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)

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.

I have two main aims. The first is general, and more philosophical. The second is specific, and more closely related to physics. The first aim is to state my general views about laws and causation at different ”levels’. The main task is to understand how the higher levels sustain notions of law and causation that ”ride free’ of reductions to the lower level or levels. I endeavour to relate my views to those of other symposiasts. The second aim is to (...) give a framework for describing dynamics at different levels, emphasizing how the various levels’ dynamics can mesh or fail to mesh. This framework is essentially that of elementary dynamical systems theory. The main idea will be, for simplicity, to work with just two levels, dubbed ”micro’ and ”macro’, which are related by coarse-graining. I use this framework to describe, in part, the first four of Ellis’ five types of top-down causation. (shrink)

Political science is divided between methodological individualists, who seek to explain political phenomena by reference to individuals and their interactions, and holists (or nonreductionists), who consider some higher-level social entities or properties such as states, institutions, or cultures ontologically or causally significant. We propose a reconciliation between these two perspectives, building on related work in philosophy. After laying out a taxonomy of different variants of each view, we observe that (i) although political phenomena result from underlying individual attitudes and behavior, (...) individual-level descriptions do not always capture all explanatorily salient properties, and (ii) nonreductionistic explanations are mandated when social regularities are robust to changes in their individual-level realization. We characterize the dividing line between phenomena requiring nonreductionistic explanation and phenomena permitting individualistic explanation and give examples from the study of ethnic conflicts, social-network theory, and international-relations theory. (shrink)

I argue that free will and determinism are compatible, even when we take free will to require the ability to do otherwise and even when we interpret that ability modally, as the possibility of doing otherwise, and not just conditionally or dispositionally. My argument draws on a distinction between physical and agential possibility. Although in a deterministic world only one future sequence of events is physically possible for each state of the world, the more coarsely defined state of an agent (...) and his or her environment can be consistent with more than one such sequence, and thus different actions can be “agentially possible”. The agential perspective is supported by our best theories of human behaviour, and so we should take it at face value when we refer to what an agent can and cannot do. On the picture I defend, free will is not a physical phenomenon, but a higher-level one on a par with other higher-level phenomena such as agency and intentionality. (shrink)

It is often argued that higher-level special-science properties cannot be causally efficacious since the lower-level physical properties on which they supervene are doing all the causal work. This claim is usually derived from an exclusion principle stating that if a higher-level property F supervenes on a physical property F* that is causally sufficient for a property G, then F cannot cause G. We employ an account of causation as difference-making to show that the truth or falsity of this principle is (...) a contingent matter and derive necessary and sufficient conditions under which a version of it holds. We argue that one important instance of the principle, far from undermining non-reductive physicalism, actually supports the causal autonomy of certain higher-level properties. (shrink)

Consider a circle and a pair of its semicircles. Which is prior, the whole or its parts? Are the semicircles dependent abstractions from their whole, or is the circle a derivative construction from its parts? Now in place of the circle consider the entire cosmos (the ultimate concrete whole), and in place of the pair of semicircles consider the myriad particles (the ultimate concrete parts). Which if either is ultimately prior, the one ultimate whole or its many ultimate parts?

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 central question of this paper is: are deterministic and indeterministic descriptions observationally equivalent in the sense that they give the same predictions? I tackle this question for measure-theoretic deterministic systems and stochastic processes, both of which are ubiquitous in science. I first show that for many measure-theoretic deterministic systems there is a stochastic process which is observationally equivalent to the deterministic system. Conversely, I show that for all stochastic processes there is a measure-theoretic deterministic system which is observationally equivalent (...) to the stochastic process. Still, one might guess that the measure-theoretic deterministic systems which are observationally equivalent to stochastic processes used in science do not include any deterministic systems used in science. I argue that this is not so because deterministic systems used in science even give rise to Bernoulli processes. Despite this, one might guess that measure-theoretic deterministic systems used in science cannot give the same predictions at every observation level as stochastic processes used in science. By proving results in ergodic theory, I show that also this guess is misguided: there are several deterministic systems used in science which give the same predictions at every observation level as Markov processes. All these results show that measure-theoretic deterministic systems and stochastic processes are observationally equivalent more often than one might perhaps expect. Furthermore, I criticise the claims of the previous philosophy papers Suppes (1993, 1999), Suppes and de Barros (1996) and Winnie (1998) on observational equivalence. (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)

