It has been argued that if the rigidity condition is satisfied, a rational agent operating with uncertain evidence should update her subjective probabilities by Jeffrey conditionalization or else a series of bets resulting in a sure loss could be made against her. We show, however, that even if the rigidity condition is satisfied, it is not always safe to update probability distributions by JC because there exist such sequences of non-misleading uncertain observations where it may be foreseen that an agent (...) who updates her subjective probabilities by JC will end up nearly certain that a false hypothesis is true. We analyze the features of JC that lead to this problem, specify the conditions in which it arises and respond to potential objections. (shrink)

An expected utility model of individual choice is formulated which allows the decision maker to specify his available actions in the form of controls (partial contingency plans) and to simultaneously choose goals and controls in end-mean pairs. It is shown that the Savage expected utility model, the Marschak- Radner team model, the Bayesian statistical decision model, and the standard optimal control model can be viewed as special cases of this goal-control expected utility model.

This paper examines the standard Bayesian solution to the Quine–Duhem problem, the problem of distributing blame between a theory and its auxiliary hypotheses in the aftermath of a failed prediction. The standard solution, I argue, begs the question against those who claim that the problem has no solution. I then provide an alternative Bayesian solution that is not question-begging and that turns out to have some interesting and desirable properties not possessed by the standard solution. This solution opens the way (...) to a satisfying treatment of a problem concerning ad hoc auxiliary hypotheses. (shrink)

Orthodox expected utility theory imposes too stringent restrictions on what attitudes to risk one can rationally hold. Focusing on a life-and-death gamble, I identify as the main culprit the theory’s Linearity property, according to which the utility of a particular change in the risk of a bad outcome is independent of the original level of risk. Finally, I argue that a recent non-standard Bayesian decision theory, that does not have this property, handles risky gambles better than the orthodox theory.

This paper develops a Multidimensional Decision Theory and argues that it better captures ordinary intuitions about fair distribution of chances than classical decision theory. The theory is an extension of Richard Jeffrey’s decision theory to counterfactual prospects and is a form of Modal Consequentialism, according to which the value of actual outcomes often depends on what could have been. Unlike existing versions of modal consequentialism, the multidimensional decision theory allows us to explicitly model the desirabilistic dependencies between actual and counterfactual (...) outcomes that, I contend, are at the heart of common intuitions about fair distribution of chances. (shrink)

This paper studies a generalization of rational choice theory. I briefly review the motivations that Helzner gives for his conditional choice construction . Then, I focus on the important class of conditional choice functions with vacuous second tiers. This class is interesting for both formal and philosophical reasons. I argue that this class makes explicit one of conditional choice’s normative motivations in terms of an account of neutrality advocated within a certain tradition in decision theory. The observations recorded—several of which (...) are generalizations of central results in the standard theory of rational choice—are intended to provide further insight into how conditional choice generalizes the standard account and are offered as additional evidence of the fruitfulness of the conditional choice framework. (shrink)

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

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 crucial premise of the standard argument for two-boxing in Newcomb's problem, a causal dominance principle, is false. We present some counterexamples. We then offer a metaethical explanation for why the counterexamples arise. Our explanation reveals a new and superior argument for two-boxing, one that eschews the causal dominance principle in favor of a principle linking rational choice to guidance and actual value maximization.

A fully adequate solution to Newcomb’s Problem (Nozick 1969) should reveal the source of its extraordinary elusiveness and persistent intractability. Recently, a few accounts have independently sought to meet this criterion of adequacy by exposing the underlying source of the problem’s profound puzzlement. Thus, Sorensen (1987), Slezak (1998), Priest (2002) and Maitzen and Wilson (2003) share the ‘no box’ view according to which the very idea that there is a right choice is misconceived since the problem is ill-formed or incoherent (...) in some way. Among proponents of this view, Richard Jeffrey (2004) recently declared that he renounces his earlier position that accepted Newcomb problems as genuine decision problems. Significantly, Jeffrey suggests that “Newcomb problems are like Escher’s famous staircase on which an unbroken ascent takes you back where you started” (Jeffrey (2004; 113)). Jeffrey’s analogy is apt for a puzzle whose specific logical features can be precisely articulated. Along the lines of these related approaches, I propose to improve and clarify them by providing such a deeper analysis that elucidates their essential, related insights. (shrink)

