The aim of this paper is to contribute to the clarification of concepts usually found in books on quantum mechanics, aided by knowledge from the field of the theory of operators in Hilbert space. Frequently the basic distinction between bounded and unbounded operators is not established in books on quantum mechanics. It is repeatedly overlooked that the condition for an unbounded operator to be symmetric (Hermitian) is not sufficient to make it self-adjoint. To make things worse, nearly all operators in (...) quantum mechanics are unbounded. Often one finds statements such as: For any linear operator A we can write a Hermitian operator HA=(A+A+)/2, where Hermitian is thought to mean self-adjoint. Along these lines, self-adjointness of the momentum operator in generalized coordinates, taken from that expression, is questioned. In particular, the redescription in terms of spherical polar coordinates and its implications for the eventual loss of self-adjointness of the momenta conjugate to them are studied. (shrink)

The construction of the quantum-mechanical Hamiltonian by canonical quantization is examined. The results are used to enlighten examples taken from slow nuclear collective motion. Hamiltonians, obtained by a thoroughly quantal method (generator-coordinate method) and by the canonical quantization of the semiclassical Hamiltonian, are compared. The resulting simplicity in the physics of a system constrained to lie in a curved space by the introduction of local Riemannian coordinates is emphasized. In conclusion, a parallel is established between the result for various coordinates (...) and a proposed procedure for quantizing the semiclassical Hamiltonian for a single coordinate. (shrink)

In January 2023, the Science and Security Board of the Bulletin of the Atomic Scientists moved the hands of the Doomsday Clock forward to 90 s before midnight.

There can be no doubt that discrimination based on sex, race, ethnicity, religion or beliefs should not be tolerated in academia. Surprisingly, however, in recent years, policies of Diversity, Inclusion and Equity (DIE), officially introduced to counteract discrimination, have increasingly led to quite the opposite result: the exclusion of individuals who do not share a radical 'woke' ideology on identity politics (feminism, other gender activisms, critical race theory, etc.), and to the suppression of the academic freedom to discuss such dogmas. (...) This subversion of academia — disguised Trojan-horse style as universal human rights advocacy — is unacceptable because academia must be politically neutral and protect freedom of speech, a cornerstone of professional scholarly activity without which universities as we know them will slowly but surely suffocate. Our purpose here is to put together some particularly illustrative cases of such repression in a single book, testifying to a ubiquitous trend within western culture, irreducible to a few isolated complaints. The essays contained here illustrate the abuse of power, censorship and witch-hunts at many universities and research centres in the name of DIE. List of coauthors in alphabetical order: Dorian Abbot, Tomonori Agoh, Gerhard Amendt, Ivar Arpi, David Benatar, Peter Boghossian, Civitas Research Team, David Díaz Pardo de Vera, Pedro Domingos, Janice Fiamengo, Étienne Forest, Jorge Gibert Galassi, Norman Goldstuck, José L. González Quirós, Lawrence M. Krauss, Patrick LaBelle, Martín López Corredoira, Heather Mac Donald, Martin Malmgren, Jordan Peterson, Constantin Polychronakos, Erik. J. Olsson, Philip C. Salzman, Alessandro Strumia, Tom Todd, Andrei Yafaev. (shrink)

A partir de J.-P. Sartre y M. Heidegger, se aborda la relación entre temporalidad, conciencia y comprensión, y se examina la experiencia de la indeterminación vinculada a la intuición del límite de lo pensable y expresable, con el fin de articular la filosofía y la poesía como formas de acercamiento a dicho límite. Se plantean dos presupuestos: el cuestionamiento de la demarcación radical entre indagación filosófica y expresión poética, y la aproximación racional, pero sin prejuicios racionalistas, a los límites del (...) pensar y del decir. Con ello se reivindica una forma de entender la filosofía que parte de M. Heidegger y alcanza brillantes expresiones en M. Foucault y J. Derrida. On the basis of J.-P. Sartre and M. Heidegger, the article addresses the relation among temporality, consciousness, and understanding, and examines the experience of indeterminacy that is linked to the intuition of the limits of what can be thought and expressed, in order to articulate philosophy and poetry as forms to approach that boundary. Two presuppositions are set forth; the questioning of the radical demarcation between philosophical inquiry and poetic expression, and the rational approach to the limits of thinking and saying, but without rationalist prejudices. Thus, we assert a way of understanding philosophy that originates in M. Heidegger and achieves a brilliant expression in M. Foucault and J. Derrida. (shrink)

