This paper discusses counterexamples to the thesis that the probabilities of conditionals are conditional probabilities. It is argued that the discrepancy is systematic and predictable, and that conditional probabilities are crucially involved in the apparently deviant interpretations. Furthermore, the examples suggest that such conditionals have a less prominent reading on which their probability is in fact the conditional probability, and that the two readings are related by a simple step of abductive inference. Central to the proposal is a distinction between (...) causal and purely stochastic dependence between variables. (shrink)

It is shown that Lewis’ ontological doctrine of Humean supervenience incorporates at its foundation the so-called separability principle of classical physics. In view of the systematic violation of the latter within quantum mechanics, the claim that contemporary physical science may posit non-supervenient relations beyond the spatiotemporal ones is reinforced on a foundational basis concerning constraints on the state representation of physical systems. Depending on the mode of assignment of states to quantum systems — unit state vectors versus statistical density operators (...) — we distinguish between strongly and weakly non-Humean, non-supervenient relations. It is demonstrated that in either case, the relations of quantum entanglement constitute prototypical examples of irreducible physical relations that do not supervene upon a spatiotemporal arrangement of Humean qualities, weakening, thereby, the thesis of Humean supervenience. In this respect, the status of Lewis’ recombination principle is examined, whereas his conception of lawhood is critically investigated. It is concluded that the assumption of ontological reductionism, as expressed in Lewis’ Humean doctrine, cannot be regarded as a reliable code of the nature of the physical world and its contents. It is proposed instead that due to the undeniable existence of non-supervenient relations, a metaphysic of relations of a moderate kind ought to be acknowledged as an indispensable part of our understanding of the natural world at a fundamental level. (shrink)

David Lewis'sPrincipal Principle states that our credence in a single case follows from the general probability of all such cases. Against this stands the Challenge Argument – to show that the inference is justified. Recent law-to-chance, Bayesian, and propensity theories of probability take up the challenge – but, I argue, fall short. Rather, we should understand propensity via Aristotle's analysis of spontaneity and probabilistic reasoning via theAnti-PPand the practice ofbundling one offs, where forced bad-odds one offsilluminate how extensive a role (...) luck plays in our lives. (shrink)

In this paper, we argue that what is often discussed under the umbrella of `spacetime emergence' in the philosophy of quantum gravity in fact consists of a plethora of distinct and even highly different problems. We therefore advocate to cast such debates more specifically in terms of the emergent spatiotemporal aspects, as is already done in the physics literature. We first show how ambiguous the notion of spacetime is already in general relativity. We then argue against three ways to reject (...) our call for specificity: the many distinct philosophical problems relating to the emergence of the various spatiotemporal aspects do not suggest any singular, overarching, or exceptional problem of spacetime emergence. We also discuss how the objections are reflected by five conceptions of spacetime. Next, we observe that different spatiotemporal aspects are emergent in the different quantum gravity approaches, whereby investigating emergence in quantum gravity collectively is problematic. Finally, we illustrate how philosophical inquiries that employ notions of spacetime emergence are aided by conducting the investigation at the level of specific spatiotemporal aspects. (shrink)

Distance, it is often argued, is the only coherent and empirically adequate world-making relation that can glue together the elements of the world. This paper offers entanglement as an alternative world-making relation. Entanglement is interesting since it is consistent even with quantum gravity theories that do not feature space at the fundamental level. The paper thereby defends the metaphysical salience of such non-spatial theories. An account of distance is the predominant problem of empirical adequacy facing entanglement as a world-making relation. (...) A resolution of this obstacle utilizes insights from the Ryu–Takayanagi formula and Susskind and Maldacena’s related ER = EPR conjecture. Together these indicate how distance can be recovered from entanglement and thus carves the way for entanglement fundamentalism. (shrink)

