The quantum state of a d-dimensional system can be represented by a probability distribution over the d 2 outcomes of a Symmetric Informationally Complete Positive Operator Valued Measure (SIC-POVM), and then this probability distribution can be represented by a vector of $\mathbb {R}^{d^{2}-1}$ in a (d 2−1)-dimensional simplex, we will call this set of vectors $\mathcal{Q}$ . Other way of represent a d-dimensional system is by the corresponding Bloch vector also in $\mathbb {R}^{d^{2}-1}$ , we will call this set (...) of vectors $\mathcal{B}$ . In this paper it is proved that with the adequate scaling $\mathcal{B}=\mathcal{Q}$ . Also we indicate some features of the shape of $\mathcal{Q}$. (shrink)

The simple concept of a SIC poses a very deep problem in algebraic number theory, as soon as the dimension of Hilbert space exceeds three. A detailed description of the simplest possible example is given.

In the discussion at hand I have attempted to pave the way for such a treatment of the principle of contradiction. In a number of respects it seems to me worthwhile to relate my critical exposition to Aristotle's train of thought. Indeed, every critique must be raised against something substantial, otherwise it generally becomes the critic's leisurely game with his own cerebral phantasies. Now Aristotle's intuitions regarding the principle of contradiction are, for the most part and clear down to the (...) present day, the usual and traditional ones; and arguments for and against the principle can be found together in the Stagirite in greater completeness than in any one modern textbook of logic. My investigation will proceed with the Aristotelian text at hand and with regard to the results of symbolic logic. The most important results shall be sketched very briefly in the following. (shrink)

Is it a mistake to use "true" or "false" in certain contexts? White sets the stage for dealing with this issue by laying out a field of usages. He develops his position by characterizing and criticizing contemporary treatments of these data, moving rapidly from case to case. His numerous summaries and conclusions, obviously based on a wider view of the material than is presented in the text, may leave the uninitiated alternately puzzled, bristling, or suspicious. While White's data are expressed (...) clearly, the goal of his arguments and his organizational principles are frequently less apparent. White's discussions of fiction and modality are of particular historic interest. Here we find Frege and Russell arguing about whether they can argue about the King of France. We meet with Aristotle's ancient problem of the future naval battle, witness latter-day skirmishes over the nature of moral language, and find Leibniz, Hume, and Kant debating the logic of necessity and contingency. Are there really different types of truth which correspond with different modalities and existence presuppositions, as White seems to assume? This question, harking back to books 5 and 6 of Plato's Republic, is passed over by White in his usage-oriented quest for the sense of "truth." Truth will suit both student and researcher alike and is to be recommended for its breadth of concern and for its 18 pages of bibliography.--M. D. P. [[sic]]. (shrink)

Lucas plays off his understandings of the problem of freedom and Gödel's Theorem, concluding that, "... a human being cannot be represented by a logistic calculus and therefore cannot be described completely in terms of physical variables, all of whose values are completely determined by the conjunction of their values at some earlier time". Lucas approaches the problem of freedom from the perspective of a computer programmer. His argument is as follows. Men can construct a logistic calculus, L, of which (...) Gödel's theorem is a theorem. Gödel's theorem is known-by-men-to-be-true, which is a fact. Facts have ontological status. Any attempt to represent this fact by a definite description must result in an infinite regress of meta-L's, for a Gödel theorem can be constructed in any meta-L powerful enough to show that Gödel's theorem is a theorem of L. Accordingly, men can do something which cannot be represented within L; men are therefore undeterminable. Lucas's position amounts to a rethinking of Fichte's position, set in the metaphor of meta-mathematical logic. However, whereas Fichte concluded that a man can choose to posit that he is free, and thereby make himself free, Lucas concludes that all men are free since some men know that Gödel's theorem is true. One question suggested by Lucas's argument is ontological, and another is epistemological. First, what is the ontological status of facts? Secondly, what is the distinction between knowing-that-p and showing-that-p? Ultimately, Lucas's demonstration pivots on equating the-completeness-of-L with knowing-the-completeness-of-L. It remains to be shown that that which is capable of knowing-that-p is governed in the act of knowing-that-p by the conditions which determine p.--M. D. P. [[sic]]. (shrink)