A partir de J.-P. Sartre y M. Heidegger, se aborda la relación entre temporalidad, conciencia y comprensión, y se examina la experiencia de la indeterminación vinculada a la intuición del límite de lo pensable y expresable, con el fin de articular la filosofía y la poesía como formas de acercamiento a dicho límite. Se plantean dos presupuestos: el cuestionamiento de la demarcación radical entre indagación filosófica y expresión poética, y la aproximación racional, pero sin prejuicios racionalistas, a los límites del (...) pensar y del decir. Con ello se reivindica una forma de entender la filosofía que parte de M. Heidegger y alcanza brillantes expresiones en M. Foucault y J. Derrida. (shrink)

SummaryIt is shown that the concept of understanding cannot be reduced to a combination of knowing that, knowing how, and knowledge by acquaintence. First, it is shown that understanding and knowledge have different objects. Then “understanding what” is analyzed along Aristotelian lines. In the central part of the paper it is shown that understanding objects defined by constitutive rules involves a non‐propositional component. This notion of “understanding” is shown to cut across the humanist‐scientist dichotomy.

SummaryWe need to classify emotions as objectual and non‐objectual. Some of the objectual emotions are dependent on the characterizations of their objects. So in these cases reason guides the emotions. But there are also other cases in which the conceptual dependency goes the other way. in the case of aesthetic judgments and certain types of judgments involving purpose, or compassion, the ability to make these judgments is dependent on being in certain emotional states. Thus in some cases emotions aid and (...) supplement reason.RésuméNous devons classer les émotions comme objectuelles et non objectuelles. Quelques‐unes des émotions objectuelles sont dépendantes des caractéristiques de leurs objets. La raison guide alors les émotions. Mais il y a aussi des cas ou la dépendance conceptuelle suit ?on;autres voies. Dans le cas de jugements esthétiques et de jugements comportant des buts, ou de la compassion, la capacityé de porter ces jugements est dépendante de certains états émotionnels dans lesquels se trouve le sujet. Ainsi, dans certains cas, les émotions aident et completent la raison.ZusammenfassungWir müssen die Gefühle in objektuelle und nicht‐objektuelle einteilen. Einige der objektuellen Gefühle sind von der Charakterisierung ihrer Objekte abhängig. In diesen Fällen lenkt die Vernunft die Gefühle. Es gibt aber auch Fälle, in welchen die begriffliche Abhängigkeit umgekehrt verläuft. Im Falle von ästhetischen Urteilen und von gewissen Urteilen, die Zwecke oder Mitgefühle betreffen, hängt die Fähigkeit, solche Urteile zu fällen, davon ab, dass man sich in bestimmten Gemütszuständen befindet. So kommt es, dass in einigen Fällen Gefühle die Vernunft unterstützen und ergänzen. (shrink)

This book is a collection of papers on the metaphysics and natural philosophy of John Buridan (ca. 1295-1361), one of the most innovative and influential ...

Open peer commentary on the article “Exploring the Depth of Dream Experience: The Enactive Framework and Methods for Neurophenomenological Research” by Elizaveta Solomonova & Xin Wei Sha. Upshot: This commentary aims to sharpen the conceptual distinction between the breadth and the depth of dream experience. I discuss several possible readings and argue that the best one construes breadth and depth as distinct but complimentary research strategies distinguished not just by the kinds of evidence they rely on, but also by the (...) degree to which different types of data are integrated and focused on the same experiential episode. I identify promising candidates for depth approaches and challenges for future research. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Routley- Meyer type relational complete semantics are constructed for intuitionistic contractionless logic with reductio. Different negation completions of positive intuitionistic logic without contraction are treated in a systematical, unified and semantically complete setting.

In lieu of an abstract, here is a brief excerpt of the content:ALBERTUS MAGNUS AND THE NOTION OF SYLLOGISTIC MIDDLE TERM J. M. HUBBARD College of St. Thomas St. Paul, Minnesota ABERT THE GREAT is recognized as one of the great scientific minds of the Middle A:ges, both for his commentaries on Aristotle's scientific works and for his own contributions to the study of nature. His contributions to the science of logic go largely unnoticed, however. This is probably due to (...) the ascendency of the Summulae tradition in medieval logic a.bout the time of Albert's death, for the Summulae traidition is quite different from the one represented in his commentaries on the logical writings of Aristotle. I should like to remedy this a bit by looking at how he understands the concept of middle term in Aristotle's Prior Analytics. There are two points with which we can begin this study. First, Albert insists that Ar.istotle's remark that second and third figure syllogisms are imperfect when compared to those of the first figure does not mean that they somehow lack the necessity cha.racteristic of syHogisms of the first figure. On the contra;ry, all syllogisms, in whatever figure, conclude necessa,rily. This is what it is to be a syllogism. First figure syllogisms are perfect with respect to us, for in them the necessity of consequence, which is the very na;bure of the syllogism, is manifest to us in a way that it is not in syllogisms of the second and third figures. Hence, the marks perfect and imperfeot refer not to the syllogisms in themselves but to the syUogisms in relation to us.1 1 Albertus Magnus, Oommentares CYn the Prior Analytics, Bk. I, Tr. 1, Ch. 8, pp. 469-71. See also Tr. 1, Ch. 6, p. 467, and Tr. 1, Chs. 5 and 6. Page 115 116 J. M. HUBBARD Seoond, the notion of syllogism is coextensive with the notion of middle term, for the middle term is the root and cause of the necessity that characterizes the syllogism. This is why some other kinds of argument, induction and example for instance, are not syllogisms strictly speaking, but only in a loose and improper sense; they lack a true middle term.2 What is it, then, to be a middle term of a syllogism on Albert's reading of Aristotle? Is the middle term middle in some quantitative sense, then? Although Albert uses the expressions scope, breadth, contain, etc., he is quite explicit that the notions of figure and term are transferred " metaphorically " from quantity to properly logical considerations.8 For logic deails not with quantity and its relations, but with relations that exist between things as conceived by the mind, the most fundamental of which is the relation of predica.bility. To be predicable is to be sayable of many things, and although a predicable can be considered a whole in relation to the things of which it is said (its parts then), such talk is metaphorical and not literal. A predicable (whole) is sayable of many things but is not constituted by them. Dog, for instance, is sayable of Fido and Rover, but being a dog is not being Fido and Rover. A whole in the ordinary sense, on the other hand, is not sayable of its parts and is composed of them. One could not say that a wall is a house, but a house is composed, among other things, of a wall. The notions of figure and term, and therefore of middle term, are taken from the quantitative aspects of things and trans£erred to properly logical things. This being so, the notion of middle term cannot be reduced to something quantatative, spatial organization for example. From these remarks one can anticipate how Albert would respond to the suggestion that the middle term is the one that is middle in universality with respect to the other two. This references will be to Oommentaria in Prioru.m A.nalytiooru.m in Opera Omnia, ed. A. Borgnet (Paris: Vives, 1890), Vol. 1. 2 Bk. II, Tr. 7, Ch. 4, p. 794. a Bk. I, Tr. I, Ch. 2, pp. 460-61. ALBERTUS MAGNUS AND THE MIDDLE TERM 117 would... (shrink)

In an article in an earlier edition of the Journal of Medical Ethics (1) Dr Iglesias bases her analysis upon the mediaeval interpretation of Platonic metaphysics and Aristotelian logic as given by Aquinas. Propositional forms are applied to the analysis of experience. This results in a very abstract analysis. The essential connection of events and their changing temporal relationships are ignored. The dichotomy between body and soul is a central concept. The unchanging elements in experience are assumed to be more (...) real than the actual world of experienced process. Such a view makes the analysis of the temporal factors in experience impossible. Its abstractness is quite unsuitable for the analysis of the ontological structure and development of the neonate from fertilisation to birth. A N Whitehead made the notion of organism central to his philosophy. He refused to place human experience outside nature, or admit dualism. His philosophy of organism is an attempt to uncover the essential elements connecting human experience with the physical and biological sciences. Time, change and process are, in his view, more real than the static abstractions obtainable by the use of the fallacy of misplaced concreteness. Use of the latter negates the essential connectedness of events and the importance of temporarily and change (2). In this paper I argue that the embryo, being an organism, is not analysable in terms of thinghood. It is a process. To apply Aristotelian logical concepts to it is to distort the real nature of the datum. (shrink)

A new description of gravitational motion will be proposed. It is part of the proper time formulation of physics as presented on the IARD 2000 conference. According to this formulation the proper time of an object is taken as its fourth coordinate. As a consequence, one obtains a circular space–time diagram where distances are measured with the Euclidean metric. The relativistic factor turns out to be of simple goniometric origin. It further follows that the Lagrangian for gravitational dynamics does not (...) require an interpretation in terms of curvature of space–time. The flat space model for gravitational dynamics leads to the correct predictions for the bending of light, the perihelion shift of Mercury and gravitational red-shift. The new theory is free of singularities. More important, the new formulation of gravitational dynamics restores the validity of the principle of addition of potentials. One therefore can find solutions for static gravitational configurations for which it is difficult to find the solution of the corresponding Einstein equations. The method will be illustrated by means of the orbital precession for non-spherical stellar mass distributions. In case of the bipole mass distribution the agreement with the predictions of the general theory of relativity is very striking. Nevertheless, the new model is far more simple. (shrink)

1. 1.5.3. The unanimous manuscript reading for this passage is The idea of an looking for an seems alien to Greek thought, and the expression is not derived from any traceable proverb. A small correction produces the reading which restores sense, and produces a meaning which is much more in line with the requirements of the passage. The corruption may well have arisen from the penchant which scribes had for making minor alterations to restore what they conceived to be the (...) required grammar of the immediate context. (shrink)