This paper is a sympathetic critique of the argument that Reichenbach develops in Chap. 2 of Experience and Prediction for the thesis that sense experience justifies belief in the existence of an external world. After discussing his attack on the positivist theory of meaning, I describe the probability ideas that Reichenbach presents. I argue that Reichenbach begins with an argument grounded in the Law of Likelihood but that he then endorses a different argument that involves prior probabilities. I try to (...) show how this second step in Reichenbach’s approach can be strengthened by using ideas that have been developed recently for understanding causation in terms of the idea of intervention. (shrink)

Currently, the most popular views about how to update de se or self-locating beliefs entail the one-third solution to the Sleeping Beauty problem.2 Another widely held view is that an agent‘s credences should be countably additive.3 In what follows, I will argue that there is a deep tension between these two positions. For the assumptions that underlie the one-third solution to the Sleeping Beauty problem entail a more general principle, which I call the Generalized Thirder Principle, and there are situations (...) in which the latter principle and the principle of Countable Additivity cannot be jointly satisfied. The most plausible response to this tension, I argue, is to accept both of these principles, and to maintain that when an agent cannot satisfy them both, she is faced with a rational dilemma. (shrink)

My dissertation explores the ways in which Rudolf Carnap sought to make philosophy scientific by further developing recent interpretive efforts to explain Carnap’s mature philosophical work as a form of engineering. It does this by looking in detail at his philosophical practice in his most sustained mature project, his work on pure and applied inductive logic. I, first, specify the sort of engineering Carnap is engaged in as involving an engineering design problem and then draw out the complications of design (...) problems from current work in history of engineering and technology studies. I then model Carnap’s practice based on those lessons and uncover ways in which Carnap’s technical work in inductive logic takes some of these lessons on board. This shows ways in which Carnap’s philosophical project subtly changes right through his late work on induction, providing an important corrective to interpretations that ignore the work on inductive logic. Specifically, I show that paying attention to the historical details of Carnap’s attempt to apply his work in inductive logic to decision theory and theoretical statistics in the 1950s and 1960s helps us understand how Carnap develops and rearticulates the philosophical point of the practical/theoretical distinction in his late work, offering thus a new interpretation of Carnap’s technical work within the broader context of philosophy of science and analytical philosophy in general. (shrink)

The paper argues that on three out of eight possible hypotheses about the EPR experiment we can construct novel and realistic decision problems on which (a) Causal Decision Theory and Evidential Decision Theory conflict (b) Causal Decision Theory and the EPR statistics conflict. We infer that anyone who fully accepts any of these three hypotheses has strong reasons to reject Causal Decision Theory. Finally, we extend the original construction to show that anyone who gives any of the three hypotheses any (...) non-zero credence has strong reasons to reject Causal Decision Theory. However, we concede that no version of the Many Worlds Interpretation (Vaidman, in Zalta, E.N. (ed.), Stanford Encyclopaedia of Philosophy 2014) gives rise to the conflicts that we point out. (shrink)

In Bayesian epistemology, the problem of the priors is this: How should we set our credences (or degrees of belief) in the absence of evidence? That is, how should we set our prior or initial credences, the credences with which we begin our credal life? David Lewis liked to call an agent at the beginning of her credal journey a superbaby. The problem of the priors asks for the norms that govern these superbabies. -/- The Principle of Indifference gives a (...) very restrictive answer. It demands that such an agent divide her credences equally over all possibilities. That is, according to the Principle of Indifference, only one initial credence function is permissible, namely, the uniform distribution. In this paper, we offer a novel argument for the Principle of Indifference. I call it the Argument from Accuracy. (shrink)

