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Additional resources for Philosophical Lectures on Probability: Collected, edited, and annotated by Alberto Mura

Example text

These rules of inference constitute the major part of the principles of formal logic. We then take any hypothesis that seems amusing, and deduce its consequences. If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. ” (emphasis added). It should be stressed that the formalistic account of pure mathematics that emerges from this passage is confined to represent Russell’s thought about mathematics at the moment in which it was written (1900–1901), influenced by Peano’s views that strongly impressed him at the Congress of Philosophy in Paris: “The most important year in my intellectual life was the year 1900, and the most important event in this year was my visit to the International Congress of Philosophy in Paris.

15. 16. 1 Introductory Lecture by the notion of refinement, introduced by Morris H. DeGroot and Stephen E. Fienberg (1982, 1983, 1986). F is said to be at least as refined as G if the distribution of probability values DG provided by G may be obtained from the distribution D F provided by F by means of a stochastic transformation so that D F stochastically dominates DG at the second degree (DeGroot and Eriksson, 1985). Roughly speaking, in this case D F is “sharper” than DG . DeGroot and Fienberg proved that for every strictly proper scoring rule, a more refined forecaster receives a better score.

Besides this example (its persuasiveness would appear to be stronger or weaker according to whether one is familiar or not with probability and the various perspectives on it) I am anxious to point out how distorted is the pretension to extend a definition or a procedure relative to a concrete field of application to wider domains, without paying due attention to see whether the resulting concrete conclusions turn out to be reasonable or absurd, whether they satisfy common sense or violate common sense in their applications to reality.

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