After defending the pluralistic approach to the interpretation of probability statements, I argue that the correctness of objective probability statements is not to be explained in terms of objective probabilities attached to propositions. Such an explanation will enable us to uphold an intuitively appealing connection between probability and action only in indeterministic contexts, whereas the objectivity of probability statements doesn’t depend on the truth of indeterminism. I show how objective probability statements can be interpreted without ascribing objective probabilities to propositions. (...) Finally, I draw a cautionary conclusion about the prospects for providing a probabilistic analysis of causation. (shrink)

Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the most important notions (...) of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

Hume thought that if you believed in powers, you believed in necessary connections in nature. He was then able to argue that there were none such because anything could follow anything else. But Hume wrong-footed his opponents. A power does not necessitate its manifestations: rather, it disposes towards them in a way that is less than necessary but more than purely contingent. -/- In this paper a dispositional theory of causation is offered. Causes dispose towards their effects and often produce (...) them. But a set of causes, even though they may succeed in producing an effect, cannot necessitate it since the effect could have been counteracted by some additional power. This would require a separation of our concepts of causal production and causal necessitation. The most conspicuous cases of causation are those where powers accumulate and pass a requisite threshold for an effect to occur. -/- We develop a model for representing powers as constituent vectors within an n-dimensional quality space, where composition of causes appears as vector addition. Even our resultant vector, however, has to be understood as having dispositional force only. This model throws new light on causal modality and cases of prevention, causation by absence and probabilistic causation. (shrink)

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

Propensities are presented as a generalization of classical determinism. They describe a physical reality intermediary between Laplacian determinism and pure randomness, such as in quantum mechanics. They are characterized by the fact that their values are determined by the collection of all actual properties. It is argued that they do not satisfy Kolmogorov axioms; other axioms are proposed.

How should we give accounts of scientific modal relations? According to the Humean, we should do so by considering the role of such relations in our lives and scientific theorizing. For example, to give a Humean account of chance, we need to identity a non-modal relation that can play the ‘role’ of chance—typically that of guiding credences and scientifically explaining events. Defenders of Humean accounts claim to be uniquely well placed to meet this aim. Humean chances are objective, and so (...) suitable for explaining. Humean chances reduce to patterns in actual events in a way that limits the possible divergence between relative frequencies and chances. So, they argue, Humean chances can uniquely be shown to satisfy chance−credence principles. I’ll argue that Humeans have no special advantage. When used in scientific contexts, Humean chances must be allowed to diverge from the relative frequencies. So, when considering the scientific question of whether agents who align their credences to the chances will do well, it is merely probable that they will. This scientific use of chance undercuts the Humean’s claimed advantage over their rivals. This undercutting also points to a deeper tension in Humeanism: Humeans must either give up the aim of recovering scientific practice, or live with a disunity between science and metaphysics. While a focus on function is laudable, the motivation for being Humean must come from elsewhere. (shrink)

Spontaneous collapse theories of quantum mechanics turn the usual Schrödinger equation into a stochastic dynamical law. In particular, in this paper, I will focus on the GRW theory. Two philosophical issues that can be raised about GRW concern (i) the ontology of the theory, in particular the nature of the wave function and its role within the theory, and (ii) the interpretation of the objective probabilities involved in the dynamics of the theory. During the last years, it has been claimed (...) that we can take advantage of dispositional properties in order to develop an ontology for GRW theory, and also in order to ground the objective probabilities which are postulated by it. However, in this paper, I will argue that the dispositional interpretations which have been discussed in the literature so far are either flawed or – at best – incomplete. If we want to endorse a dispositional interpretation of GRW theory we thus need an extended account that specifies the precise nature of those properties and which makes also clear how they can correctly ground all the probabilities postulated by the theory. Thus, after having introduced several different kinds of probabilistic dispositions, I will try to fill the gap in the literature by proposing a novel and complete dispositional account of GRW, based on what I call spontaneous weighted multi-track propensities. I claim that such an account can satisfy both of our desiderata. (shrink)

Causalists and Evidentialists can agree about the right course of action in an (apparent) Newcomb problem, if the causal facts are not as initially they seem. If declining $1,000 causes the Predictor to have placed $1m in the opaque box, CDT agrees with EDT that one-boxing is rational. This creates a difficulty for Causalists. We explain the problem with reference to Dummett's work on backward causation and Lewis's on chance and crystal balls. We show that the possibility that the causal (...) facts might be properly judged to be non-standard in Newcomb problems leads to a dilemma for Causalism. One horn embraces a subjectivist understanding of causation, in a sense analogous to Lewis's own subjectivist conception of objective chance. In this case the analogy with chance reveals a terminological choice point, such that either (i) CDT is completely reconciled with EDT, or (ii) EDT takes precedence in the cases in which the two theories give different recommendations. The other horn of the dilemma rejects subjectivism, but now the analogy with chance suggests that it is simply mysterious why causation so construed should constrain rational action. (shrink)

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already (...) in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

This chapter contains sections titled: Highlights of Past Literature Current Work Future Work.