Presenilin‐1 (PS1) is thought to regulate cell differentiation and survival by modulating the Notch signaling pathway. Mutations in PS1 have been shown to cause early‐onset inherited forms of Alzheimer's disease (AD) by a gain‐of‐function mechanism that alters proteolytic processing of the amyloid precursor protein (APP) resulting in increased production of neurotoxic forms of amyloid β‐peptide. The present article considers a second pathogenic mode of action of PS1 mutations, a defect in cellular calcium signaling characterized by overfilling of endoplasmic reticulum (ER) (...) calcium stores and altered capacitive calcium entry; this abnormality may impair synaptic plasticity and sensitize neurons to apoptosis and excitotoxicity. The calcium signaling defect has also been documented in lymphocytes, suggesting a contribution of immune dysfunction to the pathogenesis of AD. A better understanding of the calcium signaling defect resulting from PS1 mutations may lead to the development of novel preventative and therapeutic strategies for disorders of the nervous and immune systems. BioEssays 23:733–744, 2001. © 2001 John Wiley & Sons, Inc. (shrink)

Background and Aims: The COVID-19 pandemic has led to radical and unexpected changes in everyday life, and it is plausible that people’s psychophysical health has been affected. This study examined the relationship between COVID-19 related knowledge and mental health in a Croatian sample of participants.MethodsAn online survey was conducted from March 18 until March 23, 2020, and a total of 1244 participant responses were collected. Measures included eight questions regarding biological features of the virus, symptoms, and prevention, the Hospital Anxiety (...) and Depression Scale, and Optimism-Pessimism Scale. According to the answers given on the questions on COVID-19 related knowledge, participants were divided in two groups: informed and uninformed on each question. They were then compared in the expressed levels of anxiety, depression, pessimism, and optimism. Full vs. partial mediation models with optimism/pessimism as a mediator in the relationship between anxiety/depression and the accuracy of responses for questions about handwashing and ways of transmission were estimated.ResultsParticipants who responded correctly on the question about handwashing had higher levels of anxiety, depression, and pessimism than those participants whose answer was incorrect, while participants who answered correctly on the question about the percentage of patients who develop serious breathing problems had higher levels of depression than those who answered incorrectly. Lower levels of anxiety and pessimism were observed in the participants who answered correctly about ways of transmission. Higher levels of pessimism were found in participants who scored incorrectly on questions about the efficiency of antibiotics, most common symptoms, and the possibility of being infected by asymptomatic carriers. Higher levels of knowledge about handwashing were predicted by higher levels of anxiety and pessimism. Higher levels of knowledge about ways of transmission were predicted by lower levels of anxiety and lower levels of pessimism. The examined relationships between anxiety/depression and knowledge were mediated by pessimism.ConclusionThe findings of this study suggest that knowledge about COVID-19 may be useful to reduce anxiety and depression, but it must be directed to the promotion of health behaviors and to the recognition of fake news. (shrink)

This study investigated the characteristics of neural oscillation and functional connectivity in college students engaging in binge drinking using resting-state electroencephalography. Also, the associations of visual memory, evaluated by the Rey-Osterrieth Complex Figure Test, and neural oscillation with FC during the resting state were investigated. The BD and non-BD groups were selected based on scores of the Korean version of the Alcohol use disorders Identification Test and the Alcohol Use Questionnaire. EEG was performed for 6 min while the participants rested (...) with eyes closed. The theta, lower-alpha, and upper alpha powers did not differ between the BD and non-BD groups. Concerning FC, the BD group exhibited stronger theta coherence than that of the non-BD group, and in the lower and upper alpha bands, the BD group showed stronger coherence in some areas but weaker coherence in others compared with the non-BD group. However, these significant results were not observed after Bonferroni correction. The BD group showed significantly lower delayed recall scores on the RCFT than did the non-BD group. A positive correlation between the left prefrontal-parietal-occipital midline connection and performance on the delayed recall of the RCFT was observed in the BD group. The present results could suggest that binge drinkers have alterations in brain FC, which may be related to their visual memory deficits. (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)

