Acting under Uncertainty: Multidisciplinary Conceptions by George M. von Furstenberg

By George M. von Furstenberg

Uncertainty will be linked to knowledge, firm, and discovery. In usual speech, notwithstanding, it has ordinarily unfavourable connotations. there's "fear of the unknown" and "ignorance is bliss;" there are maxims to the impression that "what you do not know does not damage you" (or: "bother you") in different languages. This quantity means that we want be by way of the over the top self belief with which scientists, quite social scientists, current a few of their conclusions and overstate their diversity of program. another way a number of the questions that are meant to be raised approximately the entire significant uncertainties attending a selected factor usually might remain thwarted or suppressed. Down taking part in uncertainty doesn't result in extra dependable or surer motion, it sidetracks learn agendas, and leaves the choice makers uncovered to nasty shock. This quantity demonstrates that spotting the numerous different types of uncertainty that input into the advance of any specific subject material is a precondition for extra liable selection and deeper wisdom. Our goal is to give a contribution to a broader appreciation of uncertainty than on a regular basis accorded in any of the varied disciplines represented right here. The seventeenth-century French thinker Descartes, quoted during this quantity, wrote that "whoever is looking after fact needs to, as soon as in his existence, doubt all issues; insofar as this is often attainable. " White components left on maps of the realm in earlier centuries have been a way more efficient problem than marking the top of the identified international with the pillars of Hercules.

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12). It must mean something that the intellectual antecedents of Bernoulli's probability theory are generally taken to be such Jansenist authors as Pascal, Arnauld, and Nicole, the latter two generally assumed to have been the authors of the famous Port Royal Logic or Art of Thinking (1st edition, 1662), and yet Bernoulli came from a Protestant rather than a strict Catholic background (cf. Waldman, 1959, p. 300). Thanks to the work of Bernoulli and of such contemporary authors as Political, Moral, and Economic Decisions 23 Pierre Montmort and Abraham De Moivre, the "probable" came to be associated with a mathematical theory of chance, rather than with a theory of moral decision making, but when Bernoulli wrote The Art of Conjecturing probability was still a rhetorical rather than a mathematical concept.

An examination of the framework of ideas of Bernoulli's theory will make clear why this non-additive notion of probability was by no means as strange in its intellectual context as it may seem to some modern probability theorists (see also Cohen, 1980). I. HISTORICAL BACKGROUND TO BERNOULLI'S THEORY Our discussion will be adequate if it has as much clearness as the subject matter admits of, for precision is not to be sought for alike in all discussions, any more than in all the products of the crafts ....

324-25). But suppose, he says, there are various circumstances or indices tending to show a person's guilt, none of which by itself proves the guilt. Suppose, he says, that in each attending circumstance the person is twice as likely to be innocent as guilty. If there is one such circumstance, then the person has a two-thirds chance of being innocent, but if there are two, three, or more such pieces of evidence, then the probability of innocence will be 4/9,8/27, or in general (2/3)". Thus, each piece of evidence by itself leaves the person with a probability of innocence, but if there were ten compromising circumstances, the probability of innocence would be reduced to (2/3)10 or 1024/59049, meaning, he says, that the person's guilt is morally certain.

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