ProbabilityHighlights - Interpretations of Probability...

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Interpretations of Probability First published Mon Oct 21, 2002; substantive revision Sat Jul 7, 2007 ‘Interpreting probability’ is a commonly used but misleading name for a worthy enterprise. The so-called ‘interpretations of probability’ would be better called ‘analyses of various concepts of probability’, and ‘interpreting probability’ is the task of providing such analyses. Or perhaps better still, if our goal is to transform inexact concepts of probability familiar to ordinary folk into exact ones suitable for philosophical and scientific theorizing, then the task may be one of ‘explication’ in the sense of Carnap (1950). Normally, we speak of interpreting a formal system, that is, attaching familiar meanings to the primitive terms in its axioms and theorems, usually with an eye to turning them into true statements about some subject of interest. However, there is no single formal system that is ‘probability’, but rather a host of such systems. To be sure, Kolmogorov's axiomatization , which we will present shortly, has achieved the status of orthodoxy, and it is typically what philosophers have in mind when they think of ‘probability theory’. Nevertheless, several of the leading ‘interpretations of probability’ fail to satisfy all of Kolmogorov's axioms, yet they have not lost their title for that. Moreover, various other quantities that have nothing to do with probability do satisfy Kolmogorov's axioms , and thus are interpretations of it in a strict sense: normalized mass, length, area, volume, and indeed anything that falls under the scope of measure theory, the abstract mathematical theory that generalizes such quantities. Nobody seriously considers these to be ‘interpretations of probability’, however, because they do not play the right role in our conceptual apparatus. Instead, we will be concerned here with various probability-like concepts that purportedly do. Be all that as it may, we will follow common usage and drop the cringing scare quotes in our survey of what philosophers have taken to be the chief interpretations of probability.
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Whatever we call it, the project of finding such interpretations is an important one. Probability is virtually ubiquitous. It plays a role in almost all the sciences. It underpins much of the social sciences — witness, for example, the prevalence of the use of statistical testing, confidence intervals, regression methods, and so on. It finds its way, moreover, into much of philosophy. In epistemology, the philosophy of mind, and cognitive science , we see states of opinion being modeled by subjective probability functions, and learning being modeled by the updating of such functions. Since probability theory is central to decision theory and game theory , it has ramifications for ethics and political philosophy. It figures prominently in such staples of metaphysics as causation and laws of nature. It appears again in the philosophy of science in the analysis of confirmation of theories,
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ProbabilityHighlights - Interpretations of Probability...

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