The probability pattern emerging in two-slit experiments is a typical quantum feature whose essential ingredients are examined by translating them into the spin- $ \frac{1}{2} $ formalism. In view of the existence of extensions of quantum theory preserving some classical structure, we discuss how the two-slit probabilities behave under such extensions. We consider a generalization of the standard classical probability theory, to be called operational probability theory, that turns out to host the so called quantum probabilities.

We discuss a generalization of the standard notion of probability space and show that the emerging framework, to be called operational probability theory, can be considered as underlying quantal theories. The proposed framework makes special reference to the convex structure of states and to a family of observables which is wider than the familiar set of random variables: it appears as an alternative to the known algebraic approach to quantum probability.

We study the possibility of representing the proposition lattice associated with a quantum system by a linear vector space with coefficients from ap-adic field. We find inconsistencies if the lattice is assumed, as usual, to be irreducible, complete, orthocomplemented, atