Bertand’s paradox is a fundamental problem in probability that casts doubt on the applicability of the indifference principle by showing that it may yield contradictory results, depending on the meaning assigned to “randomness”. Jaynes claimed that symmetry requirements solve the paradox by selecting a unique solution to the problem. I show that this is not the case and that every variant obtained from the principle of indifference can also be obtained from Jaynes’ principle of transformation groups. This is because the (...) same symmetries can be mathematically implemented in different ways, depending on the procedure of random selection that one uses. I describe a simple experiment that supports a result from symmetry arguments, but the solution is different from Jaynes’. Jaynes’ method is thus best seen as a tool to obtain probability distributions when the principle of indifference is inconvenient, but it cannot resolve ambiguities inherent in the use of that principle and still depends on explicitly defining the selection procedure. (shrink)

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian (...) conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality. (shrink)

Proponents of individual-based modeling in ecology claim that their models explain the emergence of population-level behavior. This article argues that individual-based models have not, as yet, provided such explanations. Instead, individual-based models can and do demonstrate and explain the emergence of population-level behaviors from individual behaviors and interactions.

The aim of this article is to analyse the relation between the second law of thermodynamics and the so-called arrow of time. For this purpose, a number of different aspects in this arrow of time are distinguished, in particular those of time-reversal (non-)invariance and of (ir)reversibility. Next I review versions of the second law in the work of Carnot, Clausius, Kelvin, Planck, Gibbs, Caratheodory and Lieb and Yngvason, and investigate their connection with these aspects of the arrow of time. It (...) is shown that this connection varies a great deal along with these formulations of the second law. According to the famous formulation by Planck, the second law expresses the irreversibility of natural processes. But in many other formulations irreversibility or even time-reversal non-invariance plays no role. I therefore argue for the view that the second law has nothing to do with the arrow of time. (shrink)

The arrow of time is a familiar phenomenon we all know from our experience: we remember the past but not the future and control the future but not the past. However, it takes an effort to keep records of the past, and to affect the future. For example, it would take an immense effort to unmix coffee and milk, although we easily mix them. Such time directed phenomena are sub- sumed under the Second Law of Thermodynamics. This law characterizes our (...) experience of the arrow of time in terms of an increase of a theoretical magnitude called entropy. Statistical mechan- ics tries to explain the Second Law as an effect of the behavior of the microscopic particles that make up the universe. Since our senses are too coarse to see this microstructure, statistical mechanics describes our experience in terms of probability, or in terms of the partial information we have about the particles. In this paper we explain the workings of statistical mechanics; how it accounts for probability as an objective feature of the world based on the underlying dynamics; how it accounts for our memories of the past; how the statistical mechanical probability under- writes the Second Law; and how, at the same time, it leads to a violation of the Second Law by the so-called Maxwell’s Demon. (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)

It is claimed that the `problem of the arrow of time in classical dynamics' has been solved. Since all classical particles have a self-field (gravitational and in some cases also electromagnetic), their dynamics must include self-interaction. This fact and the observation that the domain of validity of classical physics is restricted to distances not less than of the order of a Compton wavelength (thus excluding point particles), leads to the conclusion that the fundamental classical equations of motion are not invariant (...) under time reversal: retarded self-interactions lead to different equations than advanced ones. Since causality (the time order of cause and effect) requires retarded rather than advanced self-interaction, it is causality which is ultimately responsible for the arrow of time. Classical motions described by equations with advanced self-interactions differ from retarded ones and do not occur in nature. (shrink)

It is commonly thought that the statistical mechanical reversibility objection implies that our putative records of the past are more likely to have arisen as spontaneous fluctuations from equilibrium states than through causal processes that correctly indicate past states of affairs. Hence, so the story goes, without some further assumption that solves the reversibility objection, such as the past hypothesis, all our beliefs about the past would almost surely be false. This claim is disputed and it is argued that at (...) least some of our records of the past can and should be thought to be veridical because the intentional contents of records are not included as part of their statistical mechanical description. The fact that the present state of the world around us coheres so well with the way we would expect it to be if our records were veridical provides good evidence for the claim that they are produced via a common causal structure. (shrink)

