In the first paper, I discussed the basic claims of Bayesianism (that degrees of belief are important, that they obey the axioms of probability theory, and that they are rationally updated by either standard or Jeffrey conditionalization) and the arguments that are often used to support them. In this paper, I will discuss some applications these ideas have had in confirmation theory, epistemol- ogy, and statistics, and criticisms of these applications.

I develop and argue for a kind of externalism about certain kinds of non-doxastic attitudes that I call policy externalism. Policy externalism about a given type of attitude is the view that all the reasonable policies for having attitudes of that type will not involve the agent's beliefs that some relevant conditions obtain. My defense primarily involves attitudes like hatred, regret, and admiration, and has two parts: a direct deductive argument and an indirect linguistic argument, an inference to the best (...) explanation of some strange ways we use certain conditionals. The main thought throughout is that attitudes we reason with, like belief, are very different from attitudes we don't reason with, in a way that constrains the former but not the latter. Finally, I investigate some consequences of policy externalism, including that it secures the possibility of genuine conditional apologies. (shrink)

There has been much discussion on the two-envelope paradox. Clark and Shackel (2000) have proposed a solution to the paradox, which has been refuted by Meacham and Weisberg (2003). Surprisingly, however, the literature still contains no axiomatic justification for the claim that one should be indifferent between the two envelopes before opening one of them. According to Meacham and Weisberg, "decision theory does not rank swapping against sticking [before opening any envelope]" (p. 686). To fill this gap in the literature, (...) we present a simple axiomatic justification for indifference, avoiding any expectation reasoning, which is often considered problematic in infinite cases. Although the two-envelope paradox assumes an expectation-maximizing agent, we show that analogous paradoxes arise for agents using different decision principles such as maximin and maximax, and that our justification for indifference before opening applies here too. (shrink)

A group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated “Groupthink”, Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever individual credences undergo Bayesian revision based on this information. To obtain a fully Bayesian group, one should often extend this requirement to non-public or even private information (learnt by not all or (...) just one individual), or to non-representable information (not representable by any event in the domain where credences are held). I pro- pose a taxonomy of six types of ‘group Bayesianism’. They differ in the information for which Bayesian revision of group credences is required: public representable information, private representable information, public non-representable information, etc. Six corre- sponding theorems establish how individual credences must (not) be aggregated to ensure group Bayesianism of any type, respectively. Aggregating through standard averaging is never permitted; instead, different forms of geometric averaging must be used. One theorem—that for public representable information—is essentially Russell et al.’s central result (with minor corrections). Another theorem—that for public non-representable information—fills a gap in the theory of externally Bayesian opinion pooling. (shrink)

Is there any distinctive aspect of rationality that deserves the label of “instrumental rationality”? Recently, Joseph Raz (2005) has argued that instrumental rationality is a “myth”. In this essay, I shall give some qualified support to Raz’s position: as I shall argue, many philosophers have indeed been seduced by certain myths about instrumental rationality. Nonetheless, Raz’s conclusion is too strong. Instrumental rationality is not itself a myth: there really is a distinctive aspect of rationality that deserves the label of “instrumental (...) rationality”. -/- In the first two sections of this essay, I shall start by giving a rough intuitive description of the phenomenon that seems to me the best candidate for the label “instrumental rationality”. As we shall see, this rough description gives us reason to reject some of the myths that surround instrumental rationality. Then in the rest of this essay, I shall try to give a more precise general specification of this phenomenon. In Sections 3 and 4, I shall consider what has been said about instrumental rationality by several other philosophers. Identifying what is missing in these other philosophers’ accounts will help me to develop my own positive specification, which I shall present in Sections 5 and 6. (shrink)

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, (...) the Theorem's central insight — that a hypothesis is confirmed by any body of data that its truth renders probable — is the cornerstone of all subjectivist methodology. (shrink)

