AuthorBURNOR, RICHARD NEAL.
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PublisherThe University of Arizona.
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AbstractIn "A Critique of Two Objective Probability Theories," I examine two extensionalist approaches to the analysis of objective probability, arguing ultimately that neither can succeed as analyses of objective probability. Beginning with extensional frequency analyses, I first examine the limiting frequency interpretation of Reichenbach and Salmon, arguing that it is unacceptable as it (1) fails to handle the single case--providing no basis for assigning a value other than 0 or 1; and (2) fails to provide a unique value for the probability as a limit of an infinite sequence--the problem of randomness. I further argue that references to "natural sequences" as a means of avoiding these problems must fail due to an interesting difficulty derived from special relativity. Turning next to Kyburg's finite frequency interpretation, I claim that while it incorporates certain gains within the extensional approach, it still succumbs to variations of the same problems inherent in the Reichenbach/Salmon interpretation. Kyburg's proposal, furthermore, is too narrow, not sufficiently encompassing the concept of objective probability desired. I conclude with an argument to the effect that no extensional frequency interpretation is able to provide an acceptable analysis of scientific conceptions of chance. I next consider a "propensity" interpretation provided by Mellor, which purports to provide an extensionalist analysis of objective chance on the basis of partial beliefs--i.e., a personalist framework. I argue that this approach fails because the dispositional (propensity) basis is an ad hoc addendum to what turns out to be merely a personalist theory. I then consider various alterations of Mellor's approach, with the conclusion that no such personalist-based approach is viable as an analysis of objective probability. I also examine Mellor's notion of dispositions, arguing that it is too deterministic, and that it must be replaced by a statistical notion better adapted to probability. Finally, these several considerations are taken both as a motivation for intensional frequency and propensity approaches, and as identifying certain pitfalls that any approach must guard against. In view of these findings, a rough outline of what would constitute an acceptable intensional frequency or propensity interpretation is indicated.