The phenomenon of probability backflow, previously quantified for a free nonrelativistic particle, is considered for a free particle obeying Dirac's equation. It is shown that probability backflow can occur in the opposite direction to the momentum; that is to say, there exist positive-energy states in which the particle certainly has a positive momentum in a given direction, but for which the component of the probability flux vector in that direction is negative. It is shown that the maximum possible amount of (...) probability that can flow “backwards,” over a given time interval of duration T, depends on the dimensionless parameter ε = (4ℏ/mc2T)1/2, where m is the mass of the particle and c is the speed of light. At ε = 0, the nonrelativistic value of approximately 0.039 for this maximum is recovered. Numerical studies suggest that the maximum decreases monotonically as ε increases from 0, and show that it depends on the size of m, ℏ, and T, unlike the nonrelativistic case. (shrink)

Charles Sanders Peirce wrote the article “The probability of induction” in 1878. It was the fourth article of the series “Illustrations of the Logic of Science” which comprised a total of six articles. According to Peirce, to get a clear idea of the conception of probability, one has ‘to consider what real and sensible difference there is between one degree of probability and another.’ He endorsed what John Venn had called the ‘materialistic view’ of the subject, namely that probability is (...) the proportion of times in which an occurrence of one kind is accompanied by an occurrence of another kind. On the other hand, Peirce recognized the existence of a different interpretation of probability, which was termed by Venn the ‘conceptualistic view’, namely the degree of belief that ought to be attached to a proposition. Peirce’s intent on writing this article seems to be to inquire about the claims of the conceptualists concerning the problem of induction. After reasoning on some examples, he concluded on the impossibility of assigning probability for induction. We show here that the arguments advanced in his article are not sufficient to support such conclusion. Peirce’s thoughts on the probability of induction surely may have influenced statisticians and research scientists of the 20th century in shaping data analysis. (shrink)

The function of philosophy may be circumscribed as consisting in ma king a keen analysis of the peculiar nature of the crisis-situation, as it has existed among mell throughout th~ centuries of human history, and as it manifested itself in definite ways at the various stages of this his tory. That is to say, philosophy may be regarded as the discipline which, again and again, will have to determine the authenticity of man's ex istence in the light of the changing (...) conditions of life, i. e., man's chang ing needs and interests. Fundamentally, these needs may be regarded as being of a material, an intellectual, an aesthetical and a spiritual kind. On the grounds of the crisis, which inevitably exists among men on ac count of the controversial nature of their various truth-perspectives, as they are postulated on a personal level, in the sciences, in history, in the fine arts and in theology, man creates and re-creates the goods of civilization and the cultural values. The task of philosophy consists then in making an ever new assessment of man's changing needs, in terests and aspirations on the basis of the specific conflicts and prob lems with which man wrestles at a certain historical stage. It is in this way that the important philosophical systems were constructed, which we still admire to-day. (shrink)

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Mitchell et al.'s claim, that their propositional theory is a single-process theory, is illusory because they relegate some learning to a secondary memory process. This renders the single-process theory untestable. The propositional account is not a process theory of learning, but rather, a heuristic that has led to interesting research.

On Roger Bacon's life and works, by A. G. Little. -- Der Einfluss des Robert Grosseteste auf die wissenschaftliche Richtung des Roger Bacon, von L. Baur. -- La place de Roger Bacon parmi les philosophes du xiie siècle, par F. Picavet. -- Roger Bacon and the Latin vulgate, by F. A. Gasquet. -- Roger Bacon and philology, by S. A. Hirsch. -- The place of Roger Bacon in the history of mathematics, by D. E. Smith. -- Roger Bacon und seine (...) Verdienste um die Optik, von E. Wiedemann. -- Roger Bacon's Lehre von der sinnlichen Spezies und vom Sehvorgange, von S. Vogl. -- Roger Bacon's art des wissenschaftlichen Arbeitens dargestellt nach seineer Schrift De speculis, von Würschmidt. -- Roger Bacon et l'horreur du vide, par P. Duhem. -- Roger Bacon : his relations to alchemy and chemistry, by M. M. P. Muir. -- Roger Bacon and gunpowder, by H. W. L. Hime. -- Roger Bacon and medicine, by E. W, Withington. -- Roger Bacon in English literature, by Sir J. E. Sandys. -- Roger Bacon's works with references to the mss. printed editions, by A, G. Little (p. [375]-425). (shrink)