Abrams, Rosenthal, and Strevens have recently presented interpretations of the objective probabilities posited by some scientific theories that build on von Kries’s idea of identifying probabilities with ranges of values in a space of possible states. These interpretations face a problem, forcefully pointed out by Rosenthal, about how to determine ‘input probabilities.’ I argue here that Abrams’s and Strevens’s attempts to solve this problem do not succeed. I also argue that the problem can be solved by recognizing the possibility of (...) laws of nature that manifest themselves not as universal regularities, but instead as constraints on relative frequencies. (shrink)

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)

Scientists often think of the world as a dynamical system, a stochastic process, or a generalization of such a system. Prominent examples of systems are the system of planets orbiting the sun or any other classical mechanical system, a hydrogen atom or any other quantum–mechanical system, and the earth’s atmosphere or any other statistical mechanical system. We introduce a general and unified framework for describing such systems and show how it can be used to examine some familiar philosophical questions, including (...) the following: how can we define nomological possibility, necessity, determinism, and indeterminism; what are symmetries and laws; what regularities must a system display to make scientific inference possible; how might principles of parsimony such as Occam’s Razor help when we make such inferences; what is the role of space and time in a system; and might they be emergent features? Our framework is intended to serve as a toolbox for the formal analysis of systems that is applicable in several areas of philosophy. (shrink)

In their influential paper “Ceteris Paribus, There is No Problem of Provisos”, Earman and Roberts (Synthese 118:439–478, 1999) propose to interpret the non-strict generalizations of the special sciences as statistical generalizations about correlations. I call this view the “statistical account”. Earman and Roberts claim that statistical generalizations are not qualified by “non-lazy” ceteris paribus conditions. The statistical account is an attractive view, since it looks exactly like what everybody wants: it is a simple and intelligible theory of special science laws (...) without the need for mysterious ceteris paribus conditions. I present two challenges to the statistical account. According to the first challenge, the statistical account does not get rid of so-called “non-lazy” ceteris paribus conditions. This result undermines one of the alleged and central advantages of the statistical account. The second challenge is that the statistical account, qua general theory of special science laws, is weakened by the fact that idealized law statements resist a purely statistical interpretation. (shrink)

Despite the burgeoning interest in new and more complex accounts of the organism-environment dyad by biologists and philosophers, little attention has been paid in the resulting discussions to the history of these ideas and to their deployment in disciplines outside biology—especially in the social sciences. Even in biology and philosophy, there is a lack of detailed conceptual models of the organism-environment relationship. This volume is designed to fill these lacunae by providing the first multidisciplinary discussion of the topic of organism-environment (...) interaction. It brings together scholars from history, philosophy, psychology, anthropology, medicine, and biology to discuss the common focus of their work: entangled life, or the complex interaction of organisms and environments. (shrink)

This chapter will review selected aspects of the terrain of discussions about probabilities in statistical mechanics (with no pretensions to exhaustiveness, though the major issues will be touched upon), and will argue for a number of claims. None of the claims to be defended is entirely original, but all deserve emphasis. The first, and least controversial, is that probabilistic notions are needed to make sense of statistical mechanics. The reason for this is the same reason that convinced Maxwell, Gibbs, and (...) Boltzmann that probabilities would be needed, namely, that the second law of thermodynamics, which in its original formulation says that certain processes are impossible, must, on the kinetic theory, be replaced by a weaker formulation according to which what the original version deems impossible is merely improbable. Second is that we ought not take the standard measures invoked in equilibrium statistical mechanics as giving, in any sense, the correct probabilities about microstates of the system. We can settle for a much weaker claim: that the probabilities for outcomes of experiments yielded by the standard distributions are effectively the same as those yielded by any distribution that we should take as a representing probabilities over microstates. Lastly, (and most controversially): in asking about the status of probabilities in statistical mechanics, the familiar dichotomy between epistemic probabilities (credences, or degrees of belief) and ontic (physical) probabilities is insufficient; the concept of probability that is best suited to the needs of statistical mechanics is one that combines epistemic and physical considerations. (shrink)

We offer a new argument for the claim that there can be non-degenerate objective chance (“true randomness”) in a deterministic world. Using a formal model of the relationship between different levels of description of a system, we show how objective chance at a higher level can coexist with its absence at a lower level. Unlike previous arguments for the level-specificity of chance, our argument shows, in a precise sense, that higher-level chance does not collapse into epistemic probability, despite higher-level properties (...) supervening on lower-level ones. We show that the distinction between objective chance and epistemic probability can be drawn, and operationalized, at every level of description. There is, therefore, not a single distinction between objective and epistemic probability, but a family of such distinctions. (shrink)