I follow Hájek (Synthese 137:273–323, 2003c) by taking objective probability to be a function of two propositional arguments—that is, I take conditional probability as primitive. Writing the objective probability of q given r as P(q, r), I argue that r may be chosen to provide less than a complete and exact description of the world’s history or of its state at any time. It follows that nontrivial objective probabilities are possible in deterministic worlds and about the past. A very simple (...) chance–credence relation is also then natural, namely that reasonable credence equals objective probability. In other words, we should set our actual credence in a proposition equal to the proposition’s objective probability conditional on available background information. One advantage of that approach is that the background information is not subject to an admissibility requirement, as it is in standard formulations of the Principal Principle. Another advantage is that the “undermining” usually thought to follow from Humean supervenience can be avoided. Taking objective probability to be a two-argument function is not merely a technical matter, but provides us with vital flexibility in addressing significant philosophical issues. (shrink)

In a recent critique of the doctrine of emergentism championed by its classic advocates up to C. D. Broad, Jaegwon Kim (Philosophical Studies 63:31–47, 1999) challenges their view about its applicability to the sciences and proposes a new account of how the opposing notion of reduction should be understood. Kim is critical of the classic conception advanced by Nagel and uses his new account in his criticism of emergentism. I question his claims about the successful reduction achieved in the sciences (...) and argue that his new account has not improved on Nagel’s and that the critique of emergentism he bases on it is question-begging in important respects. (shrink)

This pair of articles provides a critical commentary on contemporary approaches to statistical mechanical probabilities. These articles focus on the two ways of understanding these probabilities that have received the most attention in the recent literature: the epistemic indifference approach, and the Lewis-style regularity approach. These articles describe these approaches, highlight the main points of contention, and make some attempts to advance the discussion. The first of these articles provides a brief sketch of statistical mechanics, and discusses the indifference approach (...) to statistical mechanical probabilities. (shrink)

This pair of articles provides a critical commentary on contemporary approaches to statistical mechanical probabilities. These articles focus on the two ways of understanding these probabilities that have received the most attention in the recent literature: the epistemic indifference approach, and the Lewis-style regularity approach. These articles describe these approaches, highlight the main points of contention, and make some attempts to advance the discussion. The second of these articles discusses the regularity approach to statistical mechanical probabilities, and describes some areas (...) where further research is needed. (shrink)

Debates about the metaphysical compatibility between miracles and natural laws often appear to prejudge the issue by either adopting or rejecting a strong physicalist thesis (the idea that the physical is all that exists). The operative component of physicalism is a causal closure principle: that every caused event is a physically caused event. If physicalism and this strong causal closure principle are accepted, then supernatural interventions are rules out ’tout court’, while rejecting physicalism gives miracles metaphysical carte blanche. This paper (...) argues for a more moderate version of physicalism that respects important physicalist intuitions about causal closure while allowing for miracles’ logical possibility. A recent proposal for a specific mechanism for the production of miracles (Larmer 1996d) is criticized and rejected. In its place, two separate mechanisms (suitable for deterministic and indeterministic worlds, respectively) are proposed that do conform to a more moderate. (shrink)

The metaphysics of miracles put forward in my article, "Miracles: Metaphysics, Physics and Physicalism," above (125-147) are, argues Robert Larmer, both unnecessary and unworkable. Here, I try more clearly to explain that my goal of saving important physicalist intuitions that are incompatible with both the ’open-systems’ and ’exemption’ approaches’ use of powerful ’ceteris paribus’ clauses. I also defend the two mechanisms proposed in the paper from Larmer’s criticisms.

Schulman (Entropy 7(4):221–233, 2005) has argued that Boltzmann’s intuition, that the psychological arrow of time is necessarily aligned with the thermodynamic arrow, is correct. Schulman gives an explicit physical mechanism for this connection, based on the brain being representable as a computer, together with certain thermodynamic properties of computational processes. Hawking (Physical Origins of Time Asymmetry, Cambridge University Press, Cambridge, 1994) presents similar, if briefer, arguments. The purpose of this paper is to critically examine the support for the link between (...) thermodynamics and an arrow of time for computers. The principal arguments put forward by Schulman and Hawking will be shown to fail. It will be shown that any computational process that can take place in an entropy increasing universe, can equally take place in an entropy decreasing universe. This conclusion does not automatically imply a psychological arrow can run counter to the thermodynamic arrow. Some alternative possible explanations for the alignment of the two arrows will be briefly discussed. (shrink)

Ilya Prigogine was not a systematic author: his ideas, covering a wide arch of areas, are dispersed in his many writings. In particular, his philosophical thought has to be reconstructed mainly on the basis of his works in collaboration with Isabelle Stengers: La Nouvelle Alliance ( 1979 ), Order out of Chaos ( 1984 ), and Entre le Temps et l’Éternité ( 1988 ). In this paper I undertake that reconstruction in order to argue that Prigogine’s position, when read in (...) the light of Putnam’s internalist realism, can be characterized as an ontological pluralism. The main aim of this work is to show the striking parallelism between the philosophical views of Prigogine and Stengers and those of Hilary Putnam in Reason , Truth and History ( 1981 ). This task will lead me to critically review Prigogine’s general scientific program: the attempt to establish the foundations of objective irreversibility. (shrink)

