In Aristotelian logic, categorical propositions are divided in Universal Affirmative, Universal Negative, Particular Affirmative and Particular Negative. Possible relations between two of the mentioned type of propositions are encoded in the square of opposition. The square expresses the essential properties of monadic first order quantification which, in an algebraic approach, may be represented taking into account monadic Boolean algebras. More precisely, quantifiers are considered as modal operators acting on a Boolean algebra and the square of opposition is represented by relations (...) between certain terms of the language in which the algebraic structure is formulated. This representation is sometimes called the modal square of opposition. Several generalizations of the monadic first order logic can be obtained by changing the underlying Boolean structure by another one giving rise to new possible interpretations of the square. (shrink)

In this paper we solve the problem how to axiomatize a system of quantum computational gates known as the Poincaré irreversible quantum computational system. A Hilbert-style calculus is introduced obtaining a strong completeness theorem.

In the framework of algebras with infinitary operations, the equational theory of $$\bigvee _{\kappa }$$ ⋁ κ -complete Heyting algebras or Heyting $$\kappa $$ κ -frames is studied. A Hilbert style calculus algebraizable in this class is formulated. Based on the infinitary structure of Heyting $$\kappa $$ κ -frames, an equational type completeness theorem related to the $$\langle \bigvee, \wedge, \rightarrow, 0 \rangle $$ ⟨ ⋁, ∧, →, 0 ⟩ -structure of frames is also obtained.

An algebraic setting for the validity of Pavelka style completeness for some natural expansions of Łukasiewicz logic by new connectives and rational constants is given. This algebraic approach is based on the fact that the standard MV-algebra on the real segment [0, 1] is an injective MV-algebra. In particular the logics associated with MV-algebras with product and with divisible MV-algebras are considered.

In the framework of the topos approach to quantum mechanics we give a representation of physical properties in terms of modal operators on Heyting algebras. It allows us to introduce a classical type study of the mentioned properties.

In this paper we investigate a categorical equivalence between square root qMV-algehras (a variety of algebras arising from quantum computation) and a category of preordered semigroups.

In this paper we attempt to physically interpret the Modal Kochen–Specker theorem. In order to do so, we analyze the features of the possible properties of quantum systems arising from the elements in an orthomodular lattice and distinguish the use of “possibility” in the classical and quantum formalisms. Taking into account the modal and many worlds non-collapse interpretation of the projection postulate, we discuss how the MKS theorem rules the constraints to actualization, and thus, the relation between actual and possible (...) realms. (shrink)

In this paper we analyze and discuss the historical and philosophical development of the notion of logical possibility focusing on its specific meaning in classical and quantum mechanics. Taking into account the logical structure of quantum theory we continue our discussion regarding the Aristotelian Square of Opposition in orthomodular structures enriched with a monadic quantifier. Finally, we provide an interpretation of the Orthomodular Square of Opposition exposing the fact that classical possibility and quantum possibility behave formally in radically different manners.

In this note we present a completion for the variety of bounded distributive quasi lattices, and, inspired by a well-known idea of L.L. Maksimova [14], we apply this result in proving the amalgamation property for such a class of algebras.

In this paper we enrich the orthomodular structure by adding a modal operator, following a physical motivation. A logical system is developed, obtaining algebraic completeness and completeness with respect to a Kripkestyle semantic founded on Baer*-semigroups as in [22].

We present a generalization of the problem of pattern recognition to arbitrary probabilistic models. This version deals with the problem of recognizing an individual pattern among a family of different species or classes of objects which obey probabilistic laws which do not comply with Kolmogorov’s axioms. We show that such a scenario accommodates many important examples, and in particular, we provide a rigorous definition of the classical and the quantum pattern recognition problems, respectively. Our framework allows for the introduction of (...) non-trivial correlations between the different species involved, opening the door to a new way of harnessing these physical resources for solving pattern recognition problems. Finally, we present some examples and discuss the computational complexity of the quantum pattern recognition problem, showing that the most important quantum computation algorithms can be described as non-Kolmogorovian pattern recognition problems. (shrink)

In this article we discuss the contextual character of quantum mechanics in the framework of modal interpretations. We investigate its historical origin and relate contemporary modal interpretations to those proposed by M. Born and W. Heisenberg. We present then a general characterization of what we consider to be a modal interpretation. Following previous papers in which we have introduced modalities in the Kochen-Specker theorem, we investigate the consequences of these theorems in relation to the modal interpretations of quantum mechanics.

Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. We study the basic algebraic properties of this system by introducing the notion of Shi-Aharonov quantum computational structure. We show that the quotient of this structure is isomorphic to a structure based on a particular set of complex numbers (the closed disc with center \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\frac{1}{2},\frac{1}{2})$\end{document} and radius \documentclass[12pt]{minimal} (...) \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{1}{2}$\end{document} ). (shrink)

We investigate some properties of two varieties of algebras arising from quantum computation - quasi-MV algebras and $\sqrt{^{\prime }}$ quasi-MV algebras - first introduced in \cite{Ledda et al. 2006}, \cite{Giuntini et al. 200+} and tightly connected with fuzzy logic. We establish the finite model property and the congruence extension property for both varieties; we characterize the quasi-MV reducts and subreducts of $\sqrt{^{\prime }}$ quasi-MV algebras; we give a representation of semisimple $\sqrt{^{\prime }}$ quasi-MV algebras in terms of algebras of functions; (...) finally, we describe the structure of free algebras with one generator in both varieties. (shrink)

This book provides an interdisciplinary approach to one of the most fascinating and important open questions in science: What is quantum mechanics really talking about? In the last decades quantum mechanics has given rise to a new quantum technological era, a revolution taking place today especially within the field of quantum information processing; which goes from quantum teleportation and cryptography to quantum computation. Quantum theory is probably our best confirmed physical theory. However, in spite of its great empirical effectiveness it (...) stands today still without a universally accepted physical representation that allows us to understand its relation to the world and reality. The novelty of the book comes from the multiple perspectives put forward by top researchers in quantum mechanics, from Europe as well as North and South America, discussing the meaning and structure of the theory of quanta. The book comprises in a balanced manner physical, philosophical, logical and mathematical approaches to quantum mechanics and quantum information. Going from quantum superpositions and entanglement to dynamics and the problem of identity; from quantum logic, computation and quasi-set theory to the category approach and teleportation; from realism and empiricism to operationalism and instrumentalism; the book considers from different angles some of the most intriguing questions in the field. From Buenos Aires to Brussels and Cagliari, from Florence to Florianópolis, the interaction between different groups is reflected in the many different articles. This book is interesting not only to the specialists but also to the general public attempting to get a grasp on some of the most fundamental questions of present quantum physics. (shrink)

La actividad teórica y la actividad práctica han sido tradicionalmente entendidas como complementarias en el sentido que mediante la actividad teórica el sujeto se apropiaría idealmente de los objetos del mundo externo, mientras que mediante la actividad práctica realizaría sus propias metas subjetivas en el mundo. Sin embargo, dicho modelo plantea un conjunto de graves problemas exegéticos y conceptuales sobre la estructura y significado de la entera filosofía del espíritu de Hegel. En este artículo buscaremos esclarecer qué es a ojos (...) de Hegel lo propiamente específico de la actividad teórica y de la actividad práctica, para, sobre esa base, ofrecer un modelo exegético que logre dar satisfactoriamente cuenta de la particular periodización general que Hegel propone sobre las diferentes formas de actividad del espíritu humano. (shrink)

