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 mirror-image theorem and (...) a corresponding argument of exactly equal strength that concludes that rationality requires your credences not to be probabilities. Some further consideration is needed to break this symmetry in favour of probabilism. (shrink)

Begins by explaining then proving a generalized language dependence result similar to Goodman's "grue" problem. I then use this result to cast doubt on the existence of an objective evidential favoring relation (such as "the evidence confirms one hypothesis over another," "the evidence provides more reason to believe one hypothesis over the other," "the evidence justifies one hypothesis over the other," etc.). Once we understand what language dependence tells us about evidential favoring, our options are an implausibly strong conception of (...) the a priori, a hard externalism on which agents are unable to determine what their evidence favors, or a subjectivist view that makes evidential favoring relative to features of the agent. (shrink)

With this treatise, an insightful exploration of the probabilistic connection between philosophy and the history of science, the famous economist breathed new life into studies of both disciplines. Originally published in 1921, this important mathematical work represented a significant contribution to the theory regarding the logical probability of propositions. Keynes effectively dismantled the classical theory of probability, launching what has since been termed the “logical-relationist” theory. In so doing, he explored the logical relationships between classifying a proposition as “highly probable” (...) and as a “justifiable induction.” Unabridged republication of the classic 1921 edition. (shrink)

Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...

APA PsycNET abstract: This is the first volume of a two-volume work on Probability and Induction. Because the writer holds that probability logic is identical with inductive logic, this work is devoted to philosophical problems concerning the nature of probability and inductive reasoning. The author rejects a statistical frequency basis for probability in favor of a logical relation between two statements or propositions. Probability "is the degree of confirmation of a hypothesis (or conclusion) on the basis of some given evidence (...) (or premises)." Furthermore, all principles and theorems of inductive logic are analytic, and the entire system is to be constructed by means of symbolic logic and semantic methods. This means that the author confines himself to the formalistic procedures of word and symbol systems. The resulting sentence or language structures are presumed to separate off logic from all subjectivist or psychological elements. Despite the abstractionism, the claim is made that if an inductive probability system of logic can be constructed it will have its practical application in mathematical statistics, and in various sciences. 16-page bibliography. (PsycINFO Database Record (c) 2016 APA, all rights reserved). (shrink)

Information theory and statistical mechanics II.

While there are several arguments on either side, it is far from clear as to whether or not countable additivity is an acceptable axiom of subjective probability. I focus here on de Finetti's central argument against countable additivity and provide a new Dutch book proof of the principle, To argue that if we accept the Dutch book foundations of subjective probability, countable additivity is an unavoidable constraint.

Kolmogorov''s axiomatization of probability includes the familiarratio formula for conditional probability: 0).$$ " align="middle" border="0">.

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)

Jeff Paris proves a generalized Dutch Book theorem. If a belief state is not a generalized probability then one faces ‘sure loss’ books of bets. In Williams I showed that Joyce’s accuracy-domination theorem applies to the same set of generalized probabilities. What is the relationship between these two results? This note shows that both results are easy corollaries of the core result that Paris appeals to in proving his dutch book theorem. We see that every point of accuracy-domination defines a (...) dutch book, but we only have a partial converse. (shrink)

I defend the suggestion that the rational probability in the Sleeping Beauty paradox is one third. The reasoning in its favour is familiar: for every heads-waking, there are two tails-wakings. To complete the defense, I rebut the reasoning which purports to justify the competing suggestion – that the correct probability is half – by undermining its premise, that no new information has been received.

I defend the suggestion that the rational probability in the Sleeping Beauty paradox is one third. The reasoning in its favour is familiar: for every heads-waking, there are two tails-wakings. To complete the defense, I rebut the reasoning which purports to justify the competing suggestion – that the correct probability is half – by undermining its premise, that no new information has been received.