Special sciences (such as biology, psychology, economics) describe various regularities holding at some high macroscopic level. One of the central questions concerning these macroscopic regularities is how they are related to the laws of physics governing the underlying microscopic physical reality. In this paper we show how a macroscopic regularity may emerge from an underlying micro- scopic structure, and how the appearance of multiple realizability of the special sciences by physics comes about in a reductionist-physicalist framework. On this basis we (...) explain how complexity at the high level can arise due to a sort of harmony between the microscopic dynamics and observer-dependent macroscopic properties. We show that observer-dependent properties, which underlie the emergence of macroscopic properties and of macroscopic complexity, are objective physical facts. We argue that such physical properties remove the mystery from the multiple realizability of special sciences’ kinds, since the latter are grounded in shared physical properties. Finally we explain how and in what sense in our reductive physicalist approach the special sciences are still autonomous after all. (shrink)

This paper explores how the Bayesian program benefits from allowing for objective chance as well as subjective degree of belief. It applies David Lewis’s Principal Principle and David Christensen’s principle of informed preference to defend Howard Raiffa’s appeal to preferences between reference lotteries and scaling lotteries to represent degrees of belief. It goes on to outline the role of objective lotteries in an application of rationality axioms equivalent to the existence of a utility assignment to represent preferences in Savage’s famous (...) omelet example of a rational choice problem. An example motivating causal decision theory illustrates the need for representing subjunctive dependencies to do justice to intuitive examples where epistemic and causal independence come apart. We argue to extend Lewis’s account of chance as a guide to epistemic probability to include De Finetti’s convergence results. We explore Diachronic Dutch book arguments as illustrating commitments for treating transitions as learning experiences. Finally, we explore implications for Martingale convergence results for motivating commitment to objective chances. (shrink)

In their book The Road to Maxwell's Demon Hemmo & Shenker re-describe the foundations of statistical mechanics from a purely empiricist perspective. The result is refreshing, as well as intriguing, and it goes against much of the literature on the demon. Their conclusion, however, that Maxwell's demon is consistent with statistical mechanics, still leaves open the question of why such a demon hasn't yet been observed on a macroscopic scale. This essay offers a sketch of what a possible answer could (...) look like. (shrink)

This paper proposes a classification of the intertheoretic relations in physics by bringing out the conditions for a relation of reduction which is eliminative, so that a theory reduced in terms of reductionism is superfluous in principle, and by distinguishing such a relation from another one based on comparison, which will be called neighbourhood of theories; the latter is a neighbouring relation between theories and is not able to support claims of eliminative reductionism. In the first part, it will be (...) argued that this differentiation between neighbourhood and eliminative reduction permits an adequate classification of the intertheoretic relations in physics. By means of this differentiation, the second part discusses reductionism and shows that there are indeed some historical examples of reduction in the aforementioned sense, but that modern physical theories are typically only neighbouring. (shrink)

This paper aims at a logico-mathematical analysis of the concept of chaos from the point of view of a constructivist philosophy of physics. The idea of an internal logic of chaos theory is meant as an alternative to a realist conception of chaos. A brief historical overview of the theory of dynamical systems is provided in order to situate the philosophical problem in the context of probability theory. A finitary probabilistic account of chaos amounts to the theory of measurement in (...) the line of a quantum-theoretical foundational perspective and the paper concludes on the non-classical internal logic of chaos theory. Finally, deterministic chaos points to a philosophy which asserts that chaotic systems are no less measurable than other physical systems where predictable and non–predictable phenomena intermingle in a constructive theory of measurement. (shrink)

One of the most tantalizing questions about the interpretation of Quantum Theory is the objective vs. subjective meaning of quantum states. Here, by focusing on a typical EPR experiment upon which a selection procedure is performed on one side, we will confront the fully epistemic view of quantum states with its results. Our statement is that such a view cannot be considered complete, although the opposite attitude would also pose well-known problems of interpretation.