This is part A of a paper in which we defend a semantics for counterfactuals which is probabilistic in the sense that the truth condition for counterfactuals refers to a probability measure. Because of its probabilistic nature, it allows a counterfactual ‘ifAthenB’ to be true even in the presence of relevant ‘Aand notB’-worlds, as long such exceptions are not too widely spread. The semantics is made precise and studied in different versions which are related to each other by representation theorems. (...) Despite its probabilistic nature, we show that the semantics and the resulting system of logic may be regarded as a naturalistically vindicated variant of David Lewis’ truth-conditional semantics and logic of counterfactuals. At the same time, the semantics overlaps in various ways with the non-truth-conditional suppositional theory for conditionals that derives from Ernest Adams’ work. We argue that counterfactuals have two kinds of pragmatic meanings and come attached with two types of degrees of acceptability or belief, one being suppositional, the other one being truth based as determined by our probabilistic semantics; these degrees could not always coincide due to a new triviality result for counterfactuals, and they should not be identified in the light of their different interpretation and pragmatic purpose. However, for plain assertability the difference between them does not matter. Hence, if the suppositional theory of counterfactuals is formulated with sufficient care, our truth-conditional theory of counterfactuals is consistent with it. The results of our investigation are used to assess a claim considered by Hawthorne and Hájek, that is, the thesis that most ordinary counterfactuals are false. (shrink)

We will present a new lottery-style paradox on counterfactuals and chance. The upshot will be: combining natural assumptions on the truth values of ordinary counterfactuals, the conditional chances of possible but non-actual events, the manner in which and relate to each other, and a fragment of the logic of counterfactuals leads to disaster. In contrast with the usual lottery-style paradoxes, logical closure under conjunction—that is, in this case, the rule of Agglomeration of counterfactuals—will not play a role in the derivation (...) and will not be entailed by our premises either. We will sketch four obvious but problematic ways out of the dilemma, and we will end up with a new resolution strategy that is non-obvious but less problematic: contextualism about what counts as a proposition. This proposal will not just save us from the paradox, it will also save each premise in at least some context, and it will be motivated by independent considerations from measure theory and probability theory. (shrink)

The paper will show how one may rationalize one-boxing in Newcomb's problem and drinking the toxin in the Toxin puzzle within the confines of causal decision theory by ascending to so-called reflexive decision models which reflect how actions are caused by decision situations (beliefs, desires, and intentions) represented by ordinary unreflexive decision models.

The Dutch Book argument, like Route 66, is about to turn 80. It is arguably the most celebrated argument for subjective Bayesianism. Start by rejecting the Cartesian idea that doxastic attitudes are ‘all-or-nothing’; rather, they are far more nuanced degrees of belief, for short credences, susceptible to fine-grained numerical measurement. Add a coherentist assumption that the rationality of a doxastic state consists in its internal consistency. The remaining problem is to determine what consistency of credences amounts to. The Dutch Book (...) argument, in a nutshell, says that if your credences do not obey the probability calculus, you are ‘incoherent’—susceptible to sure losses at the hands of a ‘Dutch Bookie’—and thus irrational. Conclusion: rationality requires your credences to obey the probability calculus. And like Route 66, the fortunes of the Dutch Book argument have been mixed. Opinions on the argument are sharply divided. The list of its proponents is quite a ‘who’s who’ of philosophers of probability; they include de Finetti (1937, 1980), Carnap (1950, 1962, and more fully, 1955), Kemeny (1955), Lehman (1955), Shimony (1955), Adams (1962), Mellor (1971), Rosenkrantz (1981), van Fraassen (1989), Jeffrey (1983, 1992). (shrink)

The idea that beliefs may be stake-sensitive is explored. This is the idea that the strength with which a single, persistent belief is held may vary and depend upon what the believer takes to be at stake. The stakes in question are tied to the truth of the belief—not, as in Pascal’s wager and other cases, to the belief’s presence. Categorical beliefs and degrees of belief are considered; both kinds of account typically exclude the idea and treat belief as stake-invariant (...) , though an exception is briefly described. The role of the assumption of stake-invariance in familiar accounts of degrees of belief is also discussed, and morals are drawn concerning finite and countable Dutch book arguments. (shrink)

This paper is a sympathetic critique of the argument that Reichenbach develops in Chap. 2 of Experience and Prediction for the thesis that sense experience justifies belief in the existence of an external world. After discussing his attack on the positivist theory of meaning, I describe the probability ideas that Reichenbach presents. I argue that Reichenbach begins with an argument grounded in the Law of Likelihood but that he then endorses a different argument that involves prior probabilities. I try to (...) show how this second step in Reichenbach's approach can be strengthened by using ideas that have been developed recently for understanding causation in terms of the idea of intervention. (shrink)