By “physical probability” I mean the empirical concept of probability in ordinary language. It can be represented as a function of an experiment type and an outcome type, which explains how non-extreme physical probabilities are compatible with determinism. Two principles, called specification and independence, put restrictions on the existence of physical probabilities, while a principle of direct inference connects physical probability with inductive probability. This account avoids a variety of weaknesses in the theories of Levi and Lewis.

The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the reference (...) class problem. Other versions of these interpretations apparently evade the problem. But I contend that they are all “no-theory” theories of probability - accounts that leave quite obscure why probability should function as a guide to life, a suitable basis for rational inference and action. The reference class problem besets those theories that are genuinely informative and that plausibly constrain our inductive reasonings and decisions. I distinguish a “metaphysical” and an “epistemological” reference class problem. I submit that we can dissolve the former problem by recognizing that probability is fundamentally a two-place notion: conditional probability is the proper primitive of probability theory. However, I concede that the epistemological problem remains. (shrink)

Even those generally skeptical of propensity interpretations of probability must now grant the following two points. First, the above single-case propensity interpretation meets recognized formal conditions for being a genuine interpretation of probability. Second, this interpretation is not logically reducible to a hypothetical relative frequency interpretation, nor is it only vacuously different from such an interpretation.The main objection to this propensity interpretation must be not that it is too vague or vacuous, but that it is metaphysically too extravagant. It asserts (...) not only that there are physical possibilities in nature, but further that nature itself contains innate tendencies toward these possibilities, tendencies which have the logical structure of probabilities. Thus the basic dispute between advocates of an actualist relative frequency interpretation and a single-case propensity interpretation is not a matter of epistemology, but metaphysics. The frequency theorist wishes to maintain that claims about physical probabilities are nothing more than claims about relative frequencies that will occur in the actual history of the world, be it infinite or no. It is a substantial, though hardly conclusive, argument for the propensity view that the mathematical structures commonly employed in studies of stochastic processes and statistical inference are richer than can be accommodated by a relative frequency interpretation. Whether it is possible to bridge this gap without going beyond an actualist metaphysics remains to be seen.38. (shrink)

The Doomsday argument purports to show that the risk of the human species going extinct soon has been systematically underestimated. This argument has something in common with controversial forms of reasoning in other areas, including: game theoretic problems with imperfect recall, the methodology of cosmology, the epistemology of indexical belief, and the debate over so-called fine-tuning arguments for the design hypothesis. The common denominator is a certain premiss: the Self-Sampling Assumption. We present two strands of argument in favor of this (...) assumption. Through a series of thought experiments we then investigate some bizarre prima facie consequences – backward causation, psychic powers, and an apparent conflict with the Principal Principle. (shrink)

We frequently engage in activities that impose a risk of serious harm on innocent others in order to realise trivial benefits for ourselves or third parties. Many moral theories tie the evidence-relative permissibility of engaging in such activities to the size of the risk that an individual agent imposes. I argue that we should move away from such a reliance on quantified individual risks when conceptualising morally permissible risk imposition. Under most circumstances of interest, a conscientious reasoner will identify a (...) gap between the factors they deem potentially relevant to the riskiness of an agent’s behaviour, and the factors they are reasonably able to quantify. This then leads a conscientious reasoner to conclude that they cannot, in good faith, come up with a quantitative risk estimate that is genuinely tailored to the agent’s particular situation. Based on this, I argue that principles of morally permissible risk imposition fail to provide us with practical guidance if they ask us to take into account our agent-specific risks in a quantified manner. I also argue that principles of permissible risk imposition which appeal to quantified individual risks implausibly imply that it is frequently indeterminate whether engaging in some risky activity is morally permissible. For both of these reasons, I contend that principles of morally permissible risk imposition should make no reference to quantified individual risks. They should instead acknowledge that any quantitative estimates that an agent might usefully be able to consider will likely not be tailored to the agent’s idiosyncratic situation. (shrink)