I describe a realist, ontologically objective interpretation of probability, "far-flung frequency (FFF) mechanistic probability". FFF mechanistic probability is defined in terms of facts about the causal structure of devices and certain sets of frequencies in the actual world. Though defined partly in terms of frequencies, FFF mechanistic probability avoids many drawbacks of well-known frequency theories and helps causally explain stable frequencies, which will usually be close to the values of mechanistic probabilities. I also argue that it's a virtue rather than (...) a failing of FFF mechanistic probability that it does not define single-case chances, and compare some aspects of my interpretation to a recent interpretation proposed by Strevens. (shrink)

A proposal for an objective interpretation of probability is introduced and discussed: probabilities as deriving from ranges in suitably structured initial-state spaces. Roughly, the probability of an event on a chance trial is the proportion of initial states that lead to the event in question within the space of all possible initial states associated with this type of experiment, provided that the proportion is approximately the same in any not too small subregion of the space. This I would like to (...) call the “natural-range conception” of probability. Providing a substantial alternative to frequency or propensity accounts of probability in a deterministic setting, it is closely related to the so-called “method of arbitrary functions”. It is explicated, confronted with certain problems, and some ideas how these might be overcome are sketched and discussed. (shrink)

The so-called ergodic hierarchy (EH) is a central part of ergodic theory. It is a hierarchy of properties that dynamical systems can possess. Its five levels are egrodicity, weak mixing, strong mixing, Kolomogorov, and Bernoulli. Although EH is a mathematical theory, its concepts have been widely used in the foundations of statistical physics, accounts of randomness, and discussions about the nature of chaos. We introduce EH and discuss how its applications in these fields.

Pettit (2006) argues that deferring to majority testimony is not generally rational: it may lead to inconsistent beliefs. He suggests that “another ... approach will do better”: deferring to supermajority testimony. But this approach may also lead to inconsistencies. In this paper, I describe conditions under which deference to supermajority testimony ensures consistency, and conditions under which it does not. I also introduce the concept of “consistency of degree k”, which is weaker than full consistency by ruling out only “blatant” (...) inconsistencies in an agent’s beliefs while permitting less blatant ones, and show that, while super-majoritarian deference often fails to ensure full consistency, it is a route to consistency in this weaker sense. (shrink)

An adequate account of laws should satisfy at least five desiderata: it should provide a unified account of laws and chances, it should yield plausible relations between laws and chances, it should vindicate numerical chance assignments, it should accommodate dynamical and non-dynamical chances, and it should accommodate a plausible range of nomic possibilities. No extant account of laws satisfies these desiderata. This paper presents a non-Humean account of laws, the Nomic Likelihood Account, that does.

En esta entrada se mencionan las principales cuestiones en los fundamentos de la mecánica estadı́stica y la termodinámica, y las cuestiones filosóficas en las que repercuten estas áreas de la fı́sica. Al final se añaden lecturas recomendadas, enfatizando las traducidas al español.

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)

Contingency-theorists have gestured to a series of phenomena such as random mutations or rare Armageddon-like events as that which accounts for evolutionary contingency. These phenomena constitute a class, which may be aptly called the ‘sources of contingency’. In this paper, I offer a probabilistic conception of what it is to be a source of contingency and then examine two major candidates: chance variation and genetic drift, both of which have historically been taken to be ‘chancy’ in a number of different (...) senses. However,contrathe gesturing of contingency-theorists, chance variation and genetic drift are not always strong sources of contingency, as they can be non-chancy in at least one sense that opposes evolutionary contingency. The probabilistic conception offered herein allows for sources of contingency to appropriately vary in strength. To this end, I import Shannon’sinformation entropyas a statistical measure for systematically assessing the strength of a source of contingency, which is part and parcel of identifying sources of contingency. In brief, the higher the entropy, the greater the strength. This is also empirically significant because molecular, mutational, and replicative studies often contain sufficient frequency or probability data to allow for entropies to be calculated. In this way, contingency-theorists can evaluate the strength of a source of contingency in real-world cases. Moreover, the probabilistic conception also makes conceptual room for the converse of sources of contingency: ‘sources of directionality’, which ought to be recognised, as they can interact with genuine sources of contingency in undermining evolutionary contingency. (shrink)

There is widespread excitement in the literature about the method of arbitrary functions: many take it to show that it is from the dynamics of systems that the objectivity of probabilities emerge. In this paper, I differentiate three ways in which a probability function might be objective, and I argue that the method of arbitrary functions cannot help us show that dynamics objectivise probabilities in any of these senses.