What can rational deliberation indicate about belief? Belief clearly influences deliberation. The principle that rational belief is stake-invariant rules out at least one way that deliberation might influence belief. The principle is widely, if implicitly, held in work on the epistemology of categorical belief, and it is built into the model of choice-guiding degrees of belief that comes to us from Ramsey and de Finetti. Criticisms of subjective probabilism include challenges to the assumption of additive values (the package principle) employed (...) by defenses of probabilism. But the value-interaction phenomena often cited in such challenges are excluded by stake-invariance. A comparison with treatments of categorical belief suggests that the appeal to stake-invariance is not ad hoc. Whether or not to model belief as stake-invariant is a question not settled here. (shrink)

Counterexamples are constructed for classical decision theory, turning on the fact that actions must often be chosen in groups rather than individually, i.e., the objects of rational choice are plans. It is argued that there is no way to define optimality for plans that makes the finding of optimal plans the desideratum of rational decision-making. An alternative called “locally global planning” is proposed as a replacement for classical decision theory. Decision-making becomes a non-terminating process without a precise target rather than (...) a terminating search for an optimal solution. (shrink)

Probabilistic coherence is not an absolute requirement of rationality; nevertheless, it is an ideal of rationality with substantive normative import. An idealized rational agent who avoided making implicit logical errors in forming his preferences would be coherent. In response to the challenge, recently made by epistemologists such as Foley and Plantinga, that appeals to ideal rationality render probabilism either irrelevant or implausible, I argue that idealized requirements can be normatively relevant even when the ideals are unattainable, so long as they (...) define a structure that links imperfect and perfect rationality in a way that enables us to make sense of the notion of better approximations to the ideal. I then analyze the notion of approximation to the ideal of coherence by developing a generalized theory of belief functions that allows for incoherence, and showing how such belief functions can be ordered with regard to greater or lesser coherence. (shrink)

Among various cases that equally admit of evidentialist reasoning, the supposedly evidentialist solution has varying degrees of intuitive attractiveness. I suggest that cooperative reasoning may account for the appeal of apparently evidentialist behavior in the cases in which it is intuitively attractive, while the inapplicability of cooperative reasoning may account for the unattractiveness of evidentialist behaviour in other cases. A collective causal power with respect to agreed outcomes, not evidentialist reasoning, makes cooperation attractive in the Prisoners' Dilemma. And a natural (...) though unwarranted assumption of such a power may account for the intuitive appeal of the one-box response in Newcomb's Problem. (shrink)

The representation theorems of expected utility theory show that having certain types of preferences is both necessary and sufficient for being representable as having subjective probabilities. However, unless the expected utility framework is simply assumed, such preferences are also consistent with being representable as having degrees of belief that do not obey the laws of probability. This fact shows that being representable as having subjective probabilities is not necessarily the same as having subjective probabilities. Probabilism can be defended on the (...) basis of the representation theorems only if attributions of degrees of belief are understood either antirealistically or purely qualitatively, or if the representation theorems are supplemented by arguments based on other considerations (simplicity, consilience, and so on) that single out the representation of a person as having subjective probabilities as the only true representation of the mental state of any person whose preferences conform to the axioms of expected utility theory. (shrink)

We consider the dispute between causal decision theorists and evidential decision theorists over Newcomb-like problems. We introduce a framework relating causation and directed graphs developed by Spirtes et al. (1993) and evaluate several arguments in this context. We argue that much of the debate between the two camps is misplaced; the disputes turn on the distinction between conditioning on an event E as against conditioning on an event I which is an action to bring about E. We give the essential (...) machinery for calculating the effect of an intervention and consider recent work which extends the basic account given here to the case where causal Knowledge is incomplete. (shrink)

My title is intended to recall Terence Fine's excellent survey, Theories of Probability [1973]. I shall consider some developments that have occurred in the intervening years, and try to place some of the theories he discussed in what is now a slightly longer perspective. Completeness is not something one can reasonably hope to achieve in a journal article, and any selection is bound to reflect a view of what is salient. In a subject as prone to dispute as this, there (...) will inevitably be many who will disagree with any author's views, and I take the opportunity to apologize in advance to all such people for what they will see as the narrowness and distortion of mine. (shrink)