In this article, I aim at showing how powers may ground different types of probability in the universe. In Section 1 I single out several dimensions along which the probability of something can be determined. Each of such dimensions can be further specified at the type-level or at the token-level. In Section 2 I introduce some metaphysical assumptions about powers. In Section 3 I show how powers can ground single-case probabilities and frequency-probabilities in a deterministic setting. Later on, in Section (...) 4, I move to a theoretical framework where the falsity of determinism is assumed. Within such a framework, I first argue that some probabilities are grounded on basic powers. Moreover, in Section 5, I introduce tendencies and suggest that they are endowed with specific degrees of activation that may change over time. Such degrees explain why tendencies are more likely to be activated than non-activated, or vice versa. In Section 6 I compare my account of tendencies with other accounts. Finally, in Section 7, I anticipate some general objections against my account – objections that it shares with propensity-accounts of probability – and against degrees of activation of tendencies. (shrink)

Consider Phoebe and Daphne. Phoebe has credences in 1 million propositions. Daphne, on the other hand, has credences in all of these propositions, but she's also got credences in 999 million other propositions. Phoebe's credences are all very accurate. Each of Daphne's credences, in contrast, are not very accurate at all; each is a little more accurate than it is inaccurate, but not by much. Whose doxastic state is better, Phoebe's or Daphne's? It is clear that this question is analogous (...) to a question that has exercised ethicists over the past thirty years. How do we weigh a population consisting of some number of exceptionally happy and satisfied individuals against another population consisting of a much greater number of people whose lives are only just worth living? This is the question that occasions population ethics. In this paper, I go in search of the correct population ethics for credal states. (shrink)

We explore three methods for measuring the conscious status of knowledge using the artificial grammar learning paradigm. We show wagering is no more sensitive to conscious knowledge than simple verbal confidence reports but is affected by risk aversion. When people wager rather than give verbal confidence they are less ready to indicate high confidence. We introduce a “no-loss gambling” method which is insensitive to risk aversion. We show that when people are just as ready to bet on a genuine random (...) process as their own classification decisions, their classifications are still above baseline, indicating knowledge participants are not aware of having. Our results have methodological implications for any study investigating whether people are aware of knowing. (shrink)

The objective of this paper is to show that, instead of quantum probabilities, wave packets are physically real. First, Cartwright's recent argument for the reality of quantum probabilities is criticized. Then, the notion of ‘physically real’ is precisely defined and the difference between wave functions and quantum probabilities clarified. Being thus prepared, some strong reasons are discussed for considering the wave packet to be physically real. Finding the reasons inconclusive, I explain how the Aharonov—Bohm effect delivers the final punch. I (...) conclude that wave packets are the quantum objects that underlie the indeterministic quantum processes and have the propensity of displaying probabilistic (or indeterministic) behavior. (shrink)

Recent debate on the nature of probabilities in evolutionary biology has focused largely on the propensity interpretation of fitness (PIF), which defines fitness in terms of a conception of probability known as “propensity”. However, proponents of this conception of fitness have misconceived the role of probability in the constitution of fitness. First, discussions of probability and fitness have almost always focused on organism effect probability, the probability that an organism and its environment cause effects. I argue that much of the (...) probability relevant to fitness must be organism circumstance probability, the probability that an organism encounters particular, detailed circumstances within an environment, circumstances which are not the organism’s effects. Second, I argue in favor of the view that organism effect propensities either don’t exist or are not part of the basis of fitness, because they usually have values close to 0 or 1. More generally, I try to show that it is possible to develop a clearer conception of the role of probability in biological processes than earlier discussions have allowed. (shrink)

This paper argues that probability is not an objective phenomenon that can be identified with either the configurational properties of sequences, or the dynamic properties of sources that generate sequences. Instead, it is proposed that probability is a function of subjective as well as objective conditions. This is explained by formulating a nation of probability that is a modification of Laplace‘s classical enunciation. This definition is then used to explain why probability is strongly associated with disordered sequences, and is also (...) used to throw light on a number of problems in probability theory. (shrink)

We propose an interpretation of physics named potentiality realism. This view, which can be applied to classical as well as to quantum physics, regards potentialities (i.e. intrinsic, objective propensities for individual events to obtain) as elements of reality, thereby complementing the actual properties taken by physical variables. This allows one to naturally reconcile realism and fundamental indeterminism in any theoretical framework. We discuss our specific interpretation of propensities, that require them to depart from being probabilities at the formal level, though (...) allowing for statistics and the law of large numbers. This view helps reconcile classical and quantum physics by showing that most of the conceptual problems that are customarily taken to be unique issues of the latter -- such as the measurement problem -- are actually in common to all indeterministic physical theories. (shrink)