modal contingentist view that (...) meets certain conditions that I specify generates difficulties in the philosophy of chance, including a problem usually associated with Humeanism that is known as ‘the problem of undermining futures’. I consider two well-known versions of modal contingentism that face this difficulty. The first version, proposed by Hugh Chandler and Nathan Salmon, rests on an argument for the claim that many individuals have their modal features contingently. The second version is motivated by the thesis that the existence of a possible world depends on the existence of the contingent individuals inhabiting it, and that many worlds are therefore contingent existents. (shrink)

In debates between holism and reductionism in biology, from the early 20th century to more recent re-enactments involving genetic reductionism, developmental systems theory, or systems biology, the role of chance – the presence of theories invoking chance as a strong explanatory principle – is hardly ever acknowledged. Conversely, Darwinian models of chance and selection (Dennett 1995, Kupiec 1996, Kupiec 2009) sit awkwardly with reductionist and holistic concepts, which they alternately challenge or approve of. I suggest that the (...) juxtaposition of chance and the holism-reductionism pair (at multiple levels, ontological and methodological, pertaining to the vision of scientific practice as well as to the foundations of a vision of Nature, implicit or explicit) allows the theorist to shed some new light on these perennial tensions in the conceptualisation of Life. (shrink)

John Hawthorne in a recent paper takes issue with Lewisian accounts of counterfactuals, when relevant laws of nature are chancy. I respond to his arguments on behalf of the Lewisian, and conclude that while some can be rebutted, the case against the original Lewisian account is strong.I develop a neo-Lewisian account of what makes for closeness of worlds. I argue that my revised version avoids Hawthorne’s challenges. I argue that this is closer to the spirit of Lewis’s first (non-chancy) proposal (...) than is Lewis’s own suggested modification. (shrink)

The ‘rollback argument,’ pioneered by Peter van Inwagen, purports to show that indeterminism in any form is incompatible with free will. The argument has two major premises: the first claims that certain facts about chances obtain in a certain kind of hypothetical situation, and the second that these facts entail that some actual act is not free. Since the publication of the rollback argument, the second claim has been vehemently debated, but everyone seems to have taken the first claim for (...) granted. Nevertheless, the first claim is totally unjustified. Even if we accept the second claim, therefore, the argument gives us no reason to think that free will and indeterminism are incompatible. Furthermore, seeing where the rollback argument goes wrong illuminates how a certain kind of incompatibilist, the ‘chance-incompatibilist,’ ought to think about free will and chance, and points to a possibility for free will that has remained largely unexplored. (shrink)

In the article ”Against Physicalism-plus-God: How Creation Accounts for Divine Action in the World’, I defined a framework which allows us to make some progress in our understanding of how God acts in the world. In the present article, I apply this framework to the specific question of chance events. I show that chance does not provide an explanation for special divine action. Nevertheless, chance does not hamper God’s ability to act in the world, and creation provides (...) a framework for the understanding of chance, which is akin to what we see in modern science. (shrink)

Principles of chance deference face two kinds of problems. In the first place, they face difficulties with a priori knowable contingencies. In the second place, they face difficulties in cases where you've lost track of the time. I provide a principle of chance deference which handles these problem cases. This principle has a surprising consequence for Adam Elga's Sleeping Beauty Puzzle.

In this text the ancient philosophical question of determinism (“Does every event have a cause ?”) will be re-examined. In the philosophy of science and physics communities the orthodox position states that the physical world is indeterministic: quantum events would have no causes but happen by irreducible chance. Arguably the clearest theorem that leads to this conclusion is Bell’s theorem. The commonly accepted ‘solution’ to the theorem is ‘indeterminism’, in agreement with the Copenhagen interpretation. Here it is recalled that (...) indeterminism is not really a physical but rather a philosophical hypothesis, and that it has counterintuitive and far-reaching implications. At the same time another solution to Bell’s theorem exists, often termed ‘superdeterminism’ or ‘total determinism’. Superdeterminism appears to be a philosophical position that is centuries and probably millennia old: it is for instance Spinoza’s determinism. If Bell’s theorem has both indeterministic and deterministic solutions, choosing between determinism and indeterminism is a philosophical question, not a matter of physical experimentation, as is widely believed. If it is impossible to use physics for deciding between both positions, it is legitimate to ask which philosophical theories are of help. Here it is argued that probability theory – more precisely the interpretation of probability – is instrumental for advancing the debate. It appears that the hypothesis of determinism allows to answer a series of precise questions from probability theory, while indeterminism remains silent for these questions. From this point of view determinism appears to be the more reasonable assumption, after all. (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)