While the notion of chance has been central in discussions over the probabilistic nature of natural selection and genetic drift, its role in the production of variants on which populational sampling takes place has received much less philosophical attention. This article discusses the concept of chance in evolution in the light of contemporary work in evo-devo. We distinguish different levels at which randomness and chance can be defined in this context, and argue that recent research on variability and evolvability demands (...) a causal understanding of variational probabilities under which development acquires a creative, rather than a constraining role in evolution. We then provide a propensity interpretation of variational probabilities that solves a conceptual confusion between causal properties, variational probabilities and extant variation present in the literature, and explore some metaphysical consequences that follow from our interpretation, specifically with regards to the nature of developmental types. (shrink)

Philosophers of biology have worked extensively on how we ought best to interpret the probabilities which arise throughout evolutionary theory. In spite of this substantial work, however, much of the debate has remained persistently intractable. I offer the example of Bayesian models of divergence time estimation as a case study in how we might bring further resources from the biological literature to bear on these debates. These models offer us an example in which a number of different sources of uncertainty (...) are combined to produce an estimate for a complex, unobservable quantity. These models have been carefully analyzed in recent biological work, which has determined the relationship between these sources of uncertainty, both quantitatively and qualitatively. I suggest here that this case shows us the limitations of univocal analyses of probability in evolution, as well as the simple dichotomy between “subjective” and “objective” probabilities, and I conclude by gesturing toward ways in which we might introduce more sophisticated interpretive taxonomies of probability as a path toward advancing debates on probability in the life sciences. (shrink)

I present an account of deterministic chance which builds upon the physico-mathematical approach to theorizing about deterministic chance known as 'the method of arbitrary functions'. This approach promisingly yields deterministic probabilities which align with what we take the chances to be---it tells us that there is approximately a 1/2 probability of a spun roulette wheel stopping on black, and approximately a 1/2 probability of a flipped coin landing heads up---but it requires some probabilistic materials to work with. I contend that (...) the right probabilistic materials are found in reasonable initial credence distributions. I note that, with some normative assumptions, the resulting account entails that deterministic chances obey a variant of Lewis's 'principal principle'. I additionally argue that deterministic chances, so understood, are capable of explaining long-run frequencies. (shrink)

Scientists and philosophers frequently speak about levels of description, levels of explanation, and ontological levels. In this paper, I propose a unified framework for modelling levels. I give a general definition of a system of levels and show that it can accommodate descriptive, explanatory, and ontological notions of levels. I further illustrate the usefulness of this framework by applying it to some salient philosophical questions: (1) Is there a linear hierarchy of levels, with a fundamental level at the bottom? And (...) what does the answer to this question imply for physicalism, the thesis that everything supervenes on the physical? (2) Are there emergent properties? (3) Are higher-level descriptions reducible to lower-level ones? (4) Can the relationship between normative and non-normative domains be viewed as one involving levels? Although I use the terminology of “levels”, the proposed framework can also represent “scales”, “domains”, or “subject matters”, where these are not linearly but only partially ordered by relations of supervenience or inclusion. (shrink)

A conception of probability that can be traced back to Johannes von Kries is introduced: the “Spielraum” or range conception. Its close connection to the so-called method of arbitrary functions is highlighted. Possible interpretations of it are discussed, and likewise its scope and its relation to certain current interpretations of probability. Taken together, these approaches form a class of interpretations of probability in its own right, but also with its own problems. These, too, are introduced, discussed, and proposals in response (...) to them are surveyed, some of which also go back to von Kries. (shrink)

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 (...) setups. I clarify relations between probabilities and properties defined in terms of them, and argue that certain widespread uses of computer simulations in evolutionary biology show that many probabilities relevant to evolutionary outcomes are causal probabilities. This supports the claim that higher-level properties such as biological fitness and processes such as natural selection are causal properties and processes, contrary to what some authors have argued. (shrink)