According to naturalized metaphysics, metaphysics should be informed by our current best science and not rely on a priori reasoning. Consequently, naturalized metaphysics tends to dismiss metaphysicians’ attempts to quarrel with science. This paper argues that naturalized metaphysics should instead welcome such conflicts between metaphysics and science. Naturalized metaphysics is not eliminative of metaphysics. So, if such conflicts are driven by the immediate absence in science of an answer to a metaphysical question, then the conflict should not be dismissed, but (...) instead be received as an occasion to do naturalized metaphysics. That conflicts between metaphysics and science might be beneficial for naturalized metaphysics is exemplified by the case of non-spatial theories of quantum gravity. These theories are criticized by metaphysicians who, often following David Lewis, argue that spatial distance is an indispensable fundamental element in any coherent metaphysics due to its role as the world-making relation. The resulting conflict, however, is found to be well-motivated since the non-spatial theories of quantum gravity offer no alternative world-making relation to spatial distance. Rather than dismissing this conflict, naturalized metaphysics should therefore receive the Lewisians’ resistance as a call to search for one. How this plays out as a negotiation between the scientific theory and the metaphysical question is exemplified in the last part of the paper where entanglement is proposed as an alternative world-making relation in loop quantum gravity. (shrink)

David Lewis has proposed an analysis of lawhood in terms of membership of a system of regularities optimizing simplicity and strength in information content. This article studies his proposal against the broader background of the project of Humean supervenience. In particular, I claim that, in Lewis's account of lawhood, his intuition about small deviations from a given law in nearby worlds (in order to avoid backtracking and epiphenomena) leads to the conclusion that laws do not support (certain) counterfactuals and do (...) not bestow nomic necessity on (certain) facts induced by these laws. Support of counterfactuals and nomic necessity, however, are widely held to be important aspects of the concept of lawhood. In my view, therefore, it is not possible to abandon these criteria in any satisfactory analysis of the notion of laws of nature. In a final section, I suggest that the whole project of Humean supervenience is misleading. It does not sufficiently take notice of the important role that reasoning about contrary-to-fact situations plays in modern scientific practice. (shrink)

David Lewis's influential work on the epistemology and metaphysics of objective chance has convinced many philosophers of the central importance of the following two claims: First, it is a serious cost of reductionist positions about chance (such as that occupied by Lewis) that they are, apparently, forced to modify the Principal Principle--the central principle relating objective chance to rational subjective probability--in order to avoid contradiction. Second, it is a perhaps more serious cost of the rival non-reductionist position that, unlike reductionism, (...) it can give no coherent explanation for why the Principal Principle should hold. I argue that both of these claims are fundamentally mistaken. (shrink)

The 'best-system' analysis of lawhood [Lewis 1994] faces the 'zero-fit problem': that many systems of laws say that the chance of history going actually as it goes--the degree to which the theory 'fits' the actual course of history--is zero. Neither an appeal to infinitesimal probabilities nor a patch using standard measure theory avoids the difficulty. But there is a way to avoid it: replace the notion of 'fit' with the notion of a world being typical with respect to a theory.

Possible worlds, concrete or abstract as you like, are irrelevant to the truthmakers for modality—or so I shall argue in this paper. First, I present the neo-Humean picture of modality, and explain why those who accept it deny a common sense view of modality. Second, I present what I take to be the most pressing objection to the neo-Humean account, one that, I argue, applies equally well to any theory that grounds modality in possible worlds. Third, I present an alternative, (...) properties-based theory of modality and explore several specific ways to flesh the general proposal out, including my favored version, the powers theory. And, fourth, I offer a powers semantics for counterfactuals that each version of the properties-based theory of modality can accept, mutatis mutandis. Together with a definition of possibility and necessity in terms of counterfactuals, the powers semantics of counterfactuals generates a semantics for modality that appeals to causal powers and not possible worlds. (shrink)

The chance of a physical event is the objective, single-case probability that it will occur. In probabilistic physical theories like quantum mechanics, the chances of physical events play the formal role that the values of physical quantities play in classical (deterministic) physics, and there is a temptation to regard them on the model of the latter as describing intrinsic properties of the systems to which they are assigned. I argue that this understanding of chances in quantum mechanics, despite being a (...) part of the orthodox interpretation of the theory and the most prevalent view in the physical community, is incompatible with a very wide range of metaphysical views about the nature of chance. The options that remain are unlikely to be attractive to scientists and scientifically minded philosophers. (shrink)

