The Greenberger-Horne-Zeilinger state is the most famous example of a state with multiparticle entanglement. In this article we describe a group theoretic framework we have been developing for understanding the entanglement in general states of two or more quantum particles. As far as entanglement is concerned, two states of n spin-1/2 particles are equivalent if they are on the same orbit of the group of local rotations (U(2)n). We consider both pure and mixed states and calculate the number of independent (...) parameters needed to describe such states up to this equivalence. We describe how the entanglement of states in a given equivalence class may be characterized by the stability group of the action of the group of local rotations on any of the states in the class. We also show how to calculate invariants under the group of local actions for both pure and mixed states. In the case of mixed states we are able to explicitly exhibit sets of invariants which allow one to determine whether two generic mixed states are equivalent up to local unitary transformations. (shrink)

Frauchiger and Renner have recently claimed to prove that “Single-world interpretations of quantum theory cannot be self-consistent”. This is contradicted by a construction due to Bell, inspired by Bohmian mechanics, which shows that any quantum system can be modelled in such a way that there is only one “world” at any time, but the predictions of quantum theory are reproduced. This Bell–Bohmian theory is applied to the experiment proposed by Frauchiger and Renner, and their argument is critically examined. It is (...) concluded that it is their version of “standard quantum theory”, incorporating state vector collapse upon measurement, that is not self-consistent. (shrink)

According to quantum mechanics, statements about the future made by sentient beings like us are, in general, neither true nor false; they must satisfy a many-valued logic. I propose that the truth value of such a statement should be identified with the probability that the event it describes will occur. After reviewing the history of related ideas in logic, I argue that it gives an understanding of probability which is particularly satisfactory for use in quantum mechanics. I construct a lattice (...) of future-tense propositions, with truth values in the interval [0, 1], and derive logical properties of these truth values given by the usual quantum-mechanical formula for the probability of a history. (shrink)

It is argued that the conventional formulation of quantum mechanics is inadequate: the usual interpretation of the mathematical formalism in terms of the results of measurements cannot be applied to situations in which discontinuous transitions (''quantum jumps'') are observed as they happen, since nothing that can be called a measurement happens at the moment of observation. Attempts to force such observations into the standard mould lead to absurd results: ''a watched pot never boils''. Experiments show both that this result is (...) correct when the experiment does indeed consist of a series of measurements, and that it is not when the experiment consists of a period of observation: quantum jumps do happen. The possibilities for improving the formulation by incorporating transitions in the basic postulates are reviewed, and a satisfactory postulate is obtained by modifying a suggestion of Bell's. This requires a distinction between the external description of the whole of a physical system and internal descriptions which are themselves physical events in the system. It is shown that this gives correct results for simple unstable systems and for the quantum-jump experiments. (shrink)

The quantum-mechanical description of the world, including human observers, makes substantial use of entanglement. In order to understand this, we need to adopt concepts of truth, probability and time which are unfamiliar in modern scientific thought. There are two kinds of statements about the world: those made from inside the world, and those from outside. The conflict between contradictory statements which both appear to be true can be resolved by recognising that they are made in different perspectives. Probability, in an (...) objective sense, belongs in the internal perspective, and to statements in the future tense. Such statements obey a many-valued logic, in which the truth values are identified as probabilities. (shrink)

I discuss the meaning of probability in the Everett-Wheeler interpretation of quantum mechanics, together with the problem of defining histories. To resolve these, I propose an understanding of probability arising from a form of temporal logic: the probability of a future-tense proposition is identified with its truth value in a many-valued and context-dependent logic. In short, probability is degree of truth. These ideas appear to be new, but they are natural and intuitive, and relate to traditional naive ideas of time (...) and chance. Indeed, I argue that Everettian quantum mechanics is the only form of scientific theory that truly incorporates the perception that the future is open. (shrink)

We examine the possible states of subsystems of a system of bits or qubits. In the classical case (bits), this means the possible marginal distributions of a probability distribution on a finite number of binary variables; we give necessary and sufficient conditions for a set of probability distributions on all proper subsets of the variables to be the marginals of a single distribution on the full set. In the quantum case (qubits), we consider mixed states of subsets of a set (...) of qubits; in the case of three qubits we find quantum Bell inequalities—necessary conditions for a set of two-qubit states to be the reduced states of a mixed state of three qubits. We conjecture that these conditions are also sufficient. (shrink)

There are two broad opposing classes of attitudes to reality with corresponding attitudes to knowledge. I argue that these attitudes can be compatible, and that quantum theory requires us to adopt both of them.

Les Prolegomenes a la Philosophie de Platon sont un manuel d'ecole neoplatonicien. Il s'inspire d'un modele dont Proclus a du etre l'auteur, mais l'origine de ce texte est presque surement alexandrine et doit dater de la premiere moitie du Vle siecle. Cette oeuvre est essentielle pour comprendre comment etait diffuse l'enseignement platonicien, et pour mieux saisir le mouvement des idees de l'Antiquite finissante. Dans une importante introduction, L. O. Westerink a retrace l'histoire de l'ecole d'Alexandrie et celle du genre litteraire (...) de ces introductions a Platon et a Aristote. (shrink)

Purpose. To examine the existential anthropology of G. Marcel and E. Minkowski, in order to demonstrate the necessity of distinguishing the universal-spiritual, as human in human being, apart from the individual-existential in him, and to reveal the hierarchical correlation of biosocial, existential and spiritual spheres in personality. Theoretical basis. Within existential philosophy the author differentiates two separate traditions and proceeds from the insufficiency of the distinction of existential sphere, proposed by phenomenological tradition, showing the necessity of its correlation with the (...) spiritual sphere as a sphere of humanity, proposed by non-phenomenological tradition of G. Marcel and E. Minkowski. Originality. The author presents the anthropological conception of G. Marcel and E. Minkowski, in which human personality is understood as unity of individual-existential and universal-spiritual, which requires a special trans-empirical field of culture, which contains senses, images and symbols of humanity. Also, the author presents the recent developments of existential thinkers in distinguishing existential and spiritual dimensions, both not reducible to the physical and social dimensions. Conclusions. In both existential traditions, the specifically human was founded as a trans-biological and trans-social phenomenon, which appears as indefinable and non-predetermined. But in first tradition, humanity is understood as an existence, as a unique individuality, "project", variant of humanity, equivalent to other variants, and universal is understood as a community of human condition in the world. While in the second tradition, the universal is understood as spiritual. Thus, horizontal level of our private existence, as the process of movement from birth to death, is supplemented by vertical of human, universal ideals and images. Humanity appears as a task, on the way to which human being transcends beyond the limits of his individual "self" to the "super-individual", through inclusion into spiritual community, into universal culture. (shrink)

Modern scholars have been concerned with the hostility shown to Alexander by the Hellenistic schools of philosophy. Two literary portraits have been distinguished, the Peripatetic and the Stoic, the former deriving from Theophrastus' book on Callisthenes, or starting with this work the Peripatetics worked out a theory of and applied it to Alexander, in order to belittle his achievements. It was a case of giving sophisticated expression to the kind of crude resentment expressed by Demades.

The locus classicus for Plutarch's own views on his methods is in the Alexander He has begun by asking for the indulgence of his readers if they do not find all the exploits of Alexander and Caesar recounted by the biographer or if they discover him not reporting some famous incident in detail (); and he goes on to compare his own search for evidence which will indicate the kind of soul, with the activity of the painter, who, in order (...) to create a likeness, concentrates on the eyes and pays little attention to the other parts. Commentators and critics have been right to take this as a key text for the purpose of understanding Plutarch's attitude towards his biographical work; nevertheless there are other passages in the Lives where we can at least glimpse his attitude to his subject, and we can only see the Alexander-remarks in correct perspective if we take these other passages into account. I propose therefore, starting with the Alexander, to see how far these critical remarks apply to Plutarch's theory and practice elsewhere in the Lives. (shrink)

According to the Ars Amatoria the notorious rape took place on the occasion of a primitive dramatic entertainment staged in a theatre, in which the seats and furnishings were also primitive. There is no time for a description of the arts of the performers—a tibicen and a ludius—before the Romans, impatient for action, receive their signal from Romulus. Nor is there any mention of a god in whose honour the entertainment had been provided.

Catalog of the collection of the Madamkhand Museum of Art, named after the wife of Batzhargalyn Batbai︠a︡r, businessman and member of the Mongolian Khural.

This paper explores the relationship between eugenics, disability, and dehumanization, with a focus on forms of eugenics beyond Nazi eugenics.

The impressive variation amongst biological individuals generates many complexities in addressing the simple-sounding question what is a biological individual? A distinction between evolutionary and physiological individuals is useful in thinking about biological individuals, as is attention to the kinds of groups, such as superorganisms and species, that have sometimes been thought of as biological individuals. More fully understanding the conceptual space that biological individuals occupy also involves considering a range of other concepts, such as life, reproduction, and agency. There has (...) been a focus in some recent discussions by both philosophers and biologists on how evolutionary individuals are created and regulated, as well as continuing work on the evolution of individuality. (shrink)