Die Vernunft ist für Hegel die Einheit des Subjekts und des Objekts ? anders ausgedrückt: Subjekt zu sein impliziert, die Welt zu erkennen. Die Inhalte, die die Erkenntnistätigkeit spontan findet, »setzen« ihre eigene Erkenntnis nicht, weil die der Erkenntnis gegebenen Inhalte keine »unverursachten Ursachen« oder »unbewegten Beweger« des Erkennens sind. Die Erkenntnisobjekte sind für Hegel sowohl ruhend als auch in Bewegung: Unmittelbarkeit und Vermittlung sind bloße Standpunkte über die Erkenntnistätigkeit. Sich ein absolutes Nichtsein des Erkennens vorzustellen (z.B. durch die Zustimmung (...) zum cartesischen Gedankenexperiment, durch eine philosophische Deutung des psychologischen Phänomens des Unbewusstseins oder durch eine naturalistische Interpretation der Theorie der transzendentalen Subjektivität), verändert grundsätzlich unser Verständnis des Erkenntnisphänomens, weil es das Bedürfnis nach speziellen Gründungsakten erzeugt, die als absolute Ursachen der Erkenntnis fungieren sollen. Anhand von Spinozas Substanzbegriff hält Hegel dagegen das Erkennen für streng genommen unverursacht und insofern die Erkenntnisakte für innere Momente des unendlichen absoluten Elements des Erkennens, d.h. der ununterbrochenen und ununterbrechbaren Geist-Welt-Einheit. Vom Standpunkt des künstlich vorgestellten Nichtseins der Geist-Welt-Einheit muss aber der Kreislauf der Erkenntnisakte irgendwann angefangen haben; das menschliche Erkennen bzw. Denken wird dadurch zum bloß formalen Denken - in Hegels Terminologie: zum »Bewusstsein«. Damit die Tatsache begreiflich wird, dass das Erkennen schon immer einen Inhalt hat, müssen die Bestimmungen einiger Denkakte als Dinge interpretiert werden, die von außen her das Erkennen in Gang setzen und erfüllen. Erst diese hypostasierten Denkakte können die Tatsache erklären, dass der menschliche Geist die Wirklichkeit erkennt; im Gegensatz zu diesen Denkakten, denen das epistemische Privileg verliehen wird, den Geist mit der Welt in Kontakt zu bringen, werden die restlichen Denkakte zu bloß subjektiven Vorstellungen reduziert. In diesem Zusammenhang soll die sinnliche Wahrnehmung oder Empfindung den absoluten Anfang des Erkennens bilden, obwohl sie selber ein Akt und Moment des Denkens ist. Die empirische Erkenntnis soll hier ein in sich leer gewordenes Denken in Kontakt mit der Welt setzen, damit dieses erst dann zum Erkennen dessen wird, was es wirklich gibt. Für Hegel bilden dagegen die empirischen Gegenstände keinen absoluten Anfang der Erkenntnis, sondern sind bereits da im Denken als unendlicher Totalität des erkennenden Geistes und der erkannten Welt. In diesem theoretischen Rahmen gibt es - selbstverständlich! - Raum für sinnliches Erkennen, aber keinen für Empirismus. Aristoteles? Aussage, dass »die Seele in gewisser Weise alle Dinge« ist, und das scholastische Diktum, dass »ens et verum convertuntur«, paraphrasierend, behauptet Hegel: »das Absolute ist der Geist«. (shrink)

Here are crucial data for any theory of the self, self-consciousness or the structure of experience. We discuss the fundamental structure of both indexical reference, especially first-term reference, and quasi-indexical reference, used in attributing first-person reference to others. Chisholm's ingenious account of direct awareness of self is tested against the two sets of data. It satisfies neither. Chisholm's definitions raise serious questions both about philosophical methodology and about the underlying ontology of individuation, identity, and predication. Chisholm's adverbial account of non-physical (...) contents of consciousness is also examined; several questions are raised about the possible success of the linguistic technique of ontological reduction by hyphenation and creation of grammatical devices. (shrink)

Si bien se han escrito una cantidad relativamente grande de artículos y libros sobre diversos aspectos del pensamiento filosófico de Ignacio Ellacuría, hasta ahora no se cuenta con un sistemático de toda su producción filosófica que muestre la unidad de todos esos aspectos y que defina con claridad lo propio y original de su pensamiento, más allá de lo que pueda haber de la filosofía de Xavier Zubiri, filósofo vasco, de quien Ellacuría fue su amigo y su más estrecho colaborador. (...) Esta investigación se ha realizado con un doble objetico: en primer lugar, analizar y sistematizar los aspectos centrales del pensamiento filosófico de Ignacio de Ellacuría; y, en segundo lugar, estudiar la génesis y constitución de su proyecto filosófico de liberación. Queda de manifiesto cuál es la ubicación y el aporte específico de Ellacuría dentro del conjunto de las principales corrientes de la filosofía de la liberación latinoamericana. (shrink)

Philosophy is the search for the large patterns of the world and of the large patterns of experience, perceptual, theoretical, . . . , aesthetic, and practical - the patterns that, regardless of specific contents, characterize the main types of experience. In this book I carry out my search for the large patterns of practical experience: the experience of deliberation, of recognition of duties and their conflicts, of attempts to guide other person's conduct, of deciding to act, of influencing the (...) physical world with one's doings, and the like. This is the experience that makes possible our social life, the formulation of plans for teamwork, the building of institutions, the development of nations, and the adoption of the ideal of morality. Here I develop a network of theories about the most fundamental aspects of practical thinking: what is thought in such thinking; what makes that thinking correct; what makes it practical; and the structure of the doings that accrue to the world when such thinking is effective. I have attempted to build each theory in sufficient detail, so that it il luminates its subject matter with a certain degree of fullness. But I have also aimed at producing an harmonious system of theories, so that the grand pattern of practical thinking can be admired, not only for the beauty of the separate structures of its parts, but also for its architectonic unity. Chapter 1 gives the details of the many facets of this project and discusses some methodological techniques. (shrink)