A central problem facing a probabilistic approach to the problem of induction is the difficulty of sufficiently constraining prior probabilities so as to yield the conclusion that induction is cogent. The Principle of Indifference, according to which alternatives are equiprobable when one has no grounds for preferring one over another, represents one way of addressing this problem; however, the Principle faces the well-known problem that multiple interpretations of it are possible, leading to incompatible conclusions. I propose a partial solution to (...) the latter problem, drawing on the notion of explanatory priority. The resulting synthesis of Bayesian and inference-to-best-explanation approaches affords a principled defense of prior probability distributions that support induction. (shrink)

This note is a sequel to Huber. It is shown that obeying a normative principle relating counterfactual conditionals and conditional beliefs, viz. the royal rule, is a necessary and sufficient means to attaining a cognitive end that relates true beliefs in purely factual, non-modal propositions and true beliefs in purely modal propositions. Along the way I will sketch my idealism about alethic or metaphysical modality.

Philosophers typically rely on intuitions when providing a semantics for counterfactual conditionals. However, intuitions regarding counterfactual conditionals are notoriously shaky. The aim of this paper is to provide a principled account of the semantics of counterfactual conditionals. This principled account is provided by what I dub the Royal Rule, a deterministic analogue of the Principal Principle relating chance and credence. The Royal Rule says that an ideal doxastic agent’s initial grade of disbelief in a proposition \(A\) , given that the (...) counterfactual distance in a given context to the closest \(A\) -worlds equals \(n\) , and no further information that is not admissible in this context, should equal \(n\) . Under the two assumptions that the presuppositions of a given context are admissible in this context, and that the theory of deterministic alethic or metaphysical modality is admissible in any context, it follows that the counterfactual distance distribution in a given context has the structure of a ranking function. The basic conditional logic V is shown to be sound and complete with respect to the resulting rank-theoretic semantics of counterfactuals. (shrink)

A subarea of the debate over the nature of evolutionary theory addresses what the nature of the explanations yielded by evolutionary theory are. The statisticalist line is that the general principles of evolutionary theory are not only amenable to a mathematical interpretation but that they need not invoke causes to furnish explanations. Causalists object that construction of these general principles involves crucial causal assumptions. A recent view claims that some biological explanations are statistically autonomous explanations (SAEs) whereby phenomena are accounted (...) for statistically and which prescind from micro-causal details. I raise three major problems for this account and then advance a view which unifies SAEs as mathematical explanations: the MSAE view. The MSAE view not only resolves the issues bedeviling the original SAE account but serves to importantly broaden the class of non-causal explanations in population biology. (shrink)

This paper advances the view that some explanations in cognitive science are extra-mathematical explanations. Demonstrating the plausibility of this interpretation centers around certain efficient coding cases which ineliminably enlist information theoretic laws, facts and theorems to identify in-principle, mathematical constraints on neuronal information processing capacities. The explanatory structure in these cases is shown to parallel other putative instances of mathematical explanation. The upshot for cognitive mathematical explanations is thus two-fold: first, the view capably rebuts standard mechanistic objections to non-mechanistic explanation; (...) second, this view serves to importantly widen the possibility space for non-mechanistic forms of explanation in cognitive science. (shrink)

Nancy Cartwright argues that so-called capacities, not universal laws of nature, best explain the often complex way events actually unfold. On this view, science would represent a world that is fundamentally "dappled", or disunified, and not, as orthodoxy would perhaps have it, a world unified by universal laws of nature. I argue, first, that the problem Cartwright raises for laws of nature seems to arise for capacities too, so why reject laws of nature? Second, that in so far as there (...) is a problem, it concerns the role of counterfactuals in explanation; I then briefly propose a simple model of counterfactual explanation. Finally, I investigate how a sophisticated version of the regularity theory of laws of nature (that of Ramsey-Lewis) can be neutral between the empirical hypotheses that the world is unified, and that the world is disunified. (shrink)

