Dutch Books,Coherence, and Logical Consistency

In this paper I present a new way of understanding Dutch Book Arguments: the idea is that an agent is shown to be incoherent iff (s)he would accept as fair a set of bets that would result in a loss under any interpretation of the claims involved. This draws on a standard definition of logical inconsistency. On this new understanding, the Dutch Book Arguments for the probability axioms go through, but the Dutch Book Argument for Reflection fails. The question of whether we have a Dutch Book Argument for Conditionalization is left open.     

Reflection and conditionalization: Comments on Michael Rescorla

Rescorla explores the relation between Reflection, Conditionalization, and Dutch book arguments in the presence of a weakened concept of sure loss and weakened conditions of self-transparency for doxastic agents. The literature about Reflection and about Dutch Book arguments, though overlapping, are distinct, and its history illuminates the import of Rescorla's investigation. With examples from a previous debate in the 70s and results about Reflection and Conditionalization in the 80s, I propose a way of seeing the epistemic enterprise in the light of practical requirements to be met by demands for synchronic coherence and probability updating policies. This includes a defense of principles rejected by Rescorla, while allowing for the value of his results in the borderland between theories of cognition and formal epistemology.     

Reflecting on diachronic Dutch books

Conditionalization governs how to reallocate credence in light of new evidence. One prominent argument in favor of Conditionalization holds that an agent who violates it is vulnerable to a diachronic Dutch book: a series of acceptable bets offered at multiple times that inflict a sure loss. van Fraassen argues that an agent who violates the Principle of Reflection is likewise vulnerable to a diachronic Dutch book. He concludes that agents should conform to both Conditionalization and Reflection. Some authors reply that Reflection is implausible and hence that there must be something wrong with diachronic Dutch book arguments. Other authors try to isolate a principled difference between the Dutch book argument for Conditionalization and the Dutch book argument for Reflection, such that the former argument may succeed even though the latter fails. I pursue a version of this strategy. I contend that, once we properly elucidate the notion of sure loss, non-reflectors are not vulnerable to a sure loss. An agent who violates Reflection is not thereby subject to a diachronic Dutch book. Appearances to the contrary result from an unmotivated focus upon an overly narrow set of gambling scenarios.     

Conditionalization,Reflection, and Self-Knowledge

Van Fraassen famously endorses the Principle of Reflection as a constraint on rational credence, and argues that Reflection is entailed by the more traditional principle of Conditionalization. He draws two morals from this alleged entailment. First, that Reflection can be regarded as an alternative to Conditionalization – a more lenient standard of rationality. And second, that commitment to Conditionalization can be turned into support for Reflection. Van Fraassen also argues that Reflection implies Conditionalization, thus offering a new justification for Conditionalization. I argue that neither principle entails the other, and thus neither can be used to motivate the other in the way van Fraassen says. There are ways to connect Conditionalization to Reflection, but these connections depend on poor assumptions about our introspective access, and are not tight enough to draw the sorts of conclusions van Fraassen wants. Upon close examination, the two principles seem to be getting at two quite independent epistemic norms. My thanks to Frank Arntzenius, Barry Loewer, Chris Meacham, John Hawthorne, and an anonymous referee for their helpful discussion and criticism. Special thanks to Bliss Kern for bringing the topic to my attention.     

On the Expected Utility Objection to the Dutch Book Argument for Probabilism*

The Dutch Book Argument for Probabilism assumes Ramsey's Thesis (RT), which determines the prices an agent is rationally required to pay for a bet. Hedden (2013) argues that Ramsey's Thesis is wrong. He claims that Maximise Subjective Expected Utility (MSEU) determines those prices, and it often disagrees with Ramsey's Thesis. I suggest two responses to Hedden's objection. First, we might be permissive: agents are permitted to pay any price that is required or permitted by RT, and they are permitted to pay any price that is required or permitted by MSEU. This allows us to give a revised version of the Dutch Book Argument for Probabilism, which I call the Permissive Dutch Book Argument. Second, I suggest that even Hedden should admit that RT gives the correct answer in certain very limited cases, and I show that, together with MSEU, this very restricted version of RT gives a new pragmatic argument for Probabilism, which I call the Bookless Pragmatic Argument.     