It is often argued that future-directed decisions are effective at shaping our future conduct because they give rise, at the time of action, to a decisive reason to act as originally decided. In this paper, I argue that standard accounts of decision-based reasons are unsatisfactory. For they focus either on tie-breaking scenarios or cases of self-directed distal manipulation. I argue that future-directed decisions are better understood as tools for the non-manipulative, intrapersonal division of deliberative labor over time. A future-directed decision (...) to ϕ gives rise to a defeasible exclusionary reason to ϕ. This reason is grounded on the default authority that is normally granted to one’s prior self as an “expert” deliberator. I argue that this kind of exclusionary reason is the only one that can account for the effectiveness of future-directed decisions at shaping our diachronic agency without violating our autonomy over time. (shrink)

There are three questions associated with Simpson’s Paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP?, and (iii) What should be done about SP? By developing a logic-based account of SP, it is argued that (i) and (ii) must be divorced from (iii). This account shows that (i) and (ii) have nothing to do with causality, which plays a role only in addressing (iii). A counterexample is also presented against the causal account. Finally, the causal and logic-based (...) approaches are compared by means of an experiment to show that SP is not basically causal. (shrink)

Bryne & Hajek (1997) argue that Lewis’s (1988; 1996) objections to identifying desire with belief do not go through if our notion of desire is ‘causalized’ (characterized by causal, rather than evidential, decision theory). I argue that versions of the argument go through on certain assumptions about the formulation of decision theory. There is one version of causal decision theory where the original arguments cannot be formulated—the ‘imaging’ formulation that Joyce (1999) advocates. But I argue this formulation is independently objectionable. (...) If we want to maintain the desire as belief thesis, there’s no shortcut through causalization. (shrink)

Concrete Causation centers about theories of causation, their interpretation, and their embedding in metaphysical-ontological questions, as well as the application of such theories in the context of science and decision theory. The dissertation is divided into four chapters, that firstly undertake the historical-systematic localization of central problems (chapter 1) to then give a rendition of the concepts and the formalisms underlying David Lewis' and Judea Pearl's theories (chapter 2). After philosophically motivated conceptual deliberations Pearl's mathematical-technical framework is drawn on for (...) an epistemic interpretation and for emphasizing the knowledge-organizing aspect of causality in an extension of the interventionist Bayes net account of causation (chapter 3). Integrating causal and non-causal knowledge in unified structures ultimately leads to an approach towards solving problems of (causal) decision theory and at the same time facilitates the representation of logical-mathematical, synonymical, as well as reductive relationships in efficiently structured, operational nets of belief propagation (chapter 4). (shrink)

I develop and defend a version of what I call Disposition-Based Decision Theory (or DBDT). I point out important problems in David Gauthier’s (1985, 1986) formulation of DBDT, and carefully develop a more defensible formulation. I then compare my version of DBDT to the currently most widely accepted decision theory, Causal Decision Theory (CDT). Traditional intuition-based arguments fail to give us any strong reason to prefer either theory over the other, but I propose an alternative strategy for resolving this debate. (...) I argue that we should embrace DBDT because it does better than CDT at the work that we, as a matter of empirical fact, commonly call upon a notion of rationality to do. (shrink)

It is well known that de se (or ‘self-locating’) propositions complicate the standard picture of how we should respond to evidence. This has given rise to a substantial literature centered around puzzles like Sleeping Beauty, Dr. Evil, and Doomsday—and it has also sparked controversy over a style of argument that has recently been adopted by theoretical cosmologists. These discussions often dwell on intuitions about a single kind of case, but it’s worth seeking a rule that can unify our treatment of (...) all evidence, whether de dicto or de se. -/- This paper is about three candidates for such a rule, presented as replacements for the standard updating rule. Each rule stems from the idea that we should treat ourselves as a random sample, a heuristic that underlies many of the intuitions that have been pumped in treatments of the standard puzzles. But each rule also yields some strange results when applied across the board. This leaves us with some difficult options. We can seek another way to refine the random-sample heuristic, e.g. by restricting one of our rules. We can try to live with the strange results, perhaps granting that useful principles can fail at the margins. Or we can reject the random-sample heuristic as fatally flawed—which means rethinking its influence in even the simplest cases. (shrink)

I investigate the consequences for semantics, and in particular for the semantics of tense, if time is assumed to have a branching structure not out of metaphysical necessity (to solve some philosophical problem) but just as a contingent physical fact, as is suggested by a currently-popular approach to the interpretation of quantum mechanics.