The goal of this paper is to sketch and defend a new interpretation or 'theory' of objective chance, one that lets us be sure such chances exist and shows how they can play the roles we traditionally grant them. The account is 'Humean' in claiming that objective chances supervene on the totality of actual events, but does not imply or presuppose a Humean approach to other metaphysical issues such as laws or causation. Like Lewis (1994) I take the Principal Principle (...) (PP) to be the key to understanding objective chance. After describing the main features of Humean objective chance (HOC), I deduce the validity of PP for Humean chances, and end by exploring the limitations of Humean chance. (shrink)

One currently popular view about the nature of objective probabilities, or objective chances, is that they – or some of them, at least – are primitive features of the physical world, not reducible to anything else nor explicable in terms of frequencies, degrees of belief, or anything else. In this paper I explore the question of what the semantic content of primitive chance claims could be. Every attempt I look at to supply such content either comes up empty-handed, or begs (...) important questions against the skeptic who doubts the meaningfulness of primitive chance claims. In the second half of the paper I show that, by contrast, there are clear, and clearly contentful, ways to understand objective chance claims if we ground them on deterministic physical underpinnings. (shrink)

Our beliefs can have, or fail to have, a significant epistemic virtue: they can be true. What about our partial beliefs – that is, credences or subjective probabilities? Is there an epistemic virtue that credences can have or fail to have, whose nature or role with respect to credences is analogous to the role that truth has with respect to full beliefs? Van Fraassen argued in the 1980s that there is indeed such an analog virtue, and he claimed that it (...) is calibration: our credences should match, or be in tune with, some appropriately chosen frequencies of events. For example, if your credence in the proposition ‘It will rain today’ is 0.3 for any day that starts out like today did, and in fact it does rain on approximately 30% of such days, then your credence level is well‐calibrated, and is vindicated by the actual frequency of rain.In an unpublished paper Alan Hájek rejects this calibrationist answer, and proposes instead that having credences in agreement with the relevant objective chances is what it is to have vindicated credences, in the relevant sense analogous to truth for full beliefs. Although there are problems that afflict both van Fraassen's and Hájek's proposals, I will argue that Hájek and the calibrationist are both largely right – although the calibrationist answer is at bottom more right. In section I will propose an account of being in tune with the world that divides types of propositions into a few different classes; for one of those classes, Hájek's answer is exactly right, while for the others the calibrationist account gives the right answer. (shrink)

We argue that indeterminate probabilities are not only rationally permissible for a Bayesian agent, but they may even be rationally required . Our first argument begins by assuming a version of interpretivism: your mental state is the set of probability and utility functions that rationalize your behavioral dispositions as well as possible. This set may consist of multiple probability functions. Then according to interpretivism, this makes it the case that your credal state is indeterminate. Our second argument begins with our (...) describing a world that plausibly has indeterminate chances. Rationality requires a certain alignment of your credences with corresponding hypotheses about the chances. Thus, if you hypothesize the chances to be indeterminate, your will inherit their indeterminacy in your corresponding credences. Our third argument is motivated by a dilemma. Epistemic rationality requires you to stay open-minded about contingent matters about which your evidence has not definitively legislated. Practical rationality requires you to be able to act decisively at least sometimes. These requirements can conflict with each other-for thanks to your open-mindedness, some of your options may have undefined expected utility, and if you are choosing among them, decision theory has no advice to give you. Such an option is playing Nover and Hájek’s Pasadena Game , and indeed any option for which there is a positive probability of playing the Pasadena Game. You can serve both masters, epistemic rationality and practical rationality, with an indeterminate credence to the prospect of playing the Pasadena game. You serve epistemic rationality by making your upper probability positive-it ensures that you are open-minded. You serve practical rationality by making your lower probability 0-it provides guidance to your decision-making. No sharp credence could do both. (shrink)

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

According to finite frequentism, the probability of an attribute A in a finite reference class B is the relative frequency of actual occurrences of A within B. I present fifteen arguments against this position.