A compelling, and popular, thought is that ability entails control: S’s being able to φ entails that φ be, in some sense, in S’s control. But this intuition is inconsistent with a different prima facie compelling thought: that S’s succeeding in φ-ing entails that S is able to φ. In this paper, I introduce a new form of evidence to help adjudicate between these two theses: namely, probability judgments about ability ascriptions. I argue that these judgments provide evidence in favor (...) of the intuition that success entails ability, and against the intuition that ability requires control. Moreover, I argue that these judgments support one particular analysis which vindicates the success intuition, namely, the analysis of ability in terms of conditionals. (shrink)

This article gives a brief history of chance in the Christian tradition, from casting lots in the Hebrew Bible to the discovery of laws of chance in the modern period. I first discuss the deep-seated skepticism towards chance in Christian thought, as shown in the work of Augustine, Aquinas, and Calvin. The article then describes the revolution in our understanding of chance—when contemporary concepts such as probability and risk emerged—that occurred a century after Calvin. The modern (...) ability to quantify chance has transformed ideas about the universe and human nature, separating Christians today from their predecessors, but has received little attention by Christian historians and theologians. (shrink)

This is a discussion of Richard Pettigrew's book "Accuracy and the Laws of Credence". I target Pettigrew's application of the accuracy framework to derive chance-credence principles. My principal contention is that Pettigrew's preferred version of the argument might in one sense be circular and, moreover, that Pettigrew's premises have content that go beyond that of standard chance-credence principles.

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)

Many authors in ethics, economics, and political science endorse the Lottery Requirement, that is, the following thesis: where different parties have equal moral claims to one indivisible good, it is morally obligatory to let a fair lottery decide which party is to receive the good. This article defends skepticism about the Lottery Requirement. It distinguishes three broad strategies of defending such a requirement: the surrogate satisfaction account, the procedural account, and the ideal consent account, and argues that none of these (...) strategies succeed. The article then discusses and discharges some remaining grounds for resistance to these skeptical conclusions, as well as the possibility of defending a weaker version of a normative lottery principle. The conclusion is that we have no reason to believe that where equal claims conflict, we are morally required to hold a lottery, as opposed to simply picking one of the parties on more subjective grounds or out of pure whim. In addition to the practical consequences of this skeptical view, the article sketches some theoretical implications for debates about saving the greater number and about axiomatic utilitarianism. (shrink)

Why do we value higher-level scientific explanations if, ultimately, the world is physical? An attractive answer is that physical explanations often cite facts that don’t make a difference to the event in question. I claim that to properly develop this view we need to commit to a type of deterministic chance. And in doing so, we see the theoretical utility of deterministic chance, giving us reason to accept a package of views including deterministic chance.

ABSTRACT If the future is highly sensitive to the past, then many of our acts have long-term consequences whose significance well exceeds that of their foreseeable short-term consequences. According to an influential argument by James Lenman, we should think that the future is highly sensitive to acts that affect people’s identities. However, given the assumption that chancy events are ubiquitous, the effects that our acts have are likely to dissipate over a short span of time. The sets of possible futures (...) left open by alternative acts are typically very similar in the same way that large random samples drawn from the same population are typically very similar. (shrink)

It is plausible to think that it is wrong to cure many people’s headaches rather than save someone else’s life. On the other hand, it is plausible to think that it is not wrong to expose someone to a tiny risk of death when curing this person’s headache. I will argue that these claims are inconsistent. For if we keep taking this tiny risk then it is likely that one person dies, while many others’ headaches are cured. In light of (...) this inconsistency, there is a conflict in our intuitions about beneficence and chance. This conflict is perplexing. And I have not been able to find a satisfactory way of resolving it. Perhaps you can do better? (shrink)

Holm (2022) argues that a class of algorithmic fairness measures, that he refers to as the ‘performance parity criteria’, can be understood as applications of John Broome’s Fairness Principle. We argue that the performance parity criteria cannot be read this way. This is because in the relevant context, the Fairness Principle requires the equalization of actual individuals’ individual-level chances of obtaining some good (such as an accurate prediction from a predictive system), but the performance parity criteria do not guarantee any (...) such thing: the measures merely ensure that certain population-level ratios hold. (shrink)

In the article, first I present the atheistic argument from pointless evil and the argument from chance. The essence of the argument from chance consists in the incompatibility of the existence of purposeless events and the existence of a God who planned the universe to the last detail. Second, I would like to show that there is a relation between the evidential argument from evil and the argument from chance. An analysis of the theistic argument from small (...) probabilities is a helpful starting point for the presentation of how the two arguments are related. (shrink)