Climate change appears to be a classic aggregation problem, in which billions of individuals perform actions none of which seem to be morally wrong taken in isolation, and yet which combine to drive the global concentration of greenhouse gases (GHGs) ever higher toward environmental (and humanitarian) catastrophe. When an individual can choose between actions that will emit differing amounts of GHGs―such as to choose a vegan rather than carnivorous meal, to ride a bike to work rather than drive a car, (...) or to take a reusable bag to the supermarket rather than send another plastic bag to landfill―does she have any reason to choose the lower-emitting actions? In this chapter I'll reject the claim that individuals don't make a difference when it comes to climate change. I first discuss making a difference with every action, as a way of getting clearer about how individuals' actions impact causally on the harms resulting from climate change, making a distinction so far overlooked in the climate ethics discussion between 'macro' thresholds like ice-cap melt, and 'micro' thresholds like severe weather events. I set aside making a difference with every action as implausible, and then move on to discuss both low probability of major difference, and high probability of minor difference. I argue that both of these are plausible characterizations of individuals' causal contributions to climate change. I conclude by noting some policy implications of having (probabilistic) individual difference-making back in play. (shrink)

Decisions are made under uncertainty when there are distinct outcomes of a given action, and one is uncertain to which the act will lead. Decisions are made under indeterminacy when there are distinct outcomes of a given action, and it is indeterminate to which the act will lead. This paper develops a theory of (synchronic and diachronic) decision-making under indeterminacy that portrays the rational response to such situations as inconstant. Rational agents have to capriciously and randomly choose how to resolve (...) the indeterminacy relevant to a given choice-situation, but such capricious choices once made constrain how they will choose in the future. The account is illustrated by the case of self-interested action in situations where it is indeterminate whether you yourself will survive to benefit or suffer the consequences. The conclusion emphasizes some distinctive anti-hedging predictions of the account. (shrink)

Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision theorists such as Savage can be criticized for being silent about stochastic independence. From their current preference axioms, they can derive no more than the definitional properties of a probability measure. In a new framework of twofold uncertainty, we introduce preference axioms that entail not (...) only these definitional properties, but also the stochastic independence of the two sources of uncertainty. This goes some way towards filling a curious lacuna in Bayesian decision theory. (shrink)

*This is a project I hope to come back to one day. It stalled, a bit, on the absence of a positive theory of update I could be satisfied with* When should we believe a indicative conditional, and how much confidence in it should we have? Here’s one proposal: one supposes actual the antecedent; and sees under that supposition what credence attaches to the consequent. Thus we suppose that Oswald did not shot Kennedy; and note that under this assumption, Kennedy (...) was assassinated by someone other than Oswald. Thus we are highly confident in the indicative: if Oswald did not kill Kennedy, someone else did. (shrink)

Logical Probability (LP) is strictly distinguished from Statistical Probability (SP). To measure semantic information or confirm hypotheses, we need to use sampling distribution (conditional SP function) to test or confirm fuzzy truth function (conditional LP function). The Semantic Information Measure (SIM) proposed is compatible with Shannon’s information theory and Fisher’s likelihood method. It can ensure that the less the LP of a predicate is and the larger the true value of the proposition is, the more information there is. So the (...) SIM can be used as Popper's information criterion for falsification or test. The SIM also allows us to optimize the true-value of counterexamples or degrees of disbelief in a hypothesis to get the optimized degree of belief, i. e. Degree of Confirmation (DOC). To explain confirmation, this paper 1) provides the calculation method of the DOC of universal hypotheses; 2) discusses how to resolve Raven Paradox with new DOC and its increment; 3) derives the DOC of rapid HIV tests: DOC of “+” =1-(1-specificity)/sensitivity, which is similar to Likelihood Ratio (=sensitivity/(1-specificity)) but has the upper limit 1; 4) discusses negative DOC for excessive affirmations, wrong hypotheses, or lies; and 5) discusses the DOC of general hypotheses with GPS as example. (shrink)