This is the sequel to my “Fifteen Arguments Against Finite Frequentism” ( Erkenntnis 1997), the second half of a long paper that attacks the two main forms of frequentism about probability. Hypothetical frequentism asserts: The probability of an attribute A in a reference class B is p iff the limit of the relative frequency of A ’s among the B ’s would be p if there were an infinite sequence of B ’s. I offer fifteen arguments against this analysis. I (...) consider various frequentist responses, which I argue ultimately fail. I end with a positive proposal of my own, ‘hyper-hypothetical frequentism’, which I argue avoids several of the problems with hypothetical frequentism. It identifies probability with relative frequency in a hyperfinite sequence of trials. However, I argue that this account also fails, and that the prospects for frequentism are dim. (shrink)

Start with an ordinary disposition ascription, like ‘the wire is live’ or ‘the glass is fragile’. Lewis gives a canonical template for what he regards as the analysandum of such an ascription:“Something x is disposed at time t to give response r to stimulus s”.For example, the wire is disposed at noon to conduct electrical current when touched by a conductor.What Lewis calls “the simple conditional analysis” gives putatively necessary and sufficient conditions for the analysandum in terms of a counterfactual:“if (...) x were to undergo stimulus s at time t, x would give response r”.Call this the counterfactual analysans. For example: If the wire were to be touched by a conductor at noon, the wire would conduct electricity.So we have three things in play: the ordinary disposition ascription ; the canonical template that is supposed to formalize this disposition ascription; and the counterfactual analysans that is supposed to provided an analysis of the canonical template.Finkish dispositions have been widely regarded as counterexamples to the adequacy of as an analysis of. I will argue that they are not. They succeed, however, as counterexamples to the adequacy of as an analysis of. That said, the classic cases are somewhat contrived. I will introduce the notion of a minkish disposition: a disposition that something has, even though it might not display it in response to the relevant stimulus. Cases of minkish dispositions are entirely familiar. They refute the adequacy of both as an analysis of and of. I will argue that they also refute Lewis’s own, more complicated counterfactual analysis of dispositions, and bring out an internal tension in his views. (shrink)

‘If I were to toss a coin 1000 times, then it would land heads exactly n times’. Is there a specific value of n that renders this counterfactual true? According to an increasingly influential view, there is. A precursor of the view goes back to the Molinists; more recently it has been inspired by Stalnaker, and versions of it have been advocated by Hawthorne, Bradley, Moss, Schulz, and Stefánsson. More generally, I attribute to these authors what I call Counterfactual Plenitude:For (...) any antecedent A, there is a world wisuch that A ☐→ wiis true.Moreover, some of these authors are also committed to Primitive Counterfacts Realism:There exist primitive modal facts that serve as truth-makers for counterfactual claims.Call the conjunction of these italicized theses counterfactism. I clarify it and suggest some of its virtues, while ultimately rejecting it.Stefánsson’s counterfactism is motivated by and targeted at my “counterfactual skepticism”—I argue that most counterfactuals are false—and counterfactism has various other sources of support. I briefly defend that skepticism, and I seek to undercut those sources of support. I then argue more directly against counterfactism, especially on grounds of its ontological profligacy, and its leading to another kind of skepticism about counterfactuals that I believe is more problematic than my kind. In the process, I discuss how Bradley’s multidimensional semantics bears on counterfactism; I offer some new considerations against some central theses regarding conditionals ; and I reflect more generally on the epistemology of modality and the choice of primitives in our theorizing. (shrink)

An important task for metaphysicians and philosophers of science is to account for laws of nature – in particular, how they distinguish themselves from ‘mere’ regularities, and the modal force they are endowed with, ‘natural necessity’. Dispositional essentialism about laws is roughly the view that laws distinguish themselves by being grounded in the essences of natural entities. This paper does not primarily concern how essentialism compares to its main rivals – Humeanism and Armstrongeanism. Rather, it distinguishes and comparatively assesses various (...) brands of essentialism – which mainly differ as to where exactly they take laws to find their essentialist sources, and what they take to be the targets of laws, namely what they apply to. Yet, this internal comparison is not unrelated to the more general debate about laws: the main criteria with which I compare these essentialist views concern how they can deal with some of the main objections faced by essentialism in general, and how they can keep what is arguably the main intuitive advantage of essentialism over its rivals. Thus, the paper also concerns the relative position of essentialism in the larger debate about laws – ultimately bringing support to it. (shrink)