Conditionalization and Jeffrey Conditionalization cannot simultaneously satisfy two widely held desiderata on rules for empirical learning. The first desideratum is confirmational holism, which says that the evidential import of an experience is always sensitive to our background assumptions. The second desideratum is commutativity, which says that the order in which one acquires evidence shouldn't affect what conclusions one draws, provided the same total evidence is gathered in the end. (Jeffrey) Conditionalization cannot satisfy either of these desiderata without violating the other. (...) This is a surprising problem, and I offer a diagnosis of its source. I argue that (Jeffrey) Conditionalization is inherently anti-holistic in a way that is just exacerbated by the requirement of commutativity. The dilemma is thus a superficial manifestation of (Jeffrey) Conditionalization's fundamentally anti-holistic nature. (shrink)

The so-called "non-commutativity" of probability kinematics has caused much unjustified concern. When identical learning is properly represented, namely, by identical Bayes factors rather than identical posterior probabilities, then sequential probability-kinematical revisions behave just as they should. Our analysis is based on a variant of Field's reformulation of probability kinematics, divested of its (inessential) physicalist gloss.

The principle of maximum entropy is a method for assigning values to probability distributions on the basis of partial information. In usual formulations of this and related methods of inference one assumes that this partial information takes the form of a constraint on allowed probability distributions. In practical applications, however, the information consists of empirical data. A constraint rule is then employed to construct constraints on probability distributions out of these data. Usually one adopts the rule that equates the expectation (...) values of certain functions with their empirical averages. There are, however, various other ways in which one can construct constraints from empirical data, which makes the maximum entropy principle lead to very different probability assignments. This paper shows that an argument by Jaynes to justify the usual constraint rule is unsatisfactory and investigates several alternative choices. The choice of a constraint rule is also shown to be of crucial importance to the debate on the question whether there is a conflict between the methods of inference based on maximum entropy and Bayesian conditionalization. (shrink)

In this book, Michael Strevens aims to explain how simplicity can coexist with, indeed be caused by, the tangled interconnections between a complex system's ...

This essay is, primarily, a discussion of four results about the principle of maximizing entropy (MAXENT) and its connections with Bayesian theory. Result 1 provides a restricted equivalence between the two: where the Bayesian model for MAXENT inference uses an "a priori" probability that is uniform, and where all MAXENT constraints are limited to 0-1 expectations for simple indicator-variables. The other three results report on an inability to extend the equivalence beyond these specialized constraints. Result 2 established a sensitivity of (...) MAXENT inference to the choice of the algebra of possibilities even though all empirical constraints imposed on the MAXENT solution are satisfied in each measure space considered. The resulting MAXENT distribution is not invariant over the choice of measure space. Thus, old and familiar problems with the Laplacian principle of Insufficient Reason also plague MAXENT theory. Result 3 builds upon the findings of Friedman and Shimony (1971; 1973) and demonstrates the absence of an exchangeable, Bayesian model for predictive MAXENT distributions when the MAXENT constraints are interpreted according to Jaynes's (1978) prescription for his (1963) Brandeis Dice problem. Lastly, Result 4 generalizes the Friedman and Shimony objection to cross-entropy (Kullback-information) shifts subject to a constraint of a new odds-ratio for two disjoint events. (shrink)

Can there be deterministic chance? That is, can there be objective chance values other than 0 or 1, in a deterministic world? I will argue that the answer is no. In a deterministic world, the only function that can play the role of chance is one that outputs just Os and 1s. The role of chance involves connections from chance to credence, possibility, time, intrinsicness, lawhood, and causation. These connections do not allow for deterministic chance.

The existence of "undermining futures" appears to show that a contradiction can be deduced from the conjunction of Humean supervenience (HS) about chance and the Principal Principle. A number of strategies for rescuing HS from this problem have been proposed recently. In this paper, a novel way of defending HS from the threat is presented, and it is argued that this defense has advantages not shared by others. In particular, it requires no revisionism about chance, and it is equally available (...) to defenders of HS who hold HS to be necessary and those who hold it to be contingent. (shrink)

The existence of “undermining futures” appears to show that a contradiction can be deduced from the conjunction of Humean supervenience about chance and the Principal Principle. A number of strategies for rescuing HS from this problem have been proposed recently. In this paper, a novel way of defending HS from the threat is presented, and it is argued that this defense has advantages not shared by others. In particular, it requires no revisionism about chance, and it is equally available to (...) defenders of HS who hold HS to be necessary and those who hold it to be contingent. (shrink)