The main two arguments for probabilism are flawed

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.     

Implications of the Dutch Book: Following Ramsey��s axioms

The Dutch Book Argument shows that an agent will lose surely in a gamble (a Dutch Book is made) if his degrees of belief do not satisfy the laws of the probability. Yet a question arises here: What does the Dutch Book imply? This paper firstly argues that there exists a utility function following Ramsey’s axioms. And then, it explicates the properties of the utility function and degree of belief respectively. The properties show that coherence in partial beliefs for Subjective Bayesianism means that the degree of belief, representing a belief ordering, satisfies the laws of probability, and that coherence in preferences means that the preferences are represented by expected utilities. A coherent belief ordering and a utility scale induce a coherent preference ordering; a coherent preference ordering induces a coherent belief ordering which can be uniquely represented by a degree-of-belief function. The preferences (values) and beliefs are both incoherent or disordered if a Dutch Book is made.     

Generalized Probabilism: Dutch Books and Accuracy Domination

This paper explores De Finetti’s generalized versions of Dutch Book and Accuracy Domination theorems. Following proposals due to Jeff Paris, we construe these as underpinning a generalized probabilism appropriate to belief states against either a classical or a non-classical background. Both results are straightforward corollaries of the separating hyperplane theorem; their geometrical relationship is examined. It is shown that each point of Accuracy Domination for b induces a Dutch Book on b; but Dutch Books may need to be ‘scaled’ in order to find a point of Accuracy-Domination. Finally, diachronic Dutch Book defences of conditionalization are examined in the general setting. The formulation and limitations of the generalized conditionalization this delivers are examined.     

Credence and self-location

All parties to the Sleeping Beauty debate agree that it shows that some cherished principle of rationality has to go. Thirders think that it is Conditionalization and Reflection that must be given up or modified; halfers think that it is the Principal Principle. I offer an analysis of the Sleeping Beauty puzzle that allows us to retain all three principles. In brief, I argue that Sleeping Beauty’s credence in the uncentered proposition that the coin came up heads should be 1/2, but her credence in the centered proposition that the coin came up heads and it is Monday should be 1/3. I trace the source of the earlier mistakes to an unquestioned assumption in the debate, namely that an uncentered proposition is just a special kind of centered proposition. I argue that the falsity of this assumption is the real lesson of the Sleeping Beauty case.     

The a priori defended: a defense of the generality argument

One of Laurence BonJour’s main arguments for the existence of the a priori is an argument that a priori justification is indispensable for making inferences from experience to conclusions that go beyond experience. This argument has recently come under heavy fire from Albert Casullo, who has dubbed BonJour’s argument, “The Generality Argument.” In this paper I (i) defend the Generality Argument against Casullo’s criticisms, and (ii) develop a new, more plausible, version of the Generality Argument in response to some other objections of my own. Two of these objections stem out of BonJour’s failing to fully consider the importance of the distinction between being justified in believing that an inference is good and being justified in making an inference. The final version of the argument that I develop sees the Generality Argument as one part of a cumulative case argument for the existence of a priori justification, rather than as a stand-alone knock-down argument.     

Conditionalization, A New Argument For

Probabilism in epistemology does not have to be of the Bayesian variety. The probabilist represents a person's opinion as a probability function; the Bayesian adds that rational change of opinion must take the form of conditionalizing on new evidence. I will argue that this is the correct procedure under certain special conditions. Those special conditions are important, and instantiated for example in scientific experimentation, but hardly universal. My argument will be related to the much maligned Reflection Principle (van Fraassen, 1984, 1995), and partly inspired by the work of Brian Skyrms (1987).     

Against the <Emphasis Type="Italic">Mind</Emphasis> Argument

The Mind Argument is an argument for the incompatibility of indeterminism and anyone’s having a choice about anything that happens. Peter van Inwagen rejects the Mind Argument not because he is able to point out the flaw in it, but because he accepts both that determinism is incompatible with anyone’s having a choice about anything that happens and that it is possible for someone to have a choice about something that happens. In this paper I first diagnose and clear up a confusion in recent discussions of the Mind Argument and then go on to show why it is a bad argument.     