Non‐Humean theories of natural necessity invoke modally‐laden primitives to explain why nature exhibits lawlike regularities. However, they vary in the primitives they posit and in their subsequent accounts of laws of nature and related phenomena (including natural properties, natural kinds, causation, counterfactuals, and the like). This article provides a taxonomy of non‐Humean theories, discusses influential arguments for and against them, and describes some ways in which differences in goals and methods can motivate different versions of non‐Humeanism (and, for that matter, (...) Humeanism). In short, this article provides an introduction to non‐Humeanism concerning the metaphysics of laws of nature and natural necessity. (shrink)

One of the traditional desiderata for a metaphysical theory of laws of nature is that it be able to explain natural regularities. Some philosophers have postulated governing laws to fill this explanatory role. Recently, however, many have attempted to explain natural regularities without appealing to governing laws. Suppose that some fundamental properties are bare dispositions. In virtue of their dispositional nature, these properties must be (or are likely to be) distributed in regular patterns. Thus it would appear that an ontology (...) including bare dispositions can dispense with governing laws of nature. I believe that there is a problem with this line of reasoning. In this essay, I’ll argue that governing laws are indispensable for the explanation of a special sort of natural regularity: those holding among categorical properties (or, as I’ll call them, categorical regularities). This has the potential to be a serious objection to the denial of governing laws, since there may be good reasons to believe that observed regularities are categorical regularities. (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)

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)

Humeans are often accused of accounting for natural laws in such a way that the fundamental entities that are supposed to explain the laws circle back and explain themselves. Loewer (2012) contends this is only the appearance of circularity. When it comes to the laws of nature, the Humean posits two kinds of explanation: metaphysical and scientific. The circle is then cut because the kind of explanation the laws provide for the fundamental entities is distinct from the kind of explanation (...) the entities provide for the laws. Lange (2013) has replied that Loewer’s defense is a distinction without a difference. As Lange sees it, Humeanism still produces a circular explanation because scientific explanations are transmitted across metaphysical explanations. We disagree that metaphysical explanation is such a ready conduit of scientific explanation. In what follows, we clear Humeanism of all charges of circularity by exploring how different kinds of explanation can and cannot interact. Our defense of Humeanism begins by presenting the circularity objection and detailing how it relies on an implausible principle about the transitivity of explanation. Then, we turn to Lange’s (2013) transitivity principle for explanation to argue that it fairs no better. With objections neutral to the debate between Humeanism and anti-Humeanism, we will show that his principle is not able to make the circularity objection sound. (shrink)

Humean accounts of laws of nature fail to distinguish between dynamic laws and static initial conditions. But this distinction plays a central role in scientific theorizing and explanation. I motivate the claim that this distinction should matter for the Humean, and show that current views lack the resources to explain it. I then develop a regularity theory that captures this distinction. My view takes empirical accessibility to be one of the primary features of laws, and I identify features laws must (...) have to be empirically accessible. I then argue that laws with these features tend to be dynamic. _1_ The Best System _1.1_ Orthodox Humeanism _2_ The Best Is Not Good Enough _2.1_ Laws and boundary conditions _2.2_ Laws and scientific practice _2.3_ An illustrative example _3_ Laws and Epistemic Roles _3.1_ The epistemic criterion _3.2_ The epistemic role account _3.3_ Scientific virtues _3.4_ Applying the epistemic role account _4_ Conclusion. (shrink)