The question of diachronic coherence, coherence of degrees of belief across time, is investigated within the context of Richard Jeffrey’s radical probabilism. Diachronic coherence is taken as fundamental, and coherence results for degrees of belief at a single time, such as additivity, are recovered only with additional assumptions. Additivity of probabilities of probabilities is seen to be less problematic than additivity of first-order probabilities. Without any assumed model of belief change, diachronic coherence applied to higher-order degrees of belief yields the (...) martingale property. (shrink)

I present a game-theoretic way to understand the situation describing Newcomb’s Problem (NP) which helps to explain the intuition of both one-boxers and two-boxers. David Lewis has shown that the NP may be modelled as a Prisoners Dilemma game (PD) in which ‘cooperating’ corresponds to ‘taking one box’. Adopting relevant results from game theory, this means that one should take just one box if the NP is repeated an indefinite number of times, but both boxes if it is a one-shot (...) game. Causal decision theorists thus give the right answer for the one-shot situation, whereas the one-boxers’ solution applies to the indefinitely iterated case. Because Nozick’s set-up of the NP is ambiguous between a one-shot and a repeated game, both of these solutions may appear plausible – depending on whether one conceives of the situation as one-off or repeated. If the players’ aim is to maximize their payoffs, the symmetric structure of the PD implies that the two players will behave alike both when the game is one-shot and when it is played repeatedly. Therefore neither the observed outcome of both players selecting the same strategy (in the PD) nor, correspondingly, the predictor’s accurate prediction of this outcome (in the NP) is at all surprising. There is no need for a supernatural predictor to explain the NP phenomena. (shrink)

In this paper, I consider the recent resurgence of “evolutionary economics”—the idea that evolutionary theory can be very useful to push forward key debates in economics—and assess the extent to which it rests on a plausible foundation. To do this, I first distinguish two ways in which evolutionary theory can, in principle, be brought to bear on an economic problem—namely, evidentially and heuristically—and then apply this distinction to the three major hypotheses that evolutionary economists have come to defend: the implausibility (...) of rational choice theory as an account of economic rationality, the idea that firms are autonomous economic agents, and the need for a more dynamic, less equilibrium-focused economic methodology. In each of these cases, I conclude negatively: the relevant evolutionary considerations neither suggest interesting and novel hypotheses to investigate further nor are backed up by the needed data to constitute genuine evidence. I end by distinguishing this criticism of evolutionary economics from others that have been put forward in the literature: in particular, I make clear that, unlike those of other critics, the arguments of this paper are based on epistemic—not structural—considerations and therefore leave more room for a plausible form of evolutionary economics to come about in the future. (shrink)

A paper on how to adapt your probabilisitc beliefs when learning a conditional.

This paper discusses how to update one’s credences based on evidence that has initial probability 0. I advance a diachronic norm, Kolmogorov Conditionalization, that governs credal reallocation in many such learning scenarios. The norm is based upon Kolmogorov’s theory of conditional probability. I prove a Dutch book theorem and converse Dutch book theorem for Kolmogorov Conditionalization. The two theorems establish Kolmogorov Conditionalization as the unique credal reallocation rule that avoids a sure loss in the relevant learning scenarios.

Philosophers interested in the fitting attitude analysis of final value have devoted a great deal of attention to the wrong kind of reasons problem. This paper offers an example of the reverse difficulty, the wrong kind of value problem. This problem creates deeper challenges for the fitting attitude analysis and provides independent grounds for rejecting it, or at least for doubting seriously its correctness.

