This volume focuses on various questions concerning the interpretation of probability and probabilistic reasoning in biology and physics. It is inspired by the idea that philosophers of biology and philosophers of physics who work on the foundations of their disciplines encounter similar questions and problems concerning the role and application of probability, and that interaction between the two communities will be both interesting and fruitful. In this introduction we present the background to the main questions that the volume focuses on (...) and summarize the highlights of the individual contributions. (shrink)

Direct inferences identify certain probabilistic credences or confirmation-function-likelihoods with values of objective chances or relative frequencies. The best known version of a direct inference principle is David Lewis’s Principal Principle. Certain kinds of statements undermine direct inferences. Lewis calls such statements inadmissible. We show that on any Bayesian account of direct inference several kinds of intuitively innocent statements turn out to be inadmissible. This may pose a significant challenge to Bayesian accounts of direct inference. We suggest some ways in which (...) these challenges may be addressed. (shrink)

The propensity interpretation of fitness draws on the propensity interpretation of probability, but advocates of the former have not attended sufficiently to problems with the latter. The causal power of C to bring about E is not well-represented by the conditional probability Pr. Since the viability fitness of trait T is the conditional probability Pr, the viability fitness of the trait does not represent the degree to which having the trait causally promotes surviving. The same point holds for fertility fitness. (...) This failure of trait fitness to capture causal role can also be seen in the fact that coextensive traits must have the same fitness values even if one of them promotes survival and the other is neutral or deleterious. Although the fitness of a trait does not represent the trait’s causal power to promote survival and reproduction, variation in fitness in a population causally promotes change in trait frequencies; in this sense, fitness variation is a population-level propensity. (shrink)

Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the thermodynamic arrow of time can be grounded on typicality within statistical mechanics. This account, which I will call typicality frequentism, will evade the major criticisms raised against previous forms of frequentism. In this theory, probabilities arise within a physical theory from statistical (...) behavior of almost all initial conditions. The main advantage of typicality frequentism is that it shows which kinds of probabilities (that also have empirical relevance) can be derived from physics. Although one cannot recover all probability talk in this account, this is rather a virtue than a vice, because it shows which types of probabilities can in fact arise from physics and which types need to be explained in different ways, thereby opening the path for a pluralistic account of probabilities. (shrink)

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)

Gillies introduced a propensity interpretation of probability which is linked to experience by a falsifying rule for probability statements. The present paper argues that general statistical tests should qualify as falsification rules. The ‘goodness-of-fit paradox’ is introduced: the confirmation of a probability model by a test refutes the model's validity. An example is given in which an independence test introduces dependence. Several possibilities to interpret the paradox and to deal with it are discussed. It is concluded that the propensity interpretation (...) properly reflects statistical practice, but it is not as objective as some adherents claim. (shrink)

An approach to inference to the best explanation integrating a Popperianconception of natural laws together with a modified Hempelian account of explanation, one the one hand, and Hacking's law of likelihood (in its nomicguise), on the other, which provides a robust abductivist model of sciencethat appears to overcome the obstacles that confront its inductivist,deductivist, and hypothetico-deductivist alternatives.This philosophy of scienceclarifies and illuminates some fundamental aspects of ontology and epistemology, especially concerning the relations between frequencies and propensities. Among the most important (...) elements of this conception is thecentral role of degrees of nomic expectability in explanation, prediction,and inference, for which this investigation provides a theoretical defense. (shrink)

I sketch a new constraint on chance, which connects chance ascriptions closely with ascriptions of ability, and more specifically with 'CAN'-claims. This connection between chance and ability has some claim to be a platitude; moreover, it exposes the debate over deterministic chance to the extensive literature on (in)compatibilism about free will. The upshot is that a prima facie case for the tenability of deterministic chance can be made. But the main thrust of the paper is to draw attention to the (...) connection between the truth conditions of sentences involving 'CAN' and 'CHANCE', and argue for the context sensitivity of each term. Awareness of this context sensitivity has consequences for the evaluation of particular philosophical arguments for (in) compatibilism when they are presented in particular contexts. (shrink)

Inconsistency of attitudes and behavior is due to the probabilistic connection between responses or actions and the (not directly observable) dispositions on which they depend. Latent variable models provide criteria for recognizing when attitude and behavior depend on the same disposition. Statistical tests of such models and techniques of parameter estimation are described. The viewpoint proposed here and illustrated with empirical examples contrasts with the prevalent reliance on correlational models and methods.