The role of probability is one of the most contested issues in the interpretation of contemporary physics. In this paper, I’ll be reevaluating some widely held assumptions about where and how probabilities arise. Larry Sklar voices the conventional wisdom about probability in classical physics in a piece in the Stanford Online Encyclopedia of Philosophy, when he writes that “Statistical mechanics was the first foundational physical theory in which probabilistic concepts and probabilistic explanation played a fundamental role.” And the conventional wisdom (...) about quantum probabilities is that they are basic, not reducible to the types of probabilities we see in statistical mechanics. In the first section of this paper, I’ll argue that in fact classical physics was steeped in probability long before statistical mechanics came on the scene, specifically, that an objective measure over phase space is an indispensable component of any informative physical theory. In the next section, I’ll argue that this objective measure is the fundamental form of physical probability and that quantum probabilities can be defined in terms of it. In the last, I’ll raise some questions about the metaphysical status of the fundamental measure. (shrink)

I argue that there are non-trivial objective chances (that is, objective chances other than 0 and 1) even in deterministic worlds. The argument is straightforward. I observe that there are probabilistic special scientific laws even in deterministic worlds. These laws project non-trivial probabilities for the events that they concern. And these probabilities play the chance role and so should be regarded as chances as opposed, for example, to epistemic probabilities or credences. The supposition of non-trivial deterministic chances might seem to (...) land us in contradiction. The fundamental laws of deterministic worlds project trivial probabilities for the very same events that are assigned non-trivial probabilities by the special scientific laws. I argue that any appearance of tension is dissolved by recognition of the level-relativity of chances. There is therefore no obstacle to accepting non-trivial chance-role-playing deterministic probabilities as genuine chances. (shrink)

Causality offers the first comprehensive coverage of causal analysis in many sciences, including recent advances using graphical methods. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artificial intelligence, business, epidemiology, social science and economics.

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)

Evolutionary theory is awash with probabilities. For example, natural selection is said to occur when there is variation in fitness, and fitness is standardly decomposed into two components, viability and fertility, each of which is understood probabilistically. With respect to viability, a fertilized egg is said to have a certain chance of surviving to reproductive age; with respect to fertility, an adult is said to have an expected number of offspring.1 There is more to evolutionary theory than the theory of (...) natural selection, and here too one finds probabilistic concepts aplenty. When there is no selection, the theory of neutral evolution says that a gene’s chance of eventually reaching fixation is 1/(2N), where N is the number of organisms in the generation of the diploid population to which the gene belongs. The evolutionary consequences of mutation are likewise conceptualized in terms of the probability per unit time a gene has of changing from one state to another. The examples just mentioned are all “forwarddirected” probabilities; they describe the probability of later events, conditional on earlier events. However, evolutionary theory also uses “backwards probabilities” that describe the probability of a cause conditional on its effects; for example, coalescence theory allows one to calculate the expected number of generations in the past that the genes in the present generation find their most recent common ancestor. (shrink)

Perhaps the most significant contemporary theory of lawhood is the Best System (/MRL) view on which laws are true generalizations that best systematize knowledge. Our question in this paper will be how best to formulate a theory of this kind. We’ll argue that an acceptable MRL should (i) avoid inter-system comparisons of simplicity, strength, and balance, (ii) make lawhood epistemically accessible, and (iii) allow for laws in the special sciences. Attention to these problems will bring into focus a useful menu (...) of novel MRL theories, some of which solve problems the original MRL theory could not. Hence we conceive of the paper as moving toward a better Best System theory of laws. (shrink)

The issue of downward causation (and mental causation in particular), and the exclusion problem is discussed by taking into account some recent advances in the philosophy of science. The problem is viewed from the perspective of the new interventionist theory of causation developed by Woodward. It is argued that from this viewpoint, a higher-level (e.g., mental) state can sometimes truly be causally relevant, and moreover, that the underlying physical state which realizes it may fail to be such.

‘‘Thus I believe that there is no part of matter which is not—I do not say divisible—but actually divided; and consequently the least particle ought to be considered as a world full of an infinity of different creatures.’’ (Leibniz, letter to Foucher).

This paper discusses different interpretations of probability in relation to determinism. It is argued that both objective and subjective views on probability can be compatible with deterministic as well as indeterministic situations. The possibility of a conceptual independence between probability and determinism is argued to hold on a general level. The subsequent philosophical analysis of recent advances in classical statistical mechanics (ergodic theory) is of independent interest, but also adds weight to the claim that it is possible to justify an (...) objective interpretation of probabilities in a theory having as a basis the paradigmatically deterministic theory of classical mechanics. (shrink)

The goal of this paper is to sketch and defend a new interpretation or 'theory' of objective chance, one that lets us be sure such chances exist and shows how they can play the roles we traditionally grant them. The account is 'Humean' in claiming that objective chances supervene on the totality of actual events, but does not imply or presuppose a Humean approach to other metaphysical issues such as laws or causation. Like Lewis (1994) I take the Principal Principle (...) (PP) to be the key to understanding objective chance. After describing the main features of Humean objective chance (HOC), I deduce the validity of PP for Humean chances, and end by exploring the limitations of Humean chance. (shrink)

Some properties are causally relevant for a certain effect, others are not. In this paper we describe a problem for our understanding of this notion and then offer a solution in terms of the notion of a program explanation.

