The role of the environment in producing the correct classical limit in the Bohm interpretation of quantum mechanics is investigated, in the context of a model of quantum Brownian motion. One of the effects of the interaction is to produce a rapid approximate diagonalisation of the reduced density matrix in the position representation. This effect is, by itself, insufficient to produce generically quasi-classical behaviour of the Bohmian trajectory. However, it is shown that, if the system particle is initially in an (...) approximate energy eigenstate, then there is a tendency for the Bohmian trajectory to become approximately classical on a longer time-scale. The relationship between this phenomenon and the behaviour of the Wigner function post-decoherence is discussed. (shrink)

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian (...) conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality. (shrink)

Meyer, Kent and Clifton (MKC) claim to have nullified the Bell-Kochen-Specker (Bell-KS) theorem. It is true that they invalidate KS's account of the theorem's physical implications. However, they do not invalidate Bell's point, that quantum mechanics is inconsistent with the classical assumption, that a measurement tells us about a property previously possessed by the system. This failure of classical ideas about measurement is, perhaps, the single most important implication of quantum mechanics. In a conventional colouring there are some remaining patches (...) of white. MKC fill in these patches, but only at the price of introducing patches where the colouring becomes ``pathologically'' discontinuous. The discontinuities mean that the colours in these patches are empirically unknowable. We prove a general theorem which shows that their extent is at least as great as the patches of white in a conventional approach. The theorem applies, not only to the MKC colourings, but also to any other such attempt to circumvent the Bell-KS theorem (Pitowsky's colourings, for example). We go on to discuss the implications. MKC do not nullify the Bell-KS theorem. They do, however, show that we did not, hitherto, properly understand the theorem. For that reason their results (and Pitowsky's earlier results) are of major importance. (shrink)

Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought of as a restricted subset of all potentially available probabilities. A recent publication (Fuchs and Schack, arXiv:0906.2187v1, 2009) advocates such a representation using symmetric informationally complete (SIC) measurements. Building upon this work we study how this subset—quantum-state space—might be characterized. Our leading characteristic is that the inner (...) products of the probabilities are bounded, a simple condition with nontrivial consequences. To get quantum-state space something more detailed about the extreme points is needed. No definitive characterization is reached, but we see several new interesting features over those in Fuchs and Schack (arXiv:0906.2187v1, 2009), and all in conformity with quantum theory. (shrink)

The generic Bohmian trajectories are calculated for an isolated particle in an approximate energy eigenstate, for an arbitrary one-dimensional potential well. It is shown that the necessary and sufficient condition for there to be a negligible probability of the trajectory deviating significantly from the classical trajectory at any stage in the motion is that the state be a narrowly localised wave packet. The properties of the Bohmian trajectories are compared with those in the interpretation recently proposed by García de Polavieja. (...) The reasons why the latter tend to be much more nearly classical are discussed. The implications for other trajectory interpretations are considered. (shrink)

The proliferation of personal data collection practices fundamentally reshapes how society is ordered and commercialized, and demands reconsideration of the possibilities for a just and equitable s...

In a recent article Paul Cartledge and Matt Edge argue that the modern republican tradition offers a useful framework for understanding the Athenian concept of freedom, and that within this framework the Athenians protected their freedoms without reference to a concept of rights. This paper agrees with both of these conclusions but identifies and corrects three assumptions behind Cartledge and Edge’s argument: that the only purpose of rights is to protect individual freedoms against the state; that rights have no place (...) at all in the republican tradition; and that the ancient Greeks did not understand rights. In fact the Athenians did have an understanding of rights but they did not use rights to protect freedoms. The reason for this is that the protected freedom is a very modern and particularly sophisticated application of the concept of rights. (shrink)

In an article contributed to Mind in 1934, the young A. J. Ayer declared war on metaphysics, claiming that his destruction of the metaphysicians' arguments rested on the establishment of the sheerly non-sensical character of their statements. Their errors were syntactical; the combination of symbols in the sentences with which they expressed their propositions violated fundamental principles of significance.

Spanning a wide range of texts, figures, and traditions from the ancient Mediterranean world, this volume gathers far-reaching, interdisciplinary papers on Greek philosophy from an international group of scholars. The book's sixteen chapters address an array of topics and themes, extending from the formation of philosophy from its first stirrings in archaic Greek as well as Egyptian, Persian, Mesopotamian, and Indian sources, through central concepts in ancient Greek philosophy and literatures of the classical period and into the Hellenistic age. Studies (...) in Ancient Greek Philosophy offers both in-depth, rigorous, attentive investigations of canonical texts in western philosophy, such as Plato's Phaedo, Gorgias, Republic, Phaedrus, Protagoras and the Metaphysics, De Caelo, Nichomachean Ethics, Generation and Corruption of Aristotle's corpus, as well as inquiries that reach back into the rich archives of the Mediterranean Basin and forward into the traditions of classical philosophy beyond the ancient world. Studies in Ancient Greek Philosophy is of interest to students and scholars working on different aspects of ancient Greek philosophy, as well as ancient philosophy more broadly. (shrink)

The authors ably demonstrate the value and relevance of sophisticated conceptual analysis in law. Such concepts as cause, reason, consequence, condition, opportunity, and explanation are carefully investigated. The use of the causal notions in the Anglo-American tradition of tort, contract, and criminal law, as well as in continental theories, is examined in detail. A book of importance which carries out English analysis in a subtle and exciting way. It is sure to be one of the lasting contributions of the recent (...) analytic movement.--A. P. D. M. (shrink)

More than half of the book is devoted to what is almost a catalogue exposition of Western moral philosophy from Kant to Nowell-Smith. Although the author claims in the preface to have included "suitable references to Indian points of view, including the Buddhist," what references there are are usually too general, and never fully explained to be of any use to Western readers. Exposition tends to be disjointed, and the English leaves much to be desired. On the whole there is (...) much eclecticism and little originality.--A. P. D. M. (shrink)

Topics in the standard introductory logic course are all covered, with emphasis on the understanding of concepts rather than the development of skills in symbolic manipulation. Exposition is informal and rich in illustrations from reasoning in ordinary life. Exercises are also drawn from ordinary discourse, but they often call for the application of symbolic techniques. In combining accuracy and sophistication with simplicity and liveliness of style, the book is indeed a pedagogic success. --A. P. D. M.

M. Piguet believes that philosophy is, in a strict sense, a compromise between science and art. In the course of establishing this thesis he makes some interesting suggestions on the question of ordinary language. For him this idiom is the "culture language"; it embodies the cultural experience of an age; it can be neither technical nor colloquial; it is the language of the honnête homme. It is also the basic "translation language" with which all other technical and artistic idioms must (...) be ultimately coordinated.--A. P. D. M. (shrink)