In "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.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/187944 |
| Date | January 1985 |
| Creators | BURNOR, RICHARD NEAL. |
| Contributors | Pollock, John, Byerly, Henry, Schiffer, Steve |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | text, Dissertation-Reproduction (electronic) |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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