In ‘A Non-Pragmatic Vindication of Probabilism’, Jim Joyce attempts to ‘depragmatize’ de Finetti’s prevision argument for the claim that our partial beliefs ought to satisfy the axioms of probability calculus. In this paper, I adapt Joyce’s argument to give a non-pragmatic vindication of various versions of David Lewis’ Principal Principle, such as the version based on Isaac Levi's account of admissibility, Michael Thau and Ned Hall's New Principle, and Jenann Ismael's Generalized Principal Principle. Joyce enumerates properties that must be had (...) by any measure of the distance from a set of partial beliefs to the set of truth values; he shows that, on any such measure, and for any set of partial beliefs that violates the probability axioms, there is a set that satisfies those axioms that is closer to every possible set of truth values. I replace truth values by objective chances in his argument; I show that for any set of partial beliefs that violates the probability axioms or a version of the Principal Principle, there is a set that satisfies them that is closer to every possible set of objective chances. (shrink)

We often use symmetries to infer outcomes’ probabilities, as when we infer that each side of a fair coin is equally likely to come up on a given toss. Why are these inferences successful? I argue against answering this with an a priori indifference principle. Reasons to reject that principle are familiar, yet instructive. They point to a new, empirical explanation for the success of our probabilistic predictions. This has implications for indifference reasoning in general. I argue that a priori (...) symmetries need never constrain our probability attributions, even when it comes to our initial credences. (shrink)

Mellor's subject is singular causation between facts, expressed 'E because C'. His central requirement for causation is that the chance that E if C be greater than the chance that E if $\sim \text{C}\colon \ ch_{\text{C}}>ch_{\sim \text{C}}$. The book is as much about chance as it is about causation. I show that his way of distinguishing ch C from the traditional notion of conditional chance leaves him with a problem about the existence of ch Q when Q is false ; (...) and also that any notion of chance which conforms to the standard calculus has wider application than the causal instances to which Mellor's notion is restricted. Other topics discussed may be gleaned from the headings below. (shrink)

The Facts of Causation grapples with one of philosophy's most enduring issues. Causation is central to all of our lives. What we see and hear causes us to believe certain facts about the world. We need that information to know how to act and how to cause the effects we desire. D. H. Mellor, a leading scholar in the philosophy of science and metaphysics, offers a comprehensive theory of causation. Many questions about causation remain unsettled. In science, the indeterminism of (...) modern physics and genetics have made such questions considerably harder for philosophers to answer. While progress has been made, a complete account of the nature and cosequences of causation is long overdue. This major study provides that account. (shrink)

I argue that the theory of chance proposed by David Lewis has three problems: (i) it is time asymmetric in a manner incompatible with some of the chance theories of physics, (ii) it is incompatible with statistical mechanical chances, and (iii) the content of Lewis's Principal Principle depends on how admissibility is cashed out, but there is no agreement as to what admissible evidence should be. I proposes two modifications of Lewis's theory which resolve these difficulties. I conclude by tentatively (...) proposing a third modification of Lewis's theory, one which explains many of the common features shared by the chance theories of physics. (shrink)

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 (...) should reject these claims, and lay the foundations of decision theory on firmer ground. (shrink)

James Joyce's 'Nonpragmatic Vindication of Probabilism' gives a new argument for the conclusion that a person's credences ought to satisfy the laws of probability. The premises of Joyce's argument include six axioms about what counts as an adequate measure of the distance of a credence function from the truth. This paper shows that (a) Joyce's argument for one of these axioms is invalid, (b) his argument for another axiom has a false premise, (c) neither axiom is plausible, and (d) without (...) these implausible axioms Joyce's vindication of probabilism fails. (shrink)

Recently a number of authors have tried to avoid the failures of traditional Dutch book arguments by separating them from pragmatic concerns of avoiding a sure loss. In this paper I examine defenses of this kind by Howson and Urbach, Hellman, and Christensen. I construct rigorous explications of their arguments and show that they are not cogent. I advocate abandoning Dutch book arguments in favor of a representation theorem.