To clarify and illuminate the place of probability in science Ellery Eells and James H. Fetzer have brought together some of the most distinguished philosophers ...

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)

If chances are propensities, what reason do we have to expect them to be probabilities? I will offer a new answer to this question. It comes in two parts. First, I will defend an accuracy-centred account of what it is for a causal system to have precise propensities in the first place. Second, I will prove that, given some pretty weak assumptions about the nature of comparative causal dispositions, and some fairly standard assumptions about reasonable measures of inaccuracy, propensities must (...) be probabilities. (shrink)

The problem of philosophical skepticism relates to the difficulty involved in underwriting the claim that we know anything of spatio-temporal reality. It is often claimed, in fact, that proper philosophical scrutiny reveals quite the opposite from what common sense suggests. Knowledge of external reality is thought to be even quite obviously denied to us as a result of the alleged fact that we all fail to know that certain skeptical scenarios do not obtain. A skeptical scenario is one in which (...) we have neurological occurrences just like any normal situation in which we actually perceive spatio-temporal objects, but where we are deceived in some sense as a result of the manipulation of our brains from some outside source. In this work I attempt to address the problem of philosophical skepticism by claiming that most of us are able to come to know plenty about external reality, since we can come to realize that a certain philosophical theory of perception is correct. The theory I have in mind is what I call a non-cognitive theory of perception. According to this view, perceptual experience is defined by continuous, sensitive behavioral interaction with spatio-temporal objects of the appropriate size, shape, hardness, speed, etc. Knowing that this theory of perception is correct is equivalent to knowing that we know plenty about external reality. This is ultimately because by knowing that a non-cognitive theory of perception is true, we know that any skeptical scenario must fail to obtain. The structure of the work proceeds by first discussing the significance of the problem of philosophical skepticism in some detail. Chapter 1 lays out how the problem does indeed forcefully arise if it is conceded that we fail to know that the skeptical scenarios fail to obtain. Chapter 2 develops the sort of view of our epistemological situation that falls out of accepting without qualification that the problem exists. Chapter 3 examines and criticizes certain popular responses to the skeptical problem. The main goal of these first three preliminary chapters is to indicate that once it is admitted that we fail to know that the skeptical scenarios fail to obtain, the problem of philosophical skepticism forcefully presents itself. Chapter 4, however, attacks the idea that we fail to know that the skeptical scenarios fail to obtain. In this chapter I argue that this idea is wedded to the position that a certain theory of perception is correct. The theory in question is what I call a conjunctive theory of veridical experience. According to this view, normal experience of spatio-temporal objects occurs when a subject has a certain perceptual experience, and that experience also happens to match up with and/or be satisfied by what is really the case. Only when a theory of this sort is assumed, I argue, is the claim that we fail to know that the skeptical scenarios fail to obtain found to be obvious. In chapter 5 I argue that, in fact, a non-cognitive theory, rather than a conjunctive theory, is the correct view to maintain. In the final chapter 6 I develop the epistemological position that falls out of accepting a non-cognitive theory. (shrink)

In 2002 the readers of the scientific magazine 'Physics World' voted Young's double-slit experiment applied to the interference of single electrons to be 'the most beautiful experiment in physics'; this experiment, in truth, had already been carried out 30 years beforehand. The present article aims to re-examine the latter real experiment and put it into its proper historical perspective. Even though the experiment was not afforded the importance it perhaps deserved among philosophers, its philosophical mplications add new arguments to the (...) already far-reaching debate triggered off by the ideal experiment. Within the context of quantum mechanics in particular, the experiment revealed for the first time the importance that ought to be attributed at the empirical level to single-case probability, that is, to the probability of a single electron's reaching the screen. I investigate how the empirical significance of the experimental results comes within the framework of the debate over the propensity interpretation of probability in quantum mechanics. I argue that the experiment, when examined in all its technical details does in fact throw light on the evidence for the propensity, as a physical property, of micro-objects. (shrink)