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Subjective probability plays an increasingly important role in many fields concerned with human cognition and behavior. Yet there have been significant criticisms of the idea that probabilities could actually be represented in the mind. This paper presents and elaborates a view of subjective probability as a kind of sampling propensity associated with internally represented generative models. The resulting view answers to some of the most well known criticisms of subjective probability, and is also supported by empirical work in neuroscience and (...) 

Many philosophers have argued that "degree of belief" or "credence" is a more fundamental state grounding belief. Many other philosophers have been skeptical about the notion of "degree of belief", and take belief to be the only meaningful notion in the vicinity. This paper shows that one can take belief to be fundamental, and ground a notion of "degree of belief" in the patterns of belief, assuming that an agent has a collection of beliefs that isn't dominated by some other (...) 



Should economics study the psychological basis of agents' choice behaviour? I show how this question is multifaceted and profoundly ambiguous. There is no sharp distinction between "mentalist'' answers to this question and rival "behavioural'' answers. What's more, clarifying this point raises problems for mentalists of the "functionalist'' variety (Dietrich and List, 2016). Firstly, functionalist hypotheses collapse into hypotheses about inputoutput dispositions, I show, unless one places some unwelcome restrictions on what counts as a cognitive variable. Secondly, functionalist hypotheses make some (...) 

Four important arguments for probabilism—the Dutch Book, representation theorem, calibration, and gradational accuracy arguments—have a strikingly similar structure. Each begins with a mathematical theorem, a conditional with an existentially quantified consequent, of the general form: if your credences are not probabilities, then there is a way in which your rationality is impugned. Each argument concludes that rationality requires your credences to be probabilities. I contend that each argument is invalid as formulated. In each case there is a mirrorimage theorem and (...) 

Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. As a result, we (...) 

Decisiontheoretic representation theorems have been developed and appealed to in the service of two important philosophical projects: in attempts to characterise credences in terms of preferences, and in arguments for probabilism. Theorems developed within the formal framework that Savage developed have played an especially prominent role here. I argue that the use of these ‘Savagean’ theorems create significant difficulties for both projects, but particularly the latter. The origin of the problem directly relates to the question of whether we can have (...) 

Both Representation Theorem Arguments and Dutch Book Arguments support taking probabilistic coherence as an epistemic norm. Both depend on connecting beliefs to preferences, which are not clearly within the epistemic domain. Moreover, these connections are standardly grounded in questionable definitional/metaphysical claims. The paper argues that these definitional/metaphysical claims are insupportable. It offers a way of reconceiving Representation Theorem arguments which avoids the untenable premises. It then develops a parallel approach to Dutch Book Arguments, and compares the results. In each case (...) 

The standard representation theorem for expected utility theory tells us that if a subject’s preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities—and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility. However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being always probabilistically coherent with infinitely precise degrees (...) 



In a recent paper, Samir Okasha presented an argument that suggests that there is no rational way to choose among scientific theories. This would seriously undermine the view that science is a rational entreprise. In this paper I show how a suitably nuanced view of what scientific rationality requires allows us to avoid Okasha’s conclusion. I go on to argue that making further assumptions about the space of possible scientific theories allows us to make scientific rationality more contentful. I then (...) 

Belief is a familiar attitude: taking something to be the case or regarding it as true. But we are more confident in some of our beliefs than in others. For this reason, many epistemologists appeal to a second attitude, called credence, similar to a degree of confidence. This raises the question: how do belief and credence relate to each other? On a belieffirst view, beliefs are more fundamental and credences are a species of beliefs, e.g. beliefs about probabilities. On a (...) 

Handbook of the History of Logic, vol. 10, eds. Dov Gabbay, Stephan Hartmann, and John Woods, forthcoming. 

ABSTRACT In a recent article, Samir Okasha presented an argument that suggests that there is no rational way to choose among scientific theories. This would seriously undermine the view that science is a rational enterprise. In this article, I show how a suitably nuanced view of what scientific rationality requires allows us to sidestep this argument. In doing so, I present a new argument in favour of voluntarism of the type favoured by van Fraassen. I then show how such a (...) 