Some have argued that chance and determinism are compatible in order to account for the objectivity of probabilities in theories that are compatible with determinism, like Classical Statistical Mechanics (CSM) and Evolutionary Theory (ET). Contrarily, some have argued that chance and determinism are incompatible, and so such probabilities are subjective. In this paper, I argue that both of these positions are unsatisfactory. I argue that the probabilities of theories like CSM and ET are not chances, but also that they are (...) not subjective probabilities either. Rather, they are a third type of probability, which I call counterfactual probability. The main distinguishing feature of counterfactual-probability is the role it plays in conveying important counterfactual information in explanations. This distinguishes counterfactual probability from chance as a second concept of objective probability. (shrink)

The most important theories in fundamental physics, quantum mechanics and statistical mechanics, posit objective probabilities or chances. As important as chance is there is little agreement about what it is. The usual “interpretations of probability” give very different accounts of chance and there is disagreement concerning which, if any, is capable of accounting for its role in physics. David Lewis has contributed enormously to improving this situation. In his classic paper “A Subjectivist's Guide to Objective Chance” he described a framework (...) for representing single case objective chances, showed how they are connected to subjective credences, and sketched a novel account what they are within his Humean account of scientific laws. Here I will describe these contributions and add a little to them. (shrink)

It is generally thought that objective chances for particular events different from 1 and 0 and determinism are incompatible. However, there are important scientific theories whose laws are deterministic but which also assign non-trivial probabilities to events. The most important of these is statistical mechanics whose probabilities are essential to the explanations of thermodynamic phenomena. These probabilities are often construed as 'ignorance' probabilities representing our lack of knowledge concerning the microstate. I argue that this construal is incompatible with the role (...) of probability in explanation and laws. This is the 'paradox of deterministic probabilities'. After surveying the usual list of accounts of objective chance and finding them inadequate I argue that an account of chance sketched by David Lewis can be modified to solve the paradox of deterministic probabilities and provide an adequate account of the probabilities in deterministic theories like statistical mechanics. (shrink)

Tn this paper I explore and to an extent defend HS. The main philosophical challenges to HS come from philosophical views that say that nomic concepts-laws, chance, and causation-denote features of the world that fail to supervene on non-nomic features. Lewis rejects these views and has labored mightily to construct HS accounts of nomic concepts. His account of laws is fundamental to his program, since his accounts of the other nomic notions rely on it. Recently, a number of philosophers have (...) criticized Lewis's account, and Humean accounts of laws generally, for delivering, at best, a pale imitation ofthe genuine item. These philosophers think that the notion of law needed by science requires laws-if there are any-to be fundamental features of our world that are completely distinct from and not supervenient on the particular facts that they explain. I side with Lewis against these philosophers. Here I will argue that although Lewis-laws don't fulfill all our philosophical expectations, they do play the roles that science needs laws to play. The metaphysics and epistemology of Humean laws, and more specifically, Lewis-laws, are in much better shape than the metaphysics and epistemology of the main anti-Humean alternatives. However, I do have inisgivings about Lewis's account. Both he and his critics assume that the basic properties are so individuated so that the laws are not metaphysically necessary. If this assumption is rejected, then the question of Humean supervenience lapses. I conclude with a brief discussion of this position. (shrink)

One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its prequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In the prequel, we made this norm mathematically precise; in this paper, we derive its consequences. We show that the two core tenets of Bayesianism (...) follow from the norm, while the characteristic claim of the Objectivist Bayesian follows from the norm along with an extra assumption. Finally, we consider Richard Jeffrey’s proposed generalization of conditionalization. We show not only that his rule cannot be derived from the norm, unless the requirement of Rigidity is imposed from the start, but further that the norm reveals it to be illegitimate. We end by deriving an alternative updating rule for those cases in which Jeffrey’s is usually supposed to apply. (shrink)

One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its sequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In this paper, we make this norm mathematically precise in various ways. We describe three epistemic dilemmas that an agent might face if she attempts (...) to follow Accuracy, and we show that the only inaccuracy measures that do not give rise to such dilemmas are the quadratic inaccuracy measures. In the sequel, we derive the main tenets of Bayesianism from the relevant mathematical versions of Accuracy to which this characterization of the legitimate inaccuracy measures gives rise, but we also show that Jeffrey conditionalization has to be replaced by a different method of update in order for Accuracy to be satisfied. (shrink)