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This paper justifies the inference of probabilities from symmetries. I supply some examples of important and correct inferences of this variety. Two explanations of such inferences -- an explanation based on the Principle of Indifference and a proposal due to Poincaré and Reichenbach -- are considered and rejected. I conclude with my own account, in which the inferences in question are shown to be warranted a posteriori, provided that they are based on symmetries in the mechanisms of chance setups.

This book aims to explain, by appealing to the mathematical method of arbitrary functions (MAF) initiated by Hopf and Poincaré, how the many and various interactions of the parts of a complex system often result in simple probabilistic patterns of behaviour. A complex system is vaguely defined as a system of many parts (called enions) which are somewhat autonomous but strongly interacting (italicized words are Strevens’ jargon). Strevens says that a system shows simple behaviour when it can be described mathematically (...) with a small number of variables. A philosophical treatment of complex systems, the MAF, and the emergence of simple probabilistic patterns is welcome because these important topics have been rather neglected. (shrink)

To understand the behavior of a complex system, you must understand the interactions among its parts. Doing so is difficult for non-decomposable systems, in which the interactions strongly influence the short-term behavior of the parts. Science's principal tool for dealing with non-decomposable systems is a variety of probabilistic analysis that I call EPA. I show that EPA's power derives from an assumption that appears to be false of non-decomposable complex systems, in virtue of their very non-decomposability. Yet EPA is extremely (...) successful. I aim to find an interpretation of EPA's assumption that is consistent with, indeed that explains, its success. (shrink)

In this book, Michael Strevens aims to explain how simplicity can coexist with, indeed be caused by, the tangled interconnections between a complex system's ...

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)

I object to eliminativism about innateness and André Ariew’s identification of innateness with canalization, and I propose a new treatment of innateness. I first argue that the concept of innateness is serving a valuable function in a diverse set of research contexts, and in these contexts, claims about innateness are best understood as claims about the insensitivity of the appearance of a trait to certain variations in the environment. I then argue that innateness claims, like claims about canalization, should be (...) explicitly relativized to the specific range of environmental variations of interest to the scientist. My account characterizes an important way in which scientists are employing the concept and offers a way for scientists to carry on using the concept in their research while minimizing confusion and miscommunication. There is a fruitful research program, I claim, in which scientists employ the concept of innateness to help distinguish environmental factors of interest that have a causal influence on the appearance of a trait from those that do not. (shrink)

In the epigraph, Fisher is blaming two generations of theoretical biologists, from Darwin on, for ignoring Quetelet's statistical techniques and hence harboring confusions about evolution and natural selection. He is right to imply that Darwin and his contemporaries were aware of the core of Quetelet's work. Quetelet's seminal monograph, Sur L'homme, was widely discussed in Darwin's academic circles. We know that Darwin owned a copy (Schweber 1977). More importantly, we have in Darwin's notebooks two entries referring to Quetelet's work on (...) the cause of a large-scale global phenomenon where each year more boys were born than girls. The first entry is written sometime between April and July 1838. Darwin writes "Find out from the Statistical Society—where M. Quetelet has published his laws about sexes relative to age of Marriages" (C 268, Barrett et al., 1987, p. 324). The second is written sometime after October 16, 1838: "In the Atheneum Numbers 406, 407, 409, Quetelet papers are given, & I think facts there mentioned about proportion of sexes, at birth & causes" (Ibid, p. 379). So, even if Darwin did not read Sur L'homme directly it is likely (though not certain) that he read its review in the Atheneum. There is no doubt that Darwin eventually became familiar with Quetelet's work in statistics. The smoking gun is an essay that Darwin writes in 1874, entitled, "On the Males and Complemental Males of Certain Cirripedes, and on Rudimentary Structures" where he discusses Quetelet's laws of variation. (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)

Approaches to explanation -- Causal and explanatory relevance -- The kairetic account of /D making -- The kairetic account of explanation -- Extending the kairetic account -- Event explanation and causal claims -- Regularity explanation -- Abstraction in regularity explanation -- Approaches to probabilistic explanation -- Kairetic explanation of frequencies -- Kairetic explanation of single outcomes -- Looking outward -- Looking inward.

Contributors: Rodney A. Brooks, Paul M. Churchland, Andy Clark, Daniel C. Dennett, Hubert L. Dreyfus, Jerry A. Fodor, Joseph Garon, John Haugeland, Marvin...

The idea that some characteristics of an organism are explained by the organism's intrinsic nature, whilst others reflect the influence of the environment is an ancient one. It has even been argued that this distinction is itself part of the evolved psychology of the human species. The distinction played an important role in the history of philosophy as the locus of the dispute between Rationalism and Empiricism discussed in another entry in this encyclopedia. This entry, however, focuses on twentieth-century accounts (...) of the innate/acquired distinction. These accounts have for the most part been inspired by the sciences of mind and behaviour. (shrink)

This chapter explores a philosophical hypothesis about the nature of (some) probabilities encountered in social sciences. It should be of interest to those with philosophical concerns about the foundations of probability, and to social scientists and philosophers of science who are somewhat puzzled by the nature of probability in social domains. As will become clear below, the chapter is not intended as a contribution to an empirical methodology such as a particular way of applying statistics.

In this paper, a concept of chance is introduced that is compatible with deterministic physical laws, yet does justice to our use of chance-talk in connection with typical games of chance. We take our cue from what Poincaré called "the method of arbitrary functions," and elaborate upon a suggestion made by Savage in connection with this. Comparison is made between this notion of chance, and David Lewis' conception.

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)