The prospects of a causal interpretation of probability are examined. Various accounts both from the history of scientific method and from recent developments in the tradition of the method of arbitrary functions, in particular by Strevens, Rosenthal, and Abrams, are briefly introduced and assessed. I then present a specific account of causal probability with the following features: First, the link between causal probability and a particular account of induction and causation is established, namely eliminative induction and the related difference-making account (...) of causation in the tradition of Bacon, Herschel, and Mill. Second, it is shown how a causal approach is useful beyond applications of the method of arbitrary functions and is able to deal with various shades of both ontic and epistemic probabilities. Furthermore, I clarify the notion of causal symmetry as a central element of an objective version of the principle of indifference and relate probabilistic independence to causal irrelevance. (shrink)

Determinism and chance seem to be irreconcilable opposites: either something is chancy or it is deterministic but not both. Yet there are processes which appear to square the circle by being chancy and deterministic at once, and the appearance is backed by well-confirmed scientific theories such as statistical mechanics which also seem to provide us with chances for deterministic processes. Is this possible, and if so how? In this essay I discuss this question for probabilities as they occur in the (...) empirical sciences, setting aside metaphysical questions in connection with free will, divine intervention and determinism in history. (shrink)

Several authors have argued that non-extreme probabilities used in special sciences such as chemistry and biology can be objective chances, even if the true microphysical description of the world is deterministic. This article examines an influential version of this argument and shows that it depends on a particular methodology for defining the relationship between coarse-grained and fine-grained events. An alternative methodology for coarse-graining is proposed. This alternative methodology blocks this argument for the existence of emergent chances, and makes better sense (...) of two well-known subjects of philosophical discussion: the Miners Puzzle and Simpson’s Paradox. (shrink)

How should contractualists assess the permissibility of risky actions? Both main views on the question, ex ante and ex post, fail to distinguish between different kinds of risk. In this article, I argue that this overlooks a third alternative that I call “objective ex ante contractualism”. Objective ex ante substitutes discounting complaints by epistemic risk in favor of discounting by objective risk. I further argue in favor of this new view. Objective ex ante contractualism provides the best model of justifiability (...) to each. (shrink)

Sewall Wright ’s FST is a mathematical test widely used in empirical applications to characterize genetic and other differences between subpopulations, and to identify causes of those differences. Cockerham and Weir’s popular approach to statistical estimation of FST is based on an assumption sometimes formulated as a claim that actual populations tested are sampled from.

You and I lead different lives. While we share a society and a world, our existence is separate from one another. You and I matter individually, by ourselves. My dissertation is about this simple thought. I argue that this simple insight, the separateness of persons, tells us something fundamental about morality. My dissertation seeks to answer how the separateness of persons matters. I develop a precise view of the demands of the separateness of persons. The separateness of persons imposes both (...) a requirement on the justification of first-order moral principles as well as a requirement on the content of first-order moral principles. In specifying these demands, I argue that respecting the separateness of persons requires taking into consideration each person’s point of view separately. This requires taking into account the moral relations in which individuals stand to one another. I make use of this relational understanding of the separateness of persons to advance various debates in moral and political philosophy. I argue for a framework to assess to which extent the veil of ignorance can be reconciled with the separateness of persons. I also argue for a new view on the ethics of risk which is a form of contractualism that discounts risks only by their objective risk. Furthermore, I argue for a new solution to the problem of aggregation that is skeptical of aggregation and can set plausible limits to aggregation. Lastly, I provide a new relational agent-based justification for deontological constraints. In addition to answering how the separateness of persons matters, I defend the separateness of persons against challenges. Most importantly, I argue that the importance of the separateness of persons is not undermined even if we believe that our personal identity, i.e. whether we persist as the same person, is unimportant. (shrink)

This paper has the aim of making Johannes von Kries’s masterpiece, Die Principien der Wahrscheinlichkeitsrechnung of 1886, a little more accessible to the modern reader in three modest ways: first, it discusses the historical background to the book ; next, it summarizes the basic elements of von Kries’s approach ; and finally, it examines the so-called “principle of cogent reason” with which von Kries’s name is often identified in the English literature.