There are decision problems where the preferences that seem rational to many people cannot be accommodated within orthodox decision theory in the natural way. In response, a number of alternatives to the orthodoxy have been proposed. In this paper, I offer an argument against those alternatives and in favour of the orthodoxy. I focus on preferences that seem to encode sensitivity to risk. And I focus on the alternative to the orthodoxy proposed by Lara Buchak’s riskweighted expected utility theory. I (...) 

The last 20 years or so has seen an intense search carried out within Dempster–Shafer theory, with the aim of finding a generalization of the Shannon entropy for belief functions. In that time, there has also been much progress made in credal set theory—another generalization of the traditional Bayesian epistemic representation—albeit not in this particular area. In credal set theory, sets of probability functions are utilized to represent the epistemic state of rational agents instead of the single probability function of (...) 

Probabilism, the view that agents have numerical degrees of beliefs that conform to the axioms of probability, has been defended by the vast majority of its proponents by way of either of two arguments, the Dutch Book Argument and the Representation Theorems Argument. In this paper I argue that both arguments are flawed. The Dutch Book Argument is based on an unwarranted, ad hoc premise that cannot be dispensed with. The Representation Theorems Argument hinges on an invalid implication. 

I define a concept of causal probability and apply it to questions about the role of probability in evolutionary processes. Causal probability is defined in terms of manipulation of patterns in empirical outcomes by manipulating properties that realize objective probabilities. The concept of causal probability allows us see how probabilities characterized by different interpretations of probability can share a similar causal character, and does so in such way as to allow new inferences about relationships between probabilities realized in different chance (...) 

The main question of this paper is: how do we manage to know what our own degrees of belief are? Section 1 briefly reviews and criticizes the traditional functionalist view, a view notably associated with David Lewis and sometimes called the theorytheory. I use this criticism to motivate the approach I want to promote. Section 2, the bulk of the paper, examines and begins to develop the view that we have a special kind of introspective access to our degrees of (...) 

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 (...) 

This paper presents an axiomatization of the principle of maximizing expected utility that does not rely on the independence axiom or surething principle. Perhaps more importantly the new axiomatization is based on an ex ante approach, instead of the standard ex post approach. An ex post approach utilizes the decision maker's preferences among risky acts for generating a utility and a probability function, whereas in the ex ante approach a set of preferences among potential outcomes are on the input side (...) 

This chapter is a philosophical survey of some leading approaches in formal epistemology in the socalled ‘Bayesian’ tradition. According to them, a rational agent’s degrees of belief—credences—at a time are representable with probability functions. We also canvas various further putative ‘synchronic’ rationality norms on credences. We then consider ‘diachronic’ norms that are thought to constrain how credences should respond to evidence. We discuss some of the main lines of recent debate, and conclude with some prospects for future research. 









Bayesianism is a collection of positions in several related fields, centered on the interpretation of probability as something like degree of belief, as contrasted with relative frequency, or objective chance. However, Bayesianism is far from a unified movement. Bayesians are divided about the nature of the probability functions they discuss; about the normative force of this probability function for ordinary and scientific reasoning and decision making; and about what relation (if any) holds between Bayesian and nonBayesian concepts. 

Four important arguments for probabilism—the Dutch Book, representation theorem, calibration, and gradational accuracy arguments—have a strikingly similar structure. Each begins with a mathematical theorem, a conditional with an existentially quantified consequent, of the general form: if your credences are not probabilities, then there is a way in which your rationality is impugned. Each argument concludes that rationality requires your credences to be probabilities. I contend that each argument is invalid as formulated. In each case there is a mirrorimage theorem and (...) 

This paper discusses a challenge for Comparativists about belief, who hold that numerical degree of belief (in particular, subjective probability) is a useful fiction, unlike comparative belief, which they regard as real. The challenge is to make sense of claims like ‘I am twice as confident in A as in B’ in terms of comparative belief only. After showing that at least some Comparativists can meet this challenge, I discuss implications for Zynda’s [2000] and Stefánsson’s [2017] defences of Comparativism. 



The foundations of probability are viewed through the lens of the subjectivist interpretation. This article surveys conditional probability, arguments for probabilism, probability dynamics, and the evidential and subjective interpretations of probability. 