Did Jesus ever do anything wrong? Judging by the vast majority of books on New Testament ethics, the answer is a resounding No. Writers on New Testament ethics generally view Jesus as the paradigm of human standards and behaviour. But since the historical Jesus was a human being, must he not have had flaws, like everyone else? The notion of a flawless human Jesus is a paradoxical oddity in New Testament ethics. According to Avalos, it shows that New Testament ethics (...) is still primarily an apologetic enterprise despite its claim to rest on critical and historical scholarship. The Bad Jesus is a powerful and challenging study, presenting detailed case studies of fundamental ethical principles enunciated or practised by Jesus but antithetical to what would be widely deemed 'acceptable' or 'good' today. Such topics include Jesus' supposedly innovative teachings on love, along with his views on hate, violence, imperialism, animal rights, environmental ethics, Judaism, women, disabled persons and biblical hermeneutics. After closely examining arguments offered by those unwilling to find any fault with the Jesus depicted in the Gospels, Avalos concludes that current treatments of New Testament ethics are permeated by a religiocentric, ethnocentric and imperialistic orientation. But if it is to be a credible historical and critical discipline in modern academia, New Testament ethics needs to discover both a Good and a Bad Jesus. (shrink)

The aim of this paper is to explore the interaction between aesthetic properties and cognitive value in serial television. This study is based on a survey focused specifically on one television series: the second season of My Brilliant Friend, created by Saverio Costanzo. The survey was designed with the aim of getting respondents to express their perceptions of the relationship between the aesthetic qualities of the series and their assessment of it in cognitive terms. The responses obtained in the survey (...) offer a clear answer to the key question of concern for this article. The vast majority of respondents (more than 90% in almost all cases) believe that aesthetic and cognitive qualities mutually influence one another. Additionally the qualitative results invite us to further explore interactionism conceptually: the cognitive content is taken as a criterion for evaluating the season’s aesthetic value overall, suggesting a link between meaning and narrative form. (shrink)

Según una historia estándar, devenida habitual especialmente por influencia del pensamiento heideggeriano, la filosofía occidental se encuentra atrapada en la trampa de la metafísica. La trampa de la metafísica centra la crítica a la metafísica en torno a la tesis según la cual el esencialismo y una concepción de la verdad condicionada por él determinan qué significa “ser” o “existencia”. Detrás de la realidad se supone un fundamento que bajo la forma de un “trasmundo” (Hinterwelt) produce una manifestación cuasi-causal, a (...) saber: el “mundo” (Welt), el cual se deja con ello concebir como la aparición del ser que se ha retraído en sí mismo. La diferencia entre ser y apariencia mantiene al pensamiento metafísico atrapado, en la medida en que éste no es capaz de reconocer esa diferencia misma como una apariencia. En Siete ensayos sobre la muerte de la metafísica, Héctor Ferreiro ofrece frente a esta historia estándar una convincente contrahistoria. Esta contrahistoria tiene su punto de partida en Hegel, quien intenta, de modo opuesto a la lectura propuesta por Heidegger, superar a la metafísica con sus propios medios y sepultarla a partir de su propia dinámica interna. Precisamente a esta superación está dedicado el debate y discusión de Hegel con el argumento ontológico. Como Kant, Hegel ve en el argumento ontológico uno de los centros operacionales de la metafísica clásica. La cuestión es, pues, cómo abordar el argumento ontológico del modo correcto desde un punto de vista crítico a la metafísica. La estrategia que ofrece Hegel consiste, como lo expone Ferreiro, en desenmascarar la distinción misma entre el ser y la apariencia producida por él como una operación de tipo conceptual. Según Hegel, la metafísica ha sido desde siempre el intento por desarrollar una teoría de la totalidad. Pero una teoría de la totalidad que coloca al ser de un lado y a su aparición del otro lado de un límite no advierte su propia operación, dado que el trazado de un límite pertenece él mismo a la teoría de la totalidad. De lo que se trata, pues, es de examinar los trazados de límite constitutivos de la metafísica para reconocerlos como productos de la reflexión y no como hechos dados que el pensamiento tan sólo debe reflejar. El movimiento de autosuperación de la metafísica que culmina en la discusión de Kant y Hegel con el argumento ontológico pertenece ya, sin embargo, a la tradición de la metafísica. Como lo muestra Ferreiro, la metafísica está a más tardar a partir de la distinción medieval entre esencia y existencia en proceso de superarse a sí misma, pues ya Tomás de Aquino logra reconocer en dicha distinción la verdadera fuente de la producción del mundo. Tomás persiste aún, sin embargo, en una concepción sustancialista, en la medida en que considera a la distinción entre esencia y existencia como un hecho in-dependiente de la teoría y del sujeto. Sin embargo, esa distinción es una operación conceptual y no un objeto que se encuentra en el mundo. En esta medida, la tesis de la distinción de razón entre ambas categorías se presenta como un indicador de la reflexión de la metafísica sobre sí misma. Ferreiro demuestra que el célebre comienzo de la Cien-cia de la Lógica de Hegel significa precisamente una profundización y radicalización de esa autorreflexión. Ahora bien, a ojos de Hegel el ser del comienzo de la Lógica es en sí mismo como tal el resultado del argumento ontológico; en su formulación clásica, sin embargo, el argumento ontológico sólo aspira a probar que hay algo (Dios), pero el argumento mismo no es como tal capaz de determinar ulteriormente ese algo –esto constituye justamente la tarea de la ontología en el sentido de Hegel, es decir, la tarea de la Lógica. Así, lo que podría denominarse en Hegel una “metafísica” es expresamente una crítica a la metafísica tradicional. En efecto, la ontología que Hegel propone en modo alguno significa una recaída en la metafísica anterior a Kant; por el contrario, en la filosofía de Hegel metafísica y crítica a la metafísica se vinculan íntimamente y con ello se cierra un círculo que se había abierto en la metafísica teológica de la Edad Media: precisamente que este movimiento estaba contenido ya programáticamente en la ontología de la distinción entre esencia y existencia es algo que Ferreiro analiza en forma clara y meticulosa. En cuanto disciplina, la ontología está hoy nuevamente en el centro de la atención de la reflexión filosófica a nivel mundial. Siete ensayos sobre la muerte de la metafísica no sólo ofrece en este respecto un análisis de índole histórica; es también una importante contribución teórica al actual retorno a la ontología. (shrink)