In this essay I want to look at some questions concerning the relation between morality and rationality in the recommendations they make about the best way to live our lives and achieve our good. Specifically, I want to examine ways in which the virtue of practical rationality and the various moral virtues might be thought to part company, giving an agent conflicting directives regarding how best to live his life. In conducting this enquiry, I shall at some crucial points be (...) presupposing something of an Aristotelian perspective, but only in the most general way. I In what follows, I shall distinguish reason, the faculty or power, from rationality, the excellence or virtue of that faculty. By practical reason I mean that part of reason that tells us what to do and how to live. By practical rationality I mean the excellence of that part of reason in virtue of which an agent is practically rational as opposed to irrational. By a neo-Humean conception of rationality I mean one that makes the goal of practical reason the maximal satisfaction of an agent's desires and preferences, suitably corrected for the effects of misinformation, wishful thinking, and the like. There are various versions of neo-Humean theory, and I shall not here be concerned with their specific differences. Their common essence lies in an appeal to a notion of basic desires or preferences, which are not subject to intrinsic criticism as irrational and are subject to extrinsic criticism only by ways in which their joint satisfaction may not be possible, and to a notion of derived desires or preferences, which are criticizable only instrumentally. (shrink)

It seems natural to think of an unwilling addict as having a pattern of preferences that she does not endorse—preferences that, in some sense, she does not ‘identify’ with. Following Frankfurt (1971), Jeffrey (1974) proposed a way of modeling those features of an agent’s preferences by appealing to preferences among preferences.Th„e addict’s preferences are preferences she does not prefer to have. I argue that this modeling suggestion will not do, for it follows from plausible assumptions that a minimally rational agent (...) must prefer those first-order preferences she actually has. I close by considering two different but related ways to think about the initial phenomenon. (shrink)

In concrete applications of probability, statistical investigation gives us knowledge of some probabilities, but we generally want to know many others that are not directly revealed by our data. For instance, we may know prob(P/Q) (the probability of P given Q) and prob(P/R), but what we really want is prob(P/Q& R), and we may not have the data required to assess that directly. The probability calculus is of no help here. Given prob(P/Q) and prob(P/R), it is consistent with the probability (...) calculus for prob(P/Q& R) to have any value between 0 and 1. Is there any way to make a reasonable estimate of the value of prob(P/Q& R) 1 A related problem occurs when probability practitioners adopt undefended assumptions of statistical independence simply on the basis of not seeing any connection between two propositions. This is common practice, but its justification has eluded probability theorists, and researchers are typically apologetic about making such assumptions. Is there any way to defend the practice? This paper shows that on a certain conception of probability—nomic probability—there are principles of "probable probabilities" that license inferences of the above sort. These are principles telling us that although certain inferences from probabilities to probabilities are not deductively valid, nevertheless the second-order probability of their yielding correct results is 1. This makes it defeasibly reasonable to make the inferences. Thus I argue that it is defeasibly reasonable to assume statistical independence when we have no information to the contrary. And I show that there is a function Y(r, s, a) such that if prob(P/Q) = r, prob(P/R) = s, andprob(P/U) = a (where U is our background knowledge) then it is defeasibly reasonable to expect that prob(P/Q&R) = Y(r, s, a). Numerous other defeasible inferences are licensed by similar principles of probable probabilities. This has the potential to greatly enhance the usefulness of probabilities in practical application. (shrink)

The two main psychological theories of the ordinary conditional were designed to account for inferences made from assumptions, but few premises in everyday life can be simply assumed true. Useful premises usually have a probability that is less than certainty. But what is the probability of the ordinary conditional and how is it determined? We argue that people use a two stage Ramsey test that we specify to make probability judgements about indicative conditionals in natural language, and we describe experiments (...) that support this conclusion. Our account can explain why most people give the conditional probability as the probability of the conditional, but also why some give the conjunctive probability. We discuss how our psychological work is related to the analysis of ordinary indicative conditionals in philosophical logic. (shrink)