Sleeping Beauty and shifted Jeffrey conditionalization

In this paper, I argue for a view largely favorable to the Thirder view: when Sleeping Beauty wakes up on Monday, her credence in the coin’s landing heads is less than 1/2. Let’s call this “the Lesser view.” For my argument, I (i) criticize Strict Conditionalization as the rule for changing de se credences; (ii) develop a new rule; and (iii) defend it by Gaifman’s Expert Principle. Finally, I defend the Lesser view by making use of this new rule.     

Concerning the resilience of Galen Strawson’s Basic Argument

Against its prominent compatiblist and libertarian opponents, I defend Galen Strawson’s Basic Argument for the impossibility of moral responsibility. Against John Martin Fischer, I argue that the Basic Argument does not rely on the premise that an agent can be responsible for an action only if he is responsible for every factor contributing to that action. Against Alfred Mele and Randolph Clarke, I argue that it is absurd to believe that an agent can be responsible for an action when no factor contributing to that action is up to that agent. Against Derk Pereboom and Clarke, I argue that the versions of agent-causal libertarianism they claim can immunize the agent to the Basic Argument actually fail to do so. Against Robert Kane, I argue that the Basic Argument does not rely on the premise that simply the presence of indeterministic factors in the process of bringing an action about is itself what rules out the agent’s chance for being responsible for that action.     

Scotching the Dutch Book Argument

Consistent application of coherece arguments shows that fair betting quotients are subject to constraints that are too stringent to allow their identification with either degrees of belief or probabilities. The pivotal role of fair betting quotients in the Dutch Book Argument, which is said to demonstrate that a rational agent's degrees of belief are probabilities, is thus undermined from both sides.     

Max Deutscher and perception

In this paper I examine a strategy which aims to bypass the technicalities of the indispensability debate and to offer a direct route to nominalism. The starting-point for this alternative nominalist strategy is the claim that--according to the platonist picture--the existence of mathematical objects makes no difference to the concrete, physical world. My principal goal is to show that the 'Makes No Difference' (MND) Argument does not succeed in undermining platonism. The basic reason why not is that the makes-no-difference claim which the argument is based on is problematic. Arguments both for and against this claim can be found in the literature; I examine three such arguments, uncovering flaws in each one. In the second half of the paper, I take a more direct approach and present an analysis of the counterfactual which underpins the makes-no-difference claim. What this analysis reveals is that indispensability considerations are in fact crucial to the proper evaluation of the MND Argument, contrary to the claims of its supporters.     

Reconsidering the miracle argument on the supposition of transient underdetermination

In this paper, I will show that the Miracle Argument is unsound if one assumes a certain form of transient underdetermination. For this aim, I will first discuss and formalize several variants of underdetermination, especially that of transient underdetermination, by means of measure theory. I will then formalize a popular and persuasive form of the Miracle Argument that is based on “use novelty”. I will then proceed to the proof that the miracle argument is unsound by means of a mathematical example. Finally, I will expose two hidden presuppositions of the Miracle Argument that make it so immensely though deceptively persuasive.     

Divine determinism,human freedom,and the consequence argument

In this paper I consider the view, held by some Thomistic thinkers, that divine determinism is compatible with human freedom, even though natural determinism is not. After examining the purported differences between divine and natural determinism, I discuss the Consequence Argument, which has been put forward to establish the incompatibility of natural determinism and human freedom. The Consequence Argument, I note, hinges on the premise that an action ultimately determined by factors outside of the actor’s control is not free. Since, I argue, divine determinism also entails that human actions are ultimately determined by factors outside of the actors’ control, I suggest that a parallel argument to the Consequence Argument can be constructed for the incompatibility of divine determinism and human freedom. I conclude that those who reject natural compatibilism on the basis of the Consequence Argument should also reject divine compatibilism.     

What is conditionalization,and why should we do it?

Philosophical Studies - Conditionalization is one of the central norms of Bayesian epistemology. But there are a number of competing formulations, and a number of arguments that purport to...