Philosophical writing on probability theory includes a great many articles discussing relationships between rational behavior and an agent’s susceptibility to betting contexts where an overall loss is mathematically inevitable. What the dutch book theorem establishes is that this kind of susceptibility is a consequence of having betting ratios that are in violation of the Kolmogorov probability axioms. In this article it is noted that a general result to rule out arbitrage can be shown to yield the dutch book theorem as (...) a special case. A formal framework is set forth to handle marketplace transactions involving contractual arrangements; and, within that framework, necessary and sufficient conditions are given for ruling out arbitrage. It is then shown that these conditions entail that pricing functions associated with particular kinds of betting contracts must turn out to be probability functions. (shrink)

Philosophical writing on probability theory includes a great many articles discussing relationships between rational behavior and an agent’s susceptibility to betting contexts where an overall loss is mathematically inevitable. What the dutch book theorem establishes is that this kind of susceptibility is a consequence of having betting ratios that are in violation of the Kolmogorov probability axioms. In this article it is noted that a general result to rule out arbitrage can be shown to yield the dutch book theorem as (...) a special case. A formal framework is set forth to handle marketplace transactions involving contractual arrangements; and, within that framework, necessary and sufficient conditions are given for ruling out arbitrage. It is then shown that these conditions entail that pricing functions associated with particular kinds of betting contracts must turn out to be probability functions. (shrink)

The focus of this article is upon just one particularly problematic condition among seven espoused by Honderich in A Theory of Determinism, where he sets forth a counterfactual theory of causality using certain kinds of nomic conditionals. Analysis of his fifth requirement shows it not only to be subject to a variety of counterexamples, but also to be in conflict with Honderich’s remarks about experimental testability in connection with claims expressed using nomic conditionals. Honderich has acknowledged that some fine tuning (...) is needed in order to reach a suitable formal rendition of his requirement, but the nature of the new troubles pointed out here indicates that serious flaws lie at the heart of his requirement. (shrink)

The focus of this article is upon just one particularly problematic condition among seven espoused by Honderich in A Theory of Determinism, where he sets forth a counterfactual theory of causality using certain kinds of nomic conditionals. Analysis of his fifth requirement shows it not only to be subject to a variety of counterexamples, but also to be in conflict with Honderich’s remarks about experimental testability in connection with claims expressed using nomic conditionals. Honderich has acknowledged that some fine tuning (...) is needed in order to reach a suitable formal rendition of his requirement, but the nature of the new troubles pointed out here indicates that serious flaws lie at the heart of his requirement. (shrink)

Beliefs about fair prices for betting arrangements can obviously vary depending upon how the contingencies are described, even though each of the different descriptions is correct. This sort of variation in beliefs on the part of an agent has been Iinked by Ramsey and Skyrms with the agent’s susceptibility to a dutch book situation involving some combination of bets on which there is a mathematically-guaranteed net loss as the overall outcome. Clarifying the nature of that Iinkage is the purpose of (...) this paper. After a framework for analysis has been developed, it is shown precisely how several important conditions for having correct beliefs are interrelated. (shrink)

Beliefs about fair prices for betting arrangements can obviously vary depending upon how the contingencies are described, even though each of the different descriptions is correct. This sort of variation in beliefs on the part of an agent has been Iinked by Ramsey and Skyrms with the agent’s susceptibility to a dutch book situation involving some combination of bets on which there is a mathematically-guaranteed net loss as the overall outcome. Clarifying the nature of that Iinkage is the purpose of (...) this paper. After a framework for analysis has been developed, it is shown precisely how several important conditions for having correct beliefs are interrelated. (shrink)

Idealization in mathematics, by its very nature, generates a gap between the theoretical and the practical. This article constitutes an examination of two individual, yet similarly created, cases of mathematical idealization. Each involves using a theoretical extension beyond the finite limits which exist in practice regarding human activities, experiences, and perceptions. Scrutiny of details, however, brings out substantial differences between the two cases, not only in regard to the roles played by the idealized entities, but also in regard to appropriate (...) criteria for justifying the use of such entities. The background information supplied and the examples chosen for analysis in this paper were selected from the areas of measurement theory, probability theory, mathematical logic, and philosophy of mathematics. (shrink)

Idealization in mathematics, by its very nature, generates a gap between the theoretical and the practical. This article constitutes an examination of two individual, yet similarly created, cases of mathematical idealization. Each involves using a theoretical extension beyond the finite limits which exist in practice regarding human activities, experiences, and perceptions. Scrutiny of details, however, brings out substantial differences between the two cases, not only in regard to the roles played by the idealized entities, but also in regard to appropriate (...) criteria for justifying the use of such entities. The background information supplied and the examples chosen for analysis in this paper were selected from the areas of measurement theory, probability theory, mathematical logic, and philosophy of mathematics. (shrink)

Aspects of kripke's recent work in philosophy are considered in connection with the formal approach he set forth over a decade ago regarding semantics for modal logic. An ambiguity is pointed out concerning kripke's intuitive test for rigid designators and it is argued that, Relative to an appropriate framework for considering actual and possible physical objects, Certain proper names fail to be rigid designators.