Goodman draws together, in this memoir, his explorations of meaning and coincidence, and his lived experiences of chance, and his professional experiences teaching, writing, and consulting about risk. The book opens by describing the author's life-changing encounter with a Zen Buddhist monk in 1977, over a cup of tea. Returning to his beginnings, Goodman recounts his coming-of-age, from participating the 1960’s U.S. protests and Vietnam-War resistance, to finally settling down in Canada. He describes his role in a supporting, silent (...) vigil around Willard Straight Hall at Cornell University, the night after it had been occupied by protestors, and his later application for Conscientious Objector status, following the U.S. draft lottery in 1969. He reflects on the challenges and changes on his road taken, in his career and personal relationships, and in spiritual searches, to share some insights about the seamless nature of chance, and about seeing a Both/And perspective in life that encourages openness to possibilities. -/- . (shrink)

Abstract In this paper I consider an easier-to-read and improved to a certain extent version of the causal chance-based analysis of counterfactuals that I proposed and argued for in my A Theory of Counterfactuals. Sections 2, 3 and 4 form Part I: In it, I survey the analysis of the core counterfactuals (in which, very roughly, the antecedent is compatible with history prior to it). In section 2 I go through the three main aspects of this analysis, which are (...) the following. First, it is a causal analysis, in that it requires that intermediate events to which the antecedent event is not a cause be preserved in the main truth-condition schema. Second, it highlights the central notion to the semantics of counterfactuals on the account presented here -- the notion of the counterfactual probability of a given counterfactual, which is the probability of the consequent given the following: the antecedent, the prior history, and the preserved intermediate events. Third, it considers the truth conditions for counterfactuals of this sort as consisting in this counterfactual probability being higher than a threshold. In section 3, I re-formulate the analysis of preservational counterfactuals in terms of the notion of being a cause, which ends up being quite compact. In section 4 I illustrate this analysis by showing how it handles two examples that have been considered puzzling – Morgenbesser's counterfactual and Edgington's counterfactual. Sections 5 and on constitute Part II: Its main initial thrust is provided in section 5, where I present the main lines of the extension of the theory from the core counterfactuals (analyzed in part I) to counterfactuals (roughly) whose antecedents are not compatible with their prior history. In this part II, I elaborate on counterfactuals that don't belong to the core, and more specifically on so-called reconstructional counterfactuals (as opposed to the preservational counterfactuals, which constitute the core counterfactual-type). The heart of the analysis is formulated in terms of processes leading to the antecedent (event/state), and more specifically in terms of processes likely to have led to the antecedent, a notion which is analyzed entirely in terms of chance. It covers so-called reconstructional counterfactuals as opposed to the core, so-called preservational counterfactuals, which are analyzed in sections 2 and 3 of part I. The counterfactual probability of such reconstructional counterfactuals is determined via the probability of possible processes leading to the antecedent weighed, primarily and roughly, by the conditional probability of the antecedent given such process: The counterfactual probability is thus, very roughly, a weighted sum for all processes most likely to have led to the antecedent, diverging at a fixed time. In section 6 I explain and elaborate further on the main points in section 5. In section 7 I illustrate the reconstructional analysis. I specify counterfactuals which are so-called process-pointers, since their consequent specifies stages in processes likely to have led to their antecedent. I argue that so-called backtracking counterfactuals are process-pointers counterfactuals, which fit into the reconstructional analysis, and do not call for a separate reading. I then illustrate cases where a speaker unwittingly employs a certain counterfactual while charitably construable as intending to assert (or ‘having in mind’) another. Here I also cover the issue of how to construe what one can take as back-tracking counterfactuals, or counterfactuals of the reconstructional sort, and more specifically, which divergence point they should be taken as alluding to (prior to which the history is held fixed). Some such cases also give rise to what one can take as a dual reading of a counterfactual between preservational and reconstructional readings. Such cases may yield an ambiguity, where in many cases one construal is dominant. In section 8 I illustrate the analysis by applying it to the famous Bizet-Verdi counterfactuals. This detailed analysis of counterfactuals (designed for the indeterministic case) has three main distinctive elements: its being chance-based, its causal aspect, and the use it makes of processes most likely to have led to the antecedent-event. This analysis is couched in a very different conceptual base from, and is an alternative account to, analyses in terms of the standard notion of closeness or distance of possible worlds, which is the main feature of the Stalnaker-Lewis-type analyses of counterfactuals. This notion of closeness or distance plays no role whatsoever in the analysis presented here. (This notion of closeness has been left open by Stalnaker, and to significant extent also by Lewis's second account.) . (shrink)

