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)

In this stimulating work of political philosophy, acclaimed philosopher G. A. Cohen sets out to rescue the egalitarian thesis that in a society in which distributive justice prevails, peopleâes material prospects are roughly equal. Arguing against the Rawlsian version of a just society, Cohen demonstrates that distributive justice does not tolerate deep inequality. In the course of providing a deep and sophisticated critique of Rawlsâes theory of justice, Cohen demonstrates that questions of distributive justice arise not only for the state (...) but also for people in their daily lives. The right rules for the macro scale of public institutions and policies also apply, with suitable adjustments, to the micro level of individual decision-making. Cohen also charges Rawlsâes constructivism with systematically conflating the concept of justice with other concepts. Within the Rawlsian architectonic, justice is not distinguished either from other values or from optimal rules of social regulation. The elimination of those conflations brings justice closer to equality. (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)

Some ways of defending inequality against the charge that it is unjust require premises that egalitarians find easy to dismiss—statements, for example, about the contrasting deserts and/or entitlements of unequally placed people. But a defense of inequality suggested by John Rawls and elaborated by Brian Barry has often proved irresistible even to people of egalitarian outlook. The persuasive power of this defense of inequality has helped to drive authentic egalitarianism, of an old-fashioned, uncompromising kind, out of contemporary political philosophy. The (...) present essay is part of an attempt to bring it back in. (shrink)

1. The present paper is a continuation of my “Self-Ownership, World Ownership, and Equality,” which began with a description of the political philosophy of Robert Nozick. I contended in that essay that the foundational claim of Nozick's philosophy is the thesis of self-ownership, which says that each person is the morally rightful owner of his own person and powers, and, consequently, that each is free to use those powers as he wishes, provided that he does not deploy them aggressively against (...) others. To be sure, he may not harm others, and he may, if necessary, be forced not to harm them, but he should never be forced to help them, as people are in fact forced to help others, according to Nozick, by redistributive taxation. (shrink)

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"A critical study of the interdependence of philosophy as critical theory and man as a free individual."--T.p.