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

De Finetti is one of the founding fathers of the subjective school of probability. He held that probabilities are subjective, coherent degrees of expectation, and he argued that none of the objective interpretations of probability make sense. While his theory has been influential in science and philosophy, it has encountered various objections. I argue that these objections overlook central aspects of de Finetti’s philosophy of probability and are largely unfounded. I propose a new interpretation of de Finetti’s theory that highlights (...) these aspects and explains how they are an integral part of de Finetti’s instrumentalist philosophy of probability. I conclude by drawing an analogy between misconceptions about de Finetti’s philosophy of probability and common misconceptions about instrumentalism. (shrink)

The world is said to contain crystal balls whenever the present carries news of the as-yet-undetermined parts of the future. Many philosophers believe that crystal balls are metaphysically possible. In this essay, I argue that they are not. Whether crystal balls are possible matters, for at least two reasons. The first is epistemological. According to a simple, user-friendly chance norm for credence, which I call the Present Principle, agents are rationally required to conform their credences to their expectations of the (...) present chances, deferring to the present chances as they would to an expert. I would like to defend the Present Principle since its truth would do much to simplify the relation between chance and credence. But the Present Principle is counterexample-free, and hence defensible, only if crystal balls are impossible. The second reason is decision-theoretic. The problem of crystal balls is one of the main objections to causal decision theory. But crystal ball cases can be counterexample to causal decision theory only if crystal balls are possible, and, as I argue, crystal balls are not possible. (shrink)

In the Newcomb problem, the standard arguments for taking either one box or both boxes adduce what seem to be relevant considerations, but they are not complete arguments, and attempts to complete the arguments rely upon incorrect principles of rational decision making. It is argued that by considering how the predictor is making his prediction, we can generate a more complete argument, and this in turn supports a form of causal decision theory.

One can interpret the No Probabilities for Acts-Principle, namely that any adequate quantitative decision model must in no way contain subjective probabilities for actions in two ways: it can either refer to actions that are performable now and extend into the future or it can refer to actions that are not performable now, but will be in the future. In this paper, I will show that the former is the better interpretation of the principle.

The puzzle of the absentminded driver combines an unstable decision problem with a version of the Sleeping Beauty problem. Its analysis depends on the choice between “halfing” and “thirding” as well as that between “evidential” and “causal” decision theory. I show that all four combinations lead to interestingly different solutions, and draw some general lessons about the formulation of causal decision theory, the interpretation of mixed strategies and the connection between rational credence and objective chance.

There are at least three core principles that define the chance role: ill the Principal Principle, l21 the Basic Chance Principle, and l31 the Humean Principle. These principles seem mutually incompatible. At least, no extant account of chance meets more than one of them. I ofier an account of chance which meets all three: L~-chance. So the good news is that L~-chance meets ill — l31. The bad news is that L~-chance turns out unlawful and unstable. But perhaps this is (...) not such bad news: L~-chance turns out to at least approximate plausible additional core principles concerning lawfulness and stability. And perhaps there is better news: one may treat 'chance' as vague, in a way that allows every core principle of chance to be met. (shrink)

If we think, as Ramsey did, that a degree of belief that P is a stronger or weaker tendency to act as if P, then it is clear that not only uncertainty, but also vagueness, gives rise to degrees of belief. If I like hot coffee and do not know whether the coffee is hot or cold, I will have some tendency to reach for a cup; if I like hot coffee and know that the coffee is borderline hot, I (...) will have some tendency to reach for a cup. Suppose that we take degrees of belief arising from uncertainty to obey the laws of probability and that we model vagueness using degrees of truth. We then encounter a problem: it does not look as though degrees of belief arising from vagueness should obey the laws of probability. One response would be to countenance two different sorts of degrees of belief: degrees of belief arising from uncertainty, which obey the laws of probability; and degrees of belief arising from vagueness, which obey a different set of laws. I argue, however, that if a degree of belief that P is a stronger or weaker tendency to act as if P, then this option is not open. Instead, I propose an account of the behaviour of degrees of belief that integrates subjective probabilities and degrees of truth. On this account, degrees of belief are expectations of degrees of truth. The account explains why degrees of belief behave in accordance with the laws of probability in cases involving only uncertainty, while also allowing degrees of belief to behave differently in cases involving only vagueness, and in mixed cases involving both uncertainty and vagueness. Justifications of the account are given both via Dutch books and in terms of epistemic accuracy. (shrink)