The notion of chance plays an important role in some philosophical analyses and interpretations of scientific theories. The most obvious examples of that are the theories of evolution and quantum mechanics. This notion, however seems to be notoriously vague. Its application in such analyses, more often than not refers to its common-sense understanding, which, by definition, cannot be sufficient when it comes to sound philosophical interpretations of scientific achievements. The paper attempts at formulating a ‘typology of chance’. It (...) distinguishes eight different meanings of this notion. Those meanings can be found in classical philosophical accounts of chance, in the common usage of this term, or form logical possibilities of its understanding. Subsequently, the paper points to those forms of the notion in question which may and may not be properly applied to scientific theories and ideas – given usual characteristics of natural sciences. It also shows – by the examples of particular theories mentioned above – which of the distinguished forms of the notion of chance are actually applicable in the context of these theories. (shrink)

An indifference principle says that your credences should be distributed uniformly over each of the possibilities you recognise. A chance deference principle says that your credences should be aligned with the chances. My thesis is that, if we are anti-Humeans about chance, then these two principles are incompatible. Anti-Humeans think that it is possible for the actual frequencies to depart from the chances. So long as you recognise possibilities like this, you cannot both spread your credences evenly and (...) defer to the chances. I discuss some weaker forms of indifference which will allow anti-Humeans to defer to the chances. (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)

This article presents a fairness principle for evaluating decision-making based on predictions: a decision rule is unfair when the individuals directly impacted by the decisions who are equal with respect to the features that justify inequalities in outcomes do not have the same statistical prospects of being benefited or harmed by them, irrespective of their socially salient morally arbitrary traits. The principle can be used to evaluate prediction-based decision-making from the point of view of a wide range of antecedently specified (...) substantive views about justice in outcome distributions. (shrink)

In an illuminating article, Claus Beisbart argues that the recently-popular thesis that the probabilities of statistical mechanics (SM) are Best System chances runs into a serious obstacle: there is no one axiomatization of SM that is robustly best, as judged by the theoretical virtues of simplicity, strength, and fit. Beisbart takes this 'no clear winner' result to imply that the probabilities yielded by the competing axiomatizations simply fail to count as Best System chances. In this reply, we express sympathy for (...) the 'no clear winner' thesis. However, we argue that an importantly different moral should be drawn from this. We contend that the implication for Humean chances is not that there are no SM chances, but rather that SM chances fail to be sharp. (shrink)

The American political landscape exhibits significant polarization. People’s political beliefs cluster around two main camps. However, many of the issues with respect to which these two camps disagree seem to be rationally orthogonal. This feature raises an epistemic challenge for the political partisan. If she is justified in consistently adopting the party line, it must be true that her side is reliable on the issues that are the subject of disagreements. It would then follow that the other side is anti-reliable (...) with respect to a host of orthogonal political issues. Yet, it is difficult to find a psychologically plausible explanation for why one side would get things reliably wrong with respect to a wide range of orthogonal issues. While this project’s empirical discussion focuses on the US context, the argument generalizes to any situation where political polarization exists on a sufficiently large number of orthogonal claims. (shrink)

I present an account of deterministic chance which builds upon the physico-mathematical approach to theorizing about deterministic chance known as 'the method of arbitrary functions'. This approach promisingly yields deterministic probabilities which align with what we take the chances to be---it tells us that there is approximately a 1/2 probability of a spun roulette wheel stopping on black, and approximately a 1/2 probability of a flipped coin landing heads up---but it requires some probabilistic materials to work with. I (...) contend that the right probabilistic materials are found in reasonable initial credence distributions. I note that, with some normative assumptions, the resulting account entails that deterministic chances obey a variant of Lewis's 'principal principle'. I additionally argue that deterministic chances, so understood, are capable of explaining long-run frequencies. (shrink)

The aim of this paper is to respond to the discussions by John McCumber and Joshua Ramey of my monograph, Hegel, Deleuze, and the Critique of Representation. In the first part of this paper, I analyse McCumber’s claim that Deleuze’s concept of difference is already present within Hegel’s thought in the form of diversity. I make the claim that Deleuze formulates his concept of difference as the transcendental ground for Hegelian diversity, arguing that as such it differs in kind from (...) it. I show how Deleuze’s concept of difference leads him to develop an alternative solution to the one and the many to that of Hegel, and trace some of the systematic implications of this for both philosophers. In the second part of the paper, I engage with Ramey’s analysis of chance within Deleuze’s philosophy, arguing that Ramey wrongly looks for a model of chance in Deleuze in the category of the virtual, rather than in a transition between virtual and actual. I then show how a proper understanding of chance in Deleuze’s thought allows us to develop a non-teleological account of Deleuze’s ethics. (shrink)

Mellor´s theory of causation has two components, one according to which causes raise their effects´ chances, and one according to which causation links facts. I argue that these two components are not independent from each other and, in particular, that Mellor´s thesis that causation links facts requires his thesis that causes raise their effects´ chances, since without the latter thesis Mellor cannot stop the slingshot argument, an argument that is a threat to any theory postulating facts as the relata of (...) causation. (shrink)