Do unknown and unrealized risks of harm diminish an individual’s well-being? The traditional answer is no: that the security of prudential goods benefits an individual only instrumentally or by virtue of their subjective sense of security. Recent work has argued, however, that the security of prudential goods non-instrumentally benefits an individual regardless of whether or not they enjoy subjective security. In this paper, I critically examine three claims about the way in which unknown and unrealized risks of harm might diminish (...) individual well-being: it frustrates a desire to be secure, it frustrates the enjoyment of modally-robust goods, and it undermines the ability to make reasonable plans. Ultimately, I argue that all three of these hypotheses are mistaken, but that they deepen our understanding of the ways in which subjective security is an important constituent of individual well-being. (shrink)

The rejection of an infinitesimal solution to the zero-fit problem by A. Elga ([2004]) does not seem to appreciate the opportunities provided by the use of internal finitely-additive probability measures. Indeed, internal laws of probability can be used to find a satisfactory infinitesimal answer to many zero-fit problems, not only to the one suggested by Elga, but also to the Markov chain (that is, discrete and memory-less) models of reality. Moreover, the generalization of likelihoods that Elga has in mind is (...) not as hopeless as it appears to be in his article. In fact, for many practically important examples, through the use of likelihoods one can succeed in circumventing the zero-fit problem. 1 The Zero-fit Problem on Infinite State Spaces 2 Elga's Critique of the Infinitesimal Approach to the Zero-fit Problem 3 Two Examples for Infinitesimal Solutions to the Zero-fit Problem 4 Mathematical Modelling in Nonstandard Universes? 5 Are Nonstandard Models Unnatural? 6 Likelihoods and Densities A Internal Probability Measures and the Loeb Measure Construction B The (Countable) Coin Tossing Sequence Revisited C Solution to the Zero-fit Problem for a Finite-state Model without Memory D An Additional Note on ‘Integrating over Densities’ E Well-defined Continuous Versions of Density Functions. (shrink)

I argue that a attractive theory about the metaphysics of belief—the prag- matic, interpretationist theory endorsed by Stalnaker, Lewis, and Dennett, among others—implies that agents have a novel form of voluntary control over their beliefs. According to the pragmatic picture, what it is to have a given belief is in part for that belief to be part of an optimal rationalization of your actions. Since you have voluntary control over your actions, and what actions you perform in part determines what (...) beliefs you count as having, this theory entails that you have some voluntary control over your beliefs. However, the pragmatic picture doesn’t entail that you can believe something as a result of intention to believe it. Nevertheless, I argue that the limited sort of voluntary control implied by the pragmatic picture may be of use in vindicating the deontological conception of epistemic justification. (shrink)

In a deterministically evolving world, the usefulness of nontrivial probabilities can seem mysterious. I use the ‘Mentaculus’ machinery developed by David Albert and Barry Loewer to show how all probabilities in such a world can be derived from a single, initial chance event. I go on to argue that this is the only genuine chance event. Perhaps surprisingly, we have good evidence of its existence and nature. I argue that the existence of this chance event justifies our epistemic reliance on (...) nontrivial probabilities. (shrink)

I claim that, if persisting objects have temporal parts, then there are non-supervenient relations between those temporal parts. These are relations which are not determined by intrinsic properties of the temporal parts. I use the Kripke-Armstrong 'rotating homogeneous disc' argument in order to establish this claim, and in doing so I defend and develop that argument. This involves a discussion of instantaneous velocity, and of the causes and effects of rotation. Finally, I compare alternative responses to the rotating disc argument, (...) and consider the implications of my arguments for the doctrines of Humean Supervenience and unrestricted mereology. (shrink)

As is well-known, David Lewis’ counterfactual theory of causation is subject to serious counterexamples in ‘exceptional’ cases. What has not received due attention in the literature so far is that Lewis’ theory fails to provide necessary and sufficient conditions for causation in ‘ordinary’ cases, too. In particular, the theory suffers from the ‘problem of large causes’. It is argued that this problem may be fixed by imposing a minimization constraint, whilst this solution brings along substantial costs as well. In particular, (...) a precise formulation of minimization requires defining an ‘essential part of an event’ and/or an ‘essential subevent’. Although the possibility of such a definition is ultimately left open, some doubts are raised on whether the counterfactualists’ resources are fit for this purpose, and whether the challenge can be met without substantially departing from Lewis’ intention, which was to provide a reductive account of causation. (shrink)