This paper discusses different interpretations of probability in relation to determinism. It is argued that both objective and subjective views on probability can be compatible with deterministic as well as indeterministic situations. The possibility of a conceptual independence between probability and determinism is argued to hold on a general level. The subsequent philosophical analysis of recent advances in classical statistical mechanics is of independent interest, but also adds weight to the claim that it is possible to justify an objective interpretation (...) of probabilities in a theory having as a basis the paradigmatically deterministic theory of classical mechanics. (shrink)

On the face of it ‘deterministic chance’ is an oxymoron: either an event is chancy or deterministic, but not both. Nevertheless, the world is rife with events that seem to be exactly that: chancy and deterministic at once. Simple gambling devices like coins and dice are cases in point. On the one hand they are governed by deterministic laws – the laws of classical mechanics – and hence given the initial condition of, say, a coin toss it is determined whether (...) it will land heads or tails.2 On the other hand, we commonly assign probabilities to the different outcomes a coin toss, and doing so has proven successful in guiding our actions. The same dilemma also emerges in less mundane contexts. Classical statistical mechanics (which is still an important part of modern physics) assigns probabilities to the occurrence of certain events – for instance to the spreading of a gas that is originally confined to the left half of a container – but at the same time assumes that the relevant systems are deterministic. How can this apparent conflict be resolved? (shrink)

A number of writers have been attracted to the idea that some of the peculiarities of quantum theory might be manifestations of 'backward' or 'retro' causality, underlying the quantum description. This idea has been explored in the literature in two main ways: firstly in a variety of explicit models of quantum systems, and secondly at a conceptual level. This note introduces a third approach, intended to complement the other two. It describes a simple toy model, which, under a natural interpretation, (...) shows how retrocausality can emerge from simple global constraints. The model is also useful in permitting a clear distinction between the kind of retrocausality likely to be of interest in QM, and a different kind of reverse causality, with which it is liable to be confused. The model is proposed in the hope that future elaborations might throw light on the potential of retrocausality to account for quantum phenomena. (shrink)

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

in Probability is the Very Guide of Life: The Philosophical Uses of Chance, eds. Henry Kyburg, Jr. and Mariam Thalos, Open Court. Abridged version in Proceedings of the International Society for Bayesian Analysis 2002.

This definitive survey of the hottest issues in inductive logic sets the stage for further classroom discussion.

Classical statistical mechanics posits probabilities for various events to occur, and these probabilities seem to be objective chances. This does not seem to sit well with the fact that the theory’s time evolution is deterministic. We argue that the tension between the two is only apparent. We present a theory of Humean objective chance and show that chances thus understood are compatible with underlying determinism and provide an interpretation of the probabilities we find in Boltzmannian statistical mechanics.

This paper offers a metaphysics of physical probability in (or if you prefer, truth conditions for probabilistic claims about) deterministic systems based on an approach to the explanation of probabilistic patterns in deterministic systems called the method of arbitrary functions. Much of the appeal of the method is its promise to provide an account of physical probability on which probability assignments have the ability to support counterfactuals about frequencies. It is argued that the eponymous arbitrary functions are of little philosophical (...) use, but that they can be substituted for facts about frequencies without losing the ability to provide counterfactual support. The result is an account of probability in deterministic systems that has a “propensity-like” look and feel, yet which requires no supplement to the standard modern empiricist tool kit of particular matters of fact and principles of physical dynamics. (shrink)

The basic theme of Popper's philosophy--that something can come from nothing--is related to the present situation in physical theory. Popper carries his investigation right to the center of current debate in quantum physics. He proposes an interpretation of physics--and indeed an entire cosmology--which is realist, conjectural, deductivist and objectivist, anti-positivist, and anti-instrumentalist. He stresses understanding, reminding us that our ignorance grows faster than our conjectural knowledge.

In Part I, the author argued for nonreductive individualism (NRI), an account of the individual-collective relation that is ontologically individualist yet rejects methodological individualism. However, because NRI is ontologically individualist, social entities and properties would seem to be only analytic constructs, and if so, they would seem to be epiphenomenal, since only real things can have causal power. In general, a nonreductionist account is a relatively weak defense of sociological explanation if it cannot provide an account of how social properties (...) can participate in causal relations. In this article, the author extends NRI to address this weakness and provides an account of social causation that he refers to as supervenient causation. Key Words: individualism • collectivism • social realism • social causation. (shrink)