Contemporary societies are often “polarized”, in the sense that sub-groups within these societies hold stably opposing beliefs, even when there is a fact of the matter. Extant models of polarization do not capture the idea that some beliefs are true and others false. Here we present a model, based on the network epistemology framework of Bala and Goyal, 784–811 1998), in which polarization emerges even though agents gather evidence about their beliefs, and true belief yields a pay-off advantage. As we (...) discuss, these results are especially relevant to polarization in scientific communities, for these reasons. The key mechanism that generates polarization involves treating evidence generated by other agents as uncertain when their beliefs are relatively different from one’s own. (shrink)

A broad class of inductive logics that includes the probability calculus is defined by the conditions that the inductive strengths [A|B] are defined fully in terms of deductive relations in preferred partitions and that they are asymptotically stable. Inductive independence is shown to be generic for propositions in such logics; a notion of a scale-free inductive logic is identified; and a limit theorem is derived. If the presence of preferred partitions is not presumed, no inductive logic is definable. This no-go (...) result precludes many possible inductive logics, including versions of hypothetico-deductivism. (shrink)

A broad class of inductive logics that includes the probability calculus is defined by the conditions that the inductive strengths [A|B] are defined fully in terms of deductive relations in preferred partitions and that they are asymptotically stable. Inductive independence is shown to be generic for propositions in such logics; a notion of a scale-free inductive logic is identified; and a limit theorem is derived. If the presence of preferred partitions is not presumed, no inductive logic is definable. This no-go (...) result precludes many possible inductive logics, including versions of hypothetico-deductivism. (shrink)

As I head home from work, I’m not sure whether my daughter’s new bike is green, and I’m also not sure whether I’m on drugs that distort my color perception. One thing that I am sure about is that my attitudes towards those possibilities are evidentially independent of one another, in the sense that changing my confidence in one shouldn’t affect my confidence in the other. When I get home and see the bike it looks green, so I increase my (...) confidence that it is green. But something else has changed: now an increase in my confidence that I’m on color-drugs would undermine my confidence that the bike is green. Jonathan Weisberg and Jim Pryor argue that the preceding story is problematic for standard Bayesian accounts of perceptual learning. Due to the ‘rigidity’ of Conditionalization, a negative probabilistic correlation between two propositions cannot be introduced by updating on one of them. Hence if my beliefs about my own color-sobriety start out independent of my beliefs about the color of the bike, then they must remain independent after I have my perceptual experience and update accordingly. Weisberg takes this to be a reason to reject Conditionalization. I argue that this conclusion is too pessimistic: Conditionalization is only part of the Bayesian story of perceptual learning, and the other part needn’t preserve independence. Hence Bayesian accounts of perceptual learning are perfectly consistent with potential underminers for perceptual beliefs. (shrink)

We show in this paper that some expressions indicating source of evidence are part of propositional content and are best analyzed as special kind of epistemic modal. Our evidence comes from the Japanese evidential system. We consider six evidentials in Japanese, showing that they can be embedded in conditionals and under modals and that their properties with respect to modal subordination are similar to those of ordinary modals. We show that these facts are difficult for existing theories of evidentials, which (...) assign evidentials necessarily widest scope, to explain. We then provide an analysis using a logical system designed to account for evidential reasoning; this logic is the first developed system of probabilistic dynamic predicate logic. This analysis is shown to account for the data we provide that is problematic for other theories. (shrink)

In this paper we explore the connections between ethics and decision theory. In particular, we consider the question of whether decision theory carries with it a bias towards consequentialist ethical theories. We argue that there are plausible versions of the other ethical theories that can be accommodated by “standard” decision theory, but there are also variations of these ethical theories that are less easily accommodated. So while “standard” decision theory is not exclusively consequentialist, it is not necessarily ethically neutral. Moreover, (...) even if our decision-theoretic models get the right answers vis-`a-vis morally correct action, the question remains as to whether the motivation for the non-consequentialist theories and the psychological processes of the agents who subscribe to those ethical theories are lost or poorly represented in the resulting models. (shrink)