Showing that the arithmetic mean number of offspring for a trait type often fails to be a predictive measure of fitness was a welcome correction to the philosophical literature on fitness. While the higher mathematical moments of a probability-weighted offspring distribution can influence fitness measurement in distinct ways, the geometric mean number of offspring is commonly singled out as the most appropriate measure. For it is well-suited to a compounding process and is sensitive to variance in offspring number. The geometric (...) mean thus proves to be a predictively efficacious measure of fitness in examples featuring discrete generations and within- or between-generation variance in offspring output. Unfortunately, this advance has subsequently led some to conclude that the arithmetic mean is never a good measure of fitness and that the geometric mean should accordingly be the default measure of fitness. We show not only that the arithmetic mean is a perfectly reasonable measure of fitness so long as one is clear about what it refers to, but also that it functions as a more general measure when properly interpreted. It must suffice as a measure of fitness in any case where the geometric mean has been effectively deployed as a measure. We conclude with a discussion about why the mathematical equivalence we highlight cannot be dismissed as merely of mathematical interest. (shrink)

Dynamic approaches to understanding probability in the non-fundamental sciences turn on certain properties of physical processes that are apt to produce “probabilistically patterned” outcomes. The dynamic properties on their own, however, seem not quite sufficient to explain the patterns; in addition, some sort of assumption about initial conditions must be made, an assumption that itself typically takes a probabilistic form. How should such a posit be understood? That is the problem of initial conditions. Reichenbach, in his doctoral dissertation, floated a (...) Kantian solution to the problem. In this paper I provide a Reichenbachian alternative. (shrink)

Drift is often characterized in statistical terms. Yet such a purely statistical characterization is ambiguous for it can accept multiple physical interpretations. Because of this ambiguity it is important to distinguish what sorts of processes can lead to this statistical phenomenon. After presenting a physical interpretation of drift originating from the most popular interpretation of fitness, namely the propensity interpretation, I propose a different one starting from an analysis of the concept of drift made by Godfrey-Smith. Further on, I show (...) how my interpretation relates to previous attempts to make sense of the notion of expected value in deterministic setups. The upshot of my analysis is a physical conception of drift that is compatible with both a deterministic and indeterministic world. (shrink)

A symposium on Michael Strevens' book "Tychomancy", concerning the psychological roots and historical significance of physical intuition about probability in physics, biology, and elsewhere.

This article focuses on three recent discussions on determinism in the philosophy of science. First, determinism and predictability will be discussed. Then, second, the paper turns to the topic of determinism, indeterminism, observational equivalence and randomness. Finally, third, there will be a discussion about deterministic probabilities. The paper will end with a conclusion.

Why are causal generalizations in the higher-level sciences “inexact”? That is, why do they have apparent exceptions? This paper offers one explanation: many causal generalizations cite as their antecedent—the \(F\) in \(Fs\,\, {\textit{are}}\,\, G\) —a property that is not causally relevant to the consequent, but which is rather “entangled” with a causally relevant property. Entanglement is a relation that may exist for many reasons, and that allows of exceptions. Causal generalizations that specify entangled but causally irrelevant antecedents therefore tolerate exceptions.

Assumptions of stochastic independence are crucial to statistical models in science. Under what circumstances is it reasonable to suppose that two events are independent? When they are not causally or logically connected, so the standard story goes. But scientific models frequently treat causally dependent events as stochastically independent, raising the question whether there are kinds of causal connection that do not undermine stochastic independence. This paper provides one piece of an answer to this question, treating the simple case of two (...) tossed coins with and without a midair collision. (shrink)

The most promising accounts of ontic probability include the Spielraum conception of probabilities, which can be traced back to J. von Kries and H. Poincaré, and the best system account by D. Lewis. This paper aims at comparing both accounts and at combining them to obtain the best of both worlds. The extensions of both Spielraum and best system probabilities do not coincide because the former only apply to systems with a special dynamics. Conversely, Spielraum probabilities may not be part (...) of the best system, e.g. if a broad class of random devices is not often used. Spielraum probabilities have the potential to provide illuminating explanations of frequencies with which outcomes of trials on gambling devices arise. They ultimately fail to account for such frequencies though because they are compatible with frequencies that grossly differ from the values of the respective probabilities. I thus follow recent proposals by M. Strevens and M. Abrams and strengthen the definition of Spielraum probabilities by adding a further condition that restricts some actual frequencies. The resulting account remains limited in scope, but stands objections raised against it in the recent literature: it is neither circular nor based upon arbitrary choices of a measure or of physical variables. Nor does it lack any explanatory power. (shrink)