This paper explores how the Bayesian program benefits from allowing for objective chance as well as subjective degree of belief. It applies David Lewis’s Principal Principle and David Christensen’s principle of informed preference to defend Howard Raiffa’s appeal to preferences between reference lotteries and scaling lotteries to represent degrees of belief. It goes on to outline the role of objective lotteries in an application of rationality axioms equivalent to the existence of a utility assignment to represent preferences in Savage’s famous (...) omelet example of a rational choice problem. An example motivating causal decision theory illustrates the need for representing subjunctive dependencies to do justice to intuitive examples where epistemic and causal independence come apart. We argue to extend Lewis’s account of chance as a guide to epistemic probability to include De Finetti’s convergence results. We explore Diachronic Dutch book arguments as illustrating commitments for treating transitions as learning experiences. Finally, we explore implications for Martingale convergence results for motivating commitment to objective chances. (shrink)

Two types of measures of probabilistic uncertainty are introduced and investigated. Dispersion measures report how diffused the agent’s second-order probability distribution is over the range of first-order probabilities. Robustness measures reflect the extent to which the agent’s assessment of the prior (objective) probability of an event is perturbed by information about whether or not the event actually took place. The properties of both types of measures are investigated. The most obvious type of robustness measure is shown to coincide with one (...) of the major candidates for a dispersion measure, the mean square deviation measure. (shrink)

Humean metaphysics is characterized by a rejection of necessary connections between distinct existences. Dispositionalists claim that there are basic causal powers. The existence of such properties is widely held to be incompatible with the Humean rejection of necessary connections. In this paper I present a novel theory of causal powers that vindicates the dispositionalist claim that causal powers are basic, without embracing brute necessary connections. The key assumptions of the theory are that there are natural types of causal processes, and (...) that manifestations of powers are identified with certain kinds of causal processes. From these assumptions, the modal features of powers are explained in terms of internal relations between powers themselves and the process-types in which powers are manifested. (shrink)

An acceptable empiricist account of laws of nature would havesignificant implications for a number of philosophical projects. For example, such an account may vitiate argumentsthat the fundamental constants of nature are divinelydesigned so that laws produce a life permittinguniverse. On an empiricist account, laws do not produce the universe but are designed by us to systematize theevents of a universe which does in fact contain life; so any ``fine tuning'' of natural law has a naturalistic explanation.But there are problems for (...) the empiricist project. This paper develops a ``perspectival'' version of the Humean bestsystem approach and argues that this version solves the standard problems faced by the empiricist project.Furthermore, the paper argues, this version is best able to answer the proponents of divine design while leaving scientificlaw a suitably objective matter.[I]t is possible tocondense the enormous mass of results to a large extent – that is to find laws which summarize...Richard Feynman It has become fashionable in some circles to argue thatscience is ultimately a sham, that we scientists read order into nature, not out of nature, and that the laws of physicsare our laws, not nature's. I believe this is arrant nonsense. You would be hard-pressed to convince a physicist thatNewton's inverse square law of gravitation is a purely cultural concoction. The laws of physics, I submit, reallyexist in the world out there, and the job of the scientist is to uncover them, not invent them. True, at any giventime, the laws you find in the textbooks are tentative and approximate, but they mirror, albeit imperfectly, a reallyexisting order in the physical world. Of course, many scientists do not recognize that in accepting the reality of anorder in nature-the existence of laws `out there' – they are adopting a theological world view. P. C. W. Davies. (shrink)

This paper discusses some serious difficulties for what we shall call the standard account of various kinds of relative necessity, according to which any given kind of relative necessity may be defined by a strict conditional - necessarily, if C then p - where C is a suitable constant proposition, such as a conjunction of physical laws. We argue, with the help of Humberstone, that the standard account has several unpalatable consequences. We argue that Humberstone’s alternative account has certain disadvantages, (...) and offer another - considerably simpler - solution. (shrink)