According to a standard view of the second law of thermodynamics, our belief in the second law can be justified by pointing out that low-entropy macrostates are less probable than high-entropy macrostates, and then noting that a system in an improbable state will tend to evolve toward a more probable state. I would like to argue that this justification of the second law is unhelpful at best and wrong at worst, and will argue that certain puzzles sometimes associated with the (...) second law are merely artifacts of this questionable justification. *Received October 2006; revised October 2007. †To contact the author, please write to: Department of Philosophy, University of Chicago, 1115 E. 58th St., Chicago, IL 60637; e-mail: [email protected]. (shrink)

An important obstacle to lawhood in the special sciences is the worry that such laws would require metaphysically extravagant conspiracies among fundamental particles. How, short of conspiracy, is this possible? In this paper we'll review a number of strategies that allow for the projectibility of special science generalizations without positing outlandish conspiracies: non-Humean pluralism, classical MRL theories of laws, and Albert and Loewer's theory. After arguing that none of the above fully succeed, we consider the conspiracy problem through the lens (...) of our preferred view of laws, an elaboration of the MRL view that we call the Better Best System (BBS) theory. BBS offers a picture on which, although all events supervene on a fundamental level, there is no one unique locus of projectibility; rather there are a large number of loci corresponding to the different areas (ecology, economics, solid-state chemistry, etc.) in which there are simple and strong generalizations to be made. While we expect that some amount of conspiracy-fear-inducing special science projectibility is inevitable given BBS, we'll argue that this is unobjectionable. It follows from BBS that the laws of any particular special or fundamental science amount to a proper subset of the laws. From this vantage point, the existence of projectible special science generalizations not guaranteed by the fundamental laws is not an occasion for conspiracy fantasies, but a predictable fact of life in a complex world. (shrink)

Since the nineteenth century, the problem of the arrow of time has been traditionally analyzed in terms of entropy by relating the direction past-to-future to the gradient of the entropy function of the universe. In this paper, we reject this traditional perspective and argue for a global and non-entropic approach to the problem, according to which the arrow of time can be defined in terms of the geometrical properties of spacetime. In particular, we show how the global non-entropic arrow can (...) be transferred to the local level, where it takes the form of a non-spacelike local energy flow that provides the criterion for breaking the symmetry resulting from time-reversal invariant local laws. (shrink)

This article surveys several interrelated issues in the metaphysics of chance. First, what is the relationship between the probabilities associated with types of trials (for instance, the chance that a twenty‐eight‐year old develops diabetes before age thirty) and the probabilities associated with individual token trials (for instance, the chance that I develop diabetes before age thirty)? Second, which features of the the world fix the chances: are there objective chances at all, and if so, are there non‐chancy facts on which (...) they supervene? Third, can chance be reconciled with determinism, and if so, how? (shrink)

The foundations of probability are viewed through the lens of the subjectivist interpretation. This article surveys conditional probability, arguments for probabilism, probability dynamics, and the evidential and subjective interpretations of probability.

Under so-called primitive ontology approaches, in fully describing the history of a quantum system, one thereby attributes interesting properties to regions of spacetime. Primitive ontology approaches, which include some varieties of Bohmian mechanics and spontaneous collapse theories, are interesting in part because they hold out the hope that it should not be too difficult to make a connection between models of quantum mechanics and descriptions of histories of ordinary macroscopic bodies. But such approaches are dualistic, positing a quantum state as (...) well as ordinary material degrees of freedom. This paper lays out and compares some options that primitive ontologists have for making sense of the quantum state. (shrink)

This paper looks at emergence in physical theories and argues that an appropriate way to understand socalled “emergent protectorates” is via the explanatory apparatus of the renormalization group. It is argued that mathematical singularities play a crucial role in our understanding of at least some well-defined emergent features of the world.

The foundation of statistical mechanics and the explanation of the success of its methods rest on the fact that the theoretical values of physical quantities (phase averages) may be compared with the results of experimental measurements (infinite time averages). In the 1930s, this problem, called the ergodic problem, was dealt with by ergodic theory that tried to resolve the problem by making reference above all to considerations of a dynamic nature. In the present paper, this solution will be analyzed first, (...) highlighting the fact that its very general nature does not duly consider the specificities of the systems of statistical mechanics. Second, Khinchin’s approach will be presented, that starting with more specific assumptions about the nature of systems, achieves an asymptotic version of the result obtained with ergodic theory. Third, the statistical meaning of Khinchin’s approach will be analyzed and a comparison between this and the point of view of ergodic theory is proposed. It will be demonstrated that the difference consists principally of two different perspectives on the ergodic problem: that of ergodic theory puts the state of equilibrium at the center, while Khinchin’s attempts to generalize the result to non-equilibrium states. (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)