Therapy for metaphysics -- Concepts, rules, and the spirit of recognition -- Meaning and meanings -- Reference and presence -- Truth and correspondence -- Emancipating theology.

This primer on biblical criticism and key problems in religion and philosophy is intended as an introduction to these complex subjects for Spanish-speaking laypersons with little or no prior scientific training in the area. Professor Avalos critically reviews the classic arguments for the existence of God, alleged miracles and faith-healing, the belief that the Bible is the inerrant word of God, problems of good and evil in the Bible, creation stories, biblical prophecy, the resurrection of Jesus, and many other topics. (...) In the last part of the book, Avalos discusses the scientific worldview, especially as it impinges upon the question of the existence of God. A notes section allows readers to explore more deeply the areas touched on in the text; appendices provide information on the sources of many biblical stories and beliefs in Mesopotamian and other ancient Near Eastern cultures; and a final personal note briefly recounts the author’s experiences from his upbringing in fundamentalist Christianity to his current skeptical view. This informative volume is an excellent starting point for those who wish to explore with a minimum of resources basic questions in religion, philosophy, and biblical studies. (shrink)

Objective Gather information from physicians about factors contributing to unnecessary noninvasive imaging and impact of possible solutions. Methods Qualitative study of 14 physicians using a phenomenological approach and the Theoretical Domains Framework. Results Most participants self-reported that >10% of the imaging tests they order are unnecessary. External sources of pressure included: peer-review, patient demands, nursing expectations, specialist requests, as well as prior experience with patient advocates, and the compensation and pension system. Internal sources of pressure included reliance on anecdote, self-doubt (...) about diagnoses, and fear of missing a diagnosis and of professional liability. Participants expressed both optimism and concern about potential solutions, such as adopting decision support software. Conclusion Physicians are under pressure from multiple sources to order unnecessary imaging. Peer review, nursing expectations, and perceptions about Veteran compensation and pension are newly reported contributing factors. (shrink)

Evolutionarily-minded scholars working on the most puzzling aspects of human cooperation-one-shot, anonymous interactions among non-kin where reputational information is not available-can be roughly divided into two camps. In the first, researchers argue for the existence of evolved capacities for genuinely altruistic human cooperation, and in their models emphasize the role of intergroup competition and selection, as well as group norms and markers of membership that reduce intragroup variability. Researchers in the second camp explain cooperation in terms of individual-level decision-making facilitated (...) by evolved cognitive mechanisms associated with well-established self- and kin-maximization models, as well as by ‘misfires’ that may result from these mechanisms interacting with novel environments. This essay argues that the manner in which culture provides information that de-anonymizes intragroup strangers suggests that neither evolved capacities for genuine altruism nor widespread misfires are necessary to account for anonymous, one-shot cooperation. (shrink)