This is an essay in the Bayesian theory of how opinions should be revised over time. It begins with a discussion of the principle that van Fraassen has dubbed "Reflection". This principle is not a requirement of rationality; a diachronic Dutch argument, that purports to show the contrary, is fallacious. But under suitable conditions, it is irrational to actually implement shifts in probability that violate Reflection. Conditionalization and probability kinematics are special cases of the principle not to implement shifts that (...) violate Reflection; hence these principles are also requirements of rationality under suitable conditions, though not universal requirements of rationality. (shrink)

A decision theory can be useful not only as a tool for determining which action, given your desires and beliefs, is most preferable, but also as a means for analyzing the nature of rational deliberation. In this paper, I turn to two classic proposals for a causal decision theory, that of Lewis and that of Sobel :407–437, 1986. doi: 10.1080/00048408612342621). As Rabinowicz revealed, Lewis’ proposal is unable to be applied to as broad a set of decision problems as a version (...) of CDT offered by Sobel, an account of decision theory that Lewis thought was equivalent to his own. Rabinowicz argued by offering a counterexample to Lewis’ account. In this essay, I build on that approach, offering a novel counterexample, the “Faulty Signal Problem,” which proves that Lewis’ theory fails to provide a recommendation in an even broader class decision problems than Rabinowicz recognized, particularly those that exhibit what I refer to as counterfactual asymmetries. The problem for Lewis, however, is not just a technicality. Lewis and Sobel’s theories, respectively, conceptualize rational deliberation in two different ways. Lewis’ proposal, which utilized conditionalization as its form of belief revision, shares with evidential decision theory the same underlying attitude toward the agent as evidence-maker. In contrast, Sobel’s theory, based on imaging, captures the idea that deliberation requires a distinctly suppositional attitude that respects the agent’s causal views. The Faulty Signal Problem not only gives reason to favor Sobel’s proposal over Lewis’; it also provides justification for seeing imaging as necessary for a genuinely causal decision theory. (shrink)

This paper makes explicit the way in which many theorists of the epistemology of uncertainty, or formal epistemologists, are committed to a version of noncognitivism—one about thoughts that something is likely. It does so by drawing an analogy with metaethical noncognitivism. I explore the degree to which the motivations for both views are similar and how both views have to grapple with the Frege‐Geach Problem about complex thoughts. The major upshot of recognizing this noncognitivism is that it presents challenges and (...) opportunities not only in the philosophy of mind and language but also in epistemology itself. I present some examples where attention to the implicit noncognitivism in formal epistemology has affected or should affect epistemological theory. And I suggest that it is likely that further examples of this sort will arise. (shrink)

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.

Consider the following claim: given the choice between saving a life and preventing any number of people from temporarily experiencing a mild headache, you should always save the life. Many moral theorists accept this claim. In doing so, they commit themselves to some form of ‘moral absolutism’: the view that there are some moral considerations that cannot be outweighed by any number of lesser moral considerations. In contexts of certainty, it is clear what moral absolutism requires of you. However, what (...) does it require of you when deciding under risk? What ought you to do when there is a chance that, say, you will not succeed in saving the life? In recent years, various critics have argued that moral absolutism cannot satisfactorily deal with risk and should, therefore, be abandoned. In this paper, we show that moral absolutism can answer its critics by drawing on—of all things—orthodox expected utility theory. (shrink)

We argue that a Bayesian explanation of strategic choices in games requires introducing a psychological theory of belief formation. We highlight that beliefs in epistemic game theory are derived from the actual choice of the players, and cannot therefore explain why Bayesian rational players should play the strategy they actually chose. We introduce the players’ capacity of mindreading in a game theoretical framework with the simulation theory, and characterise the beliefs that Bayes rational players could endogenously form in games. We (...) show in particular that those beliefs need not be ratifiable, and therefore that rational players can form action-dependent beliefs. (shrink)

