Talking About Probabilities: A Logical Problem for Or/MS (original) (raw)
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Resurrecting logical probability
Erkenntnis, 2001
The logical interpretation of probability, or “objective Bayesianism” – the theory that (some) probabilities are strictly logical degrees of partial implication – is defended. The main argument against it is that it requires the assignment of prior probabilities, and that any attempt to determine them by symmetry via a “principle of insufficient reason” inevitably leads to paradox. Three replies are advanced: that priors are imprecise or of little weight, so that disagreement about them does not matter, within limits; that it is possible to distinguish reasonable from unreasonable priors on logical grounds; and that in real cases disagreement about priors can usually be explained by differences in the background information. It is argued also that proponents of alternative conceptions of probability, such as frequentists, Bayesians and Popperians, are unable to avoid committing themselves to the basic principles of logical probability.
The Concept of Probability. Historical Review And Future Prospects
During the Synod of Constance (Konstanz) (1414 -1418) the controversial topic of probabilism was publicly discussed probably for the first time in history. But only one hundred years later the Spanish Dominican Bartholomé de Medina (1527 -1581) led the way to probabilism as an acknowledged principle in the moral teaching of the Catholic Church. Soon afterwards probabilism was taken up by the Jesuits and subsequently further developed to a formal theory. In 1662 the book La Logique ou l'Art de Penser (in Latin Ars cogitandi) was published anonymously in Paris. In this influential book the concept of probability is used in the context of chance. Since then, numerous scientists have given various interpretations of the notion of probability, which invariably proved to be ineligible. In this paper the historical development of the notion probability is sketched and, finally, based on Jakob Bernoulli's ideas, a sustainable solution is presented.
Journal of Logic, Language and Information, 2012
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Arguments in the practical reasoning underlying constructed probability responses
Journal of Behavioral Decision Making, 1995
Reasoning is an important cognitive activity in probability assessment, and one that has been understudied. This proposition motivates the paper's three general aims. First, based on research in rhetoric, we present a theoretical means of analyzing the arguments constructed during the reasoning that occurs in probability assessment. Second, from verbal protocol data, we establish that subjects constructed arguments in forming beliefs and assessing the associated probabilities. Third, we analyze the data for the structure of subjects' arguments, including argument content and form. Subjects used a limited amount of relevant evidence and used a variety of argument forms that could be characterized by the nature of the knowledge that subjects brought to bear in forming the arguments. Subjects predominantly used causal reasoning, but also employed hierarchical category knowledge, resemblance relationships, and arguments from authority. These findings form a basis for expanding our accounts of probability assessment and for improving assessment practice.
Mathematical Structures in Computer Science, 2014
In this paper, we discuss the crucial but little-known fact that, as Kolmogorov himself claimed, the mathematical theory of probabilities cannot be applied to factual probabilistic situations. This is because it is nowhere specified how, for any given particular random phenomenon, we should construct, effectively and without circularity, the specific and stable distribution law that gives the individual numerical probabilities for the set of possible outcomes. Furthermore, we do not even know what significance we should attach to the simple assertion that such a distribution law “exists”. We call this problem Kolmogorov's aporia†.We provide a solution to this aporia in this paper. To do this, we first propose a general interpretation of the concept of probability on the basis of an example, and then develop it into a non-circular and effective general algorithm of semantic integration for the factual probability law involved in a specific factual probabilistic situation. The dev...
You Can't Always Get What You Want: Some considerations regarding conditional probability
Forthcoming in Erkenntnis, 2014
The standard treatment of conditional probability leaves conditional probability undefined when the conditioning proposition has zero probability. Nonetheless, some find the option of extending the scope of conditional probability to include zero-probability conditions attractive or even compelling. This articles reviews some of the pitfalls associated with this move, and concludes that, for the most part, probabilities conditional on zero-probability propositions are more trouble than they are worth. * But if you try, sometimes, you might find you get what you need.