In this paper we review some properties of fuzzy observables, mainly as realized by commutative positive operator valued measures. In this context we discuss two representation theorems for commutative positive operator valued measures in terms of projection valued measures and describe, in some detail, the general notion of fuzzification. We also make some related observations on joint measurements.

The problem of constructing maximal equiangular tight frames or SICs was raised by Zauner in 1998. Four years ago it was realized that the problem is closely connected to a major open problem in number theory. We discuss why such a connection was perhaps to be expected, and give a simplified sketch of some developments that have taken place in the past 4 years. The aim, so far unfulfilled, is to prove existence of SICs in an infinite sequence of dimensions.

Symmetric informationally complete quantum measurements, or SICs, are mathematically intriguing structures, which in practice have turned out to exhibit even more symmetry than their definition requires. Recently, Zhu classified all the SICs whose symmetry groups act doubly transitively. I show that lattices of integers in the complex numbers, the quaternions and the octonions yield the key parts of these symmetry groups.

Madhyamakahrdayam [sic] Bhavyakrtam: Madhyamakahrdayam of Bhavya. Edited by Chr. Lindtner. The Adyar Library and Research Centre, Adyar 2001. liii, 169 pp. $75.00. ISBN 81-85141-40-1.

In order to defend the regress argument for foundationalism against Post’s objection that relevant forms of inferential justification are not transitive, Lydia McGrew and Timothy McGrew define a relation E of positive evidence, which, they contend, has the following features: It is a necessary condition for any inferential justification; it is transitive and irreflexive; and it enables both a strengthened regress argument proof against Post’s objection and an argument that nothing can ever appear in its own justificational ancestry. In reply, (...) we construct in their own terms both a counterexample to the would-be transitivity of E, and a related objection to their never-in-its-own-ancestry argument. We also rebut their rejection of certain counterexamples to the would-be transitivity of some forms of inferential justification. By doing so, and by questioning their transitivity claim for E, we aim to further the project of undermining the circularity arguments advanced by a zoo of skeptics, relativists, antirealists and internalists against realism and externalism. (shrink)

Dans ce nouveau livre consacré à la morale, Yvon Quiniou poursuit et approfondit la réflexion matérialiste qu'il lui consacre depuis longtemps. Il le fait ici en s'appuyant sur des auteurs dont la présence pourra surprendre, mais qu'il considère comme proches du matérialisme : Hume, Rousseau, mais aussi le pragmatiste Dewey, le rationaliste intransigeant Russell, ainsi que Marx et Gramsci, dont il marque fortement l'originalité sur la question des valeurs. Car ces auteurs ont bien en commun de prêter une forte attention, (...) théorique et pratique, à la morale, quitte à la confondre avec l'éthique et à se retrouver confrontés à la difficulté de penser un Universel moral... que leur philosophie admet cependant, fût-ce en pointillé. Cette dimension morale paraît essentielle à l'auteur, surtout si l'on pense à son prolongement politique. Il s'agit pour lui de lutter contre une indifférence morale désespérante qui a envahi la politique au nom de la seule efficacité rentable et qui, face à un capitalisme fondamentalement immoral parce qu'inhumain, nous mène à une impasse mondiale catastrophique."--Page 4 of cover. (shrink)