*These notes were folded into the published paper "Probability and nonclassical logic*. Revising semantics and logic has consequences for the theory of mind. Standard formal treatments of rational belief and desire make classical assumptions. If we are to challenge the presuppositions, we indicate what is kind of theory is going to take their place. Consider probability theory interpreted as an account of ideal partial belief. But if some propositions are neither true nor false, or are half true, or whatever—then it’s (...) far from clear that our degrees of belief in it and its negation should sum to 1, as classical probability theory requires (?, cf.). There are extant proposals in the literature for generalizing (categorical) probability theory to a non-classical setting, and we will use these below. But subjective probabilities themselves stand in functional relations to other mental states, and we need to trace the knock-on consequences of revisionism for this interrelationship (arguably, degrees of belief only count as kinds of belief in virtue of standing in these functional relationships). (shrink)

It seems very important to us whether or not a generalization offers counter-factual support—but why? Surely what happens in other possible worlds can neither help nor hurt us? This paper explores the question whether counter-factual support does, nevertheless, have some practical value. (The question of theoretical value will be addressed but then put aside.) The following thesis is proposed: the counterfactual-supporting generalizations are those for which there exists a compact and under normal circumstances knowable basis determining the fine-grained pattern of (...) actual variation between the properties associated by the generalization (e.g., for the generalization Fs tend to be G, the exact circumstances under which any particular F is G); further, the better we understand the basis and the scope of the support offered, the greater our knowledge of fine-grained variation. We care about counterfactual support because we care about actual fine-grained variation. (shrink)

Consider a group of people whose preferences satisfy the axioms of one of the current versions of utility theory, such as von Neumann-Morgenstern (1944), Savage (1954), or Bolker-Jeffrey (1965). There are political and economic contexts in which it is of interest to find ways of aggregating these individual preferences into a group preference ranking. The question then arises of whether methods of aggregation exist in which the group’s preferences also satisfy the axioms of the chosen utility theory, and in which (...) at the same time the aggregation process satisfies certain plausible conditions (e.g., the Pareto conditions below). (shrink)

What kinds of fundamental limits are there in how capable artificial intelligence (AI) systems might become? Two questions in particular are of interest: (1) How much more capable could AI become relative to humans, and (2) how easily could superhuman capability be acquired? To answer these questions, we will consider the literature on human expertise and intelligence, discuss its relevance for AI, and consider how AI could improve on humans in two major aspects of thought and expertise, namely simulation and (...) pattern recognition. We find that although there are very real limits to prediction, it seems like AI could still substantially improve on human intelligence. (shrink)

The technique of imaging was first introduced by Lewis, in order to provide a novel account of the probability of conditional propositions. In the intervening years, imaging has been the object of significant interest in both AI and philosophy, and has come to be seen as a philosophically important approach to probabilistic updating and belief revision. In this paper, we consider the possibility of generalising imaging to deal with uncertain evidence and partial belief revision. In particular, we introduce a new (...) logical criterion that any update rule should satisfy, and use it to evaluate a range of different approaches to generalising imaging to situations involving uncertain evidence. We show that none of the currently prevalent approaches to imaging allow for such a generalisation, although a lesser known version of imaging, introduced by Joyce, can be generalised in a way that mitigates these problems. (shrink)

The Precautionary Principle (PP) is an influential principle of risk management. It has been widely introduced into environmental legislation, and it plays an important role in most international environmental agreements. Yet, there is little consensus on precisely how to understand and formulate the principle. In this paper I prove some impossibility results for two plausible formulations of the PP as a decision-rule. These results illustrate the difficulty in making the PP consistent with the acceptance of any trade-offs between catastrophic risks (...) and more ordinary goods. (shrink)

There are numerous (Bayesian) confirmation measures in the literature. Festa provides a formal characterization of a certain class of such measures. He calls the members of this class “incremental measures”. Festa then introduces six rather interesting properties called “Matthew properties” and puts forward two theses, hereafter “T1” and “T2”, concerning which of the various extant incremental measures have which of the various Matthew properties. Festa’s discussion is potentially helpful with the problem of measure sensitivity. I argue, that, while Festa’s discussion (...) is illuminating on the whole and worthy of careful study, T1 and T2 are strictly speaking incorrect (though on the right track) and should be rejected in favor of two similar but distinct theses. (shrink)