The thesis that probabilities of conditionals are conditional probabilities has putatively been refuted many times by so-called ‘triviality results’, although it has also enjoyed a number of resurrections. In this paper I assault it yet again with a new such result. I begin by motivating the thesis and discussing some of the philosophical ramifications of its fluctuating fortunes. I will canvas various reasons, old and new, why the thesis seems plausible, and why we should care about its fate. I will (...) look at some objections to Lewis’s famous triviality results, and thus some reasons for the pursuit of further triviality results. I will generalize Lewis’s results in ways that meet the objections. I will conclude with some reflections on the demise of the thesis—or otherwise. (shrink)

Conditional probability and selection-function approaches to chancy subjunctive conditionals are compared in a simple and transparent setting. They are seen to be alternative ways of calculating the same quantity. This unification extends from core cases to more peripheral cases.

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)

I argue that one central aspect of the epistemology of causation, the use of causes as evidence for their effects, is largely independent of the metaphysics of causation. In particular, I use the formalism of Bayesian causal graphs to factor the incremental evidential impact of a cause for its effect into a direct cause-to-effect component and a backtracking component. While the “backtracking” evidence that causes provide about earlier events often obscures things, once we our restrict attention to the cause-to-effect component (...) it is true to say promoting (inhibiting) causes raise (lower) the probabilities of their effects. This factoring assumes the same form whether causation is given an interventionist, counterfactual or probabilistic interpretation. Whether we think about causation in terms of interventions and causal graphs, counterfactuals and imaging functions, or probability raising against the background of causally homogenous partitions, if we describe the essential features of a situation correctly then the incremental evidence that a cause provides for its effect in virtue of being its cause will be the same. (shrink)

Examples involving common causes — most prominently, examples involving genetically influenced choices — are analytically equivalent not to standard Newcomb Problems — in which the Predictor genuinely predicts the agent's decision — but to non-standard Newcomb Problems — in which the Predictor guarantees the truth of her predictions by interfering with the agent's decision to make the agent choose as it was predicted she would. When properly qualified, causal and epistemic decision theories diverge only on standard — not on non-standard (...) — Newcomb Problems, and thus not on examples involving common causes. (shrink)

Marx criticized political economy for propounding an inverted, mystical view of economic reality. But he went beyond asserting the falsity and apologetic character of the doctrine to characterize it as reflecting a social practice of inversion or mystification — an inverted social world — in which individuals incorporate their own actions into a process whose dynamic lies beyond their control. Caught up in this process, individuals confront aspects of their own agency in the alien or reified form of a given, (...) determining reality. Marx leaves unclear exactly how the process exerts and maintains its hold on agents, the nature of the reasons they might have for wanting to free themselves of it, and under what conditions they could do so. However, it is possible to abstract somewhat from Marx's specific concerns and to model a self-reproducing practice of reification that works through the informational environment of decision. Though of wider interest, this more general conception can shed light on the nature and critique of Marx's inverted world. It draws on conceptual resources from decision theory, game theory and general equilibrium theory. (shrink)

Known as an upholder of subjectivism, Bruno de finetti (1906-1985) put forward a totally original philosophy of probability. This can be qualified as a combination of empiricism and pragmatism within an entirely coherent antirealistic perspective. The paper aims at clarifying the central features of such a philosophical position, Which is not only incompatible with any perspective based on an objective notion, But cannot be assimilated to other subjective views of probability either.

I defend evidential decision theory and the theory of deliberation-probability dynamics from a recent criticism advanced by Jordan Howard Sobel. I argue that his alleged counterexample to the theories, called the Popcorn Problem is not a genuine counterexample.