Bayesian networks are computer programs which represent probabilitistic relationships graphically as directed acyclic graphs, and which can use those graphs to reason probabilistically , often at relatively low computational cost. Almost every expert system in the past tried to support probabilistic reasoning, but because of the computational difficulties they took approximating short-cuts, such as those afforded by MYCIN's certainty factors. That all changed with the publication of Judea Pearl's Probabilistic Reasoning in Intelligent Systems, in 1988, which synthesized a decade of (...) research making accurate graphical probabilistic reasoning computationally achievable.Bayesian network technology is now one of the fastest growing fields of research in artificial intelligence. That it has become a publication industry in its own right is shown by a search on Google scholar :This development, together with a parallel related growth in the use of causal discovery algorithms which automate the learning of Bayesian networks from sample data, has generated considerable interest, and controversy, within the philosophy-of-science community.Three central questions bringing together AI researchers and philosophers of science are: Are Bayesian networks Bayesian? What is the relation between probability and causality? Are the assumptions behind causal discovery of Bayesian networks realistic or fantastical?Jon Williamson, as a philosopher of science with a keen interest in the technology, asks and answers these questions in his new book. Although it is self-contained, his book is not very likely as an introduction to the technology , nor is it optimal even as an introduction to the philosophical problems in interpreting Bayesian networks . Rather Williamson's book is an attempt to move the debate forward by solving the central problems of the …. (shrink)

Impossible worlds are representations of impossible things and impossible happenings. They earn their keep in a semantic or metaphysical theory if they do the right theoretical work for us. As it happens, a worlds-based account provides the best philosophical story about semantic content, knowledge and belief states, cognitive significance and cognitive information, and informative deductive reasoning. A worlds-based story may also provide the best semantics for counterfactuals. But to function well, all these accounts need use of impossible and as well (...) as possible worlds. So what are impossible worlds? Graham Priest claims that any of the usual stories about possible worlds can be told about impossible worlds, too. But far from it. I'll argue that impossible worlds cannot be genuine worlds, of the kind proposed by Lewis, McDaniel or Yagisawa. Nor can they be ersatz worlds on the model proposed by Melia or Sider. Constructing impossible worlds, it turns out, requires novel metaphysical resources. (shrink)

We consider here an important family of conditional bets, those that proceed to settlement if and only if some agreed evidence is received that a condition has been met. Despite an opinion widespread in the literature, we observe that when the evidence is strong enough to generate certainty as to whether the condition has been met or not, using traditional conditional probabilities for such bets will NOT preserve a gambler from having a synchronic Dutch Book imposed upon him. On the (...) contrary (I show) the gambler can be Dutch-Booked if his betting ratios ever depart from a rather different probability, one that involves the probability of the agreed evidence being provided. We note furthermore that this same alternative probability assessment is necessary if the evidence is weaker (i.e. if it fails to provide knowledge whether or not the condition has been met.) By contrast, some of the (rather different) probability assessments proposed by Jeffrey, precisely for such situations, still expose the gambler to a Dutch-Book. (shrink)

The paper provides an argument for the thesis that an agent’s degrees of disbelief should obey the ranking calculus. This Consistency Argument is based on the Consistency Theorem. The latter says that an agent’s belief set is and will always be consistent and deductively closed iff her degrees of entrenchment satisfy the ranking axioms and are updated according to the ranktheoretic update rules.

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)

Weisberg introduces a phenomenon he terms perceptual undermining. He argues that it poses a problem for Jeffrey conditionalization, and Bayesian epistemology in general. This is Weisberg’s paradox. Weisberg argues that perceptual undermining also poses a problem for ranking theory and for Dempster-Shafer theory. In this note I argue that perceptual undermining does not pose a problem for any of these theories: for true conditionalizers Weisberg’s paradox is a false alarm.