The geometry of the state space of a finite-dimensional quantum mechanical system, with particular reference to four dimensions, is studied. Many novel features, not evident in the two-dimensional space of a single spin, are found. Although the state space is a convex set, it is not a ball, and its boundary contains mixed states in addition to the pure states, which form a low-dimensional submanifold. The appropriate language to describe the role of the observer is that of flag manifolds.

On the one hand, non-reflexive logics are logics in which the principle of identity does not hold in general. On the other hand, quantum mechanics has difficulties regarding the interpretation of ‘particles’ and their identity, also known in the literature as ‘the problem of indistinguishable particles’. In this article, we will argue that non-reflexive logics can be a useful tool to account for such quantum indistinguishability. In particular, we will provide a particular non-reflexive logic that can help us to analyze (...) and discuss this problem. From a more general physical perspective, we will also analyze the limits imposed by the orthodox quantum formalism to consider the existence of indistinguishable particles in the first place, and argue that non-reflexive logics can also help us to think beyond the limits of classical identity. (shrink)

Provability, Computability and Reflection.

In this paper we study the systemsP andP * (see Arruda and da Costa,O paradoxo de Curry-Moh Shaw-Kwei, Boletim da Sociedade Matemtica de São Paulo 18 (1966)) and some related systems. In the last section, we prove that certain set theories havingP andP * as their underlying logics are non-trivial.

'Uncertainty and chance' is a subject with a broad span, in that there is no academic discipline or walk of life that is not beset by uncertainty and chance. In this book a range of approaches is represented by authors from varied disciplines: natural sciences, mathematics, social sciences and medical sciences. At one extreme, this volume is concerned with the foundations of probability. At the other extreme, we have scholars who acknowledge the concept of chance and uncertainty but do not (...) cope with it by means of systematic measurement or quantative analysis. (shrink)

Civilizational analysis has not concerned itself too greatly with the historical experiences of the American New World. There are good reasons to correct this position and Shmuel Eisenstadt’s principal work on America’s distinct modernities goes some way to establishing the colonization of the Atlantic world as an opening phase of modernity. Nonetheless, a more far-reaching analysis of the distinctiveness of diverse American societies can be developed that goes beyond the image of a Protestant North America contrasted with southern Latin cultures. (...) This article outlines the basis for a more nuanced approach in three steps: a focus on intercivilizational engagement, examination of civilizational factors neglected by Eisenstadt and reconsideration of the conceptual range of the notion of ‘civilization’ itself. The archetype of two Americas is replaced by a model of four with some consideration given to indigenous civilizations as a fifth America. (shrink)

This six volume backlist collection brings together an assortment of seminal works by highly influential British philosopher A. C. Ewing. This comprehensive and diverse collection encompasses a fantastic selection of his work in the field of moral philosophy and the history of philosophy; ranging from the definition of good, through to his views on punishment and a study on the work of Emmanuel Kant. Spanning more than 30 years in Professor Ewing’s distinguished career, the reissued volumes in this collection, originally (...) published between 1924 and 1959, offer a thorough and engaging insight into Professor Ewing’s work. (shrink)

In this work, the first of a series, we study the nature of informal inconsistency in physics, focusing mainly on the foundations of quantum theory, and appealing to the concept of quasi-truth. We defend a pluralistic view of the philosophy of science, grounded on the existence of inconsistencies and on quasi-truth. Here, we treat only the ‘classical aspects’ of the subject, leaving for a forthcoming paper the ‘non-classical’ part.

Most philosophers of science now believe that scientific data are theory laden, i.e., the evaluation of data is influenced by prior theoretical beliefs. Although there is historical and psychological evidence that is consistent with the theory-laden position, experimental evidence is needed to directly test whether prior beliefs influence the evaluation of scientific data. In a fully counterbalanced design, one group of subjects received evidence that dinosaurs were cold-blooded, and another group of subjects received evidence that dinosaurs were warm-blooded. The subjects (...) reported a strong belief in whichever theory they had read about. Then subjects were presented with a piece of data that supported one theory and contradicted the other theory. The identical piece of data was rated as more believable when it was consistent with the subject's theory than when it was inconsistent. These results provide clear support for the position that scientific data are theory laden. (shrink)

C. A. J. Coady; VIII*—Descartes' Other Myth, Proceedings of the Aristotelian Society, Volume 83, Issue 1, 1 June 1983, Pages 121–142, https://doi.org/10.1093/ar.

One of the theses defended by Aristotle in Nicomachean Ethics books VII and X is that pleasure is good or is one of the good things : and Aristotle thinks that it follows from this that the best thing is a pleasure, or is pleasure in a certain way. Among his arguments for the latter we find the following:The fact that all things, both brutes and men, pursue pleasure is an indication that the best thing is in a certain way (...) that. (shrink)