This article analyzes how the conceptualization LIFE IS A JOURNEY is conveyed within a series of paintings ranging from the fifteenth century to the twentieth century. While the previous research on visual metaphor generally aims to describe how the domains of metaphorical conceptualization interact or discusses the rhetorical effect that visual metaphor is able to induce, this article takes a historical perspective in order to identify the main conceptual aspects shared by the paintings under consideration. It is proposed that the (...) concept of a JOURNEY is associated with a PURPOSIVE ACTIVITY that involves the start of the journey and its termination as two qualitatively different moments that are faced as a collective/shared experience and that are inspired by some human wish. This article also shows how the conceptual potential of metaphor tends to maintain a coherent representation although the paintings represent different historical sensitivities and artistic approaches. (shrink)

We give an overview of some remarkable connections between symmetric informationally complete measurements and algebraic number theory, in particular, a connection with Hilbert’s 12th problem. The paper is meant to be intelligible to a physicist who has no prior knowledge of either Galois theory or algebraic number theory.

Anna Jaroszewska Sic et Non – Pierre Abelard’s Problematic Reasoning. Pierre Abelard, the philosopher called by many “the bee,” aroused much controversy because of his views. He was the most famous dialectician of his time. He used his logical and rational methods of truth investigation in the field of philosophy and theology. His thesis aroused much opposition, as evidenced by the double condemnation of the thinker by synods and his actions, intended to strengthen the role and independence of philosophy, were (...) not greeted with widespread acclaim. Abelard’s thesis Sic et Non had the purpose of correcting mistakes and ambiguities which appeared in the statements of the Church Fathers. That thesis is a perfect example of the dialectical method and serves as a textbook for students of this art – no answers given, only the arguments supporting the thesis and those against it. Does Abelard, twice condemned and conflicted with many famous thinkers, remain in his thesis a neutral person, who only quotes contradictory statements of the Church Fathers and theologians? What contradicts this thesis is the ampleness of the work and comprehensive clarifications in the first entries thereof. Despite the lack of any author comments in Sic et Non, what is clearly observable is the criticism of scholastic authority — the authority that was at Abelard’s time widely respected, without a word of opposition to the views represented. -/- Keywords: authority, dialectics, logic, rational investigation of the truth, criticism, truth, doubts. (shrink)

From the beginning of the xx century onwards, European art has gone through a remarkable mutation since Picasso shattered and chopped forms in painting through cubism, and Duchamp contemporaneously sabotaged the very idea of art with his invention of the ready made. Starting from an extensive consideration of this mutation, we tried and questioned the impact of the duchampean gesture and other subsequent artistic practices, by means of a frame of esthetic and philosophical reflection focused on the notions of art, (...) work of art, beauty, sublime, judgment of taste, spectator, ready made, and esthetic experience, inter alia. Also, our discussion questions the role of fiction in art, by means of an excerpt of a literary narration whose protagonists, a painter and his slave, seek, by the workings of drawing, to inscribe suffering and pardon at the heart of the creation act. We are thus led to think that whatever lies at the source of any interpretation of the [work of] art is an enigma and a conflict which cannot be seen through. (shrink)

From the beginning of the xx century onwards, European art has gone through a remarkable mutation since Picasso shattered and chopped forms in painting through cubism, and Duchamp contemporaneously sabotaged the very idea of art with his invention of the ready made. Starting from an extensive consideration of this mutation, we tried and questioned the impact of the duchampean gesture and other subsequent artistic practices, by means of a frame of esthetic and philosophical reflection focused on the notions of art, (...) work of art, beauty, sublime, judgment of taste, spectator, ready made, and esthetic experience, inter alia. Also, our discussion questions the role of fiction in art, by means of an excerpt of a literary narration whose protagonists, a painter and his slave, seek, by the workings of drawing, to inscribe suffering and pardon at the heart of the creation act. We are thus led to think that whatever lies at the source of any interpretation of the [work of] art is an enigma and a conflict which cannot be seen through. (shrink)

This book consists in a collection of studies composed by different researchers; every study focuses on an author or on some authors of the history of philosophy who has/have analysed, endorsed or criticized the concept of substance. Both positions for and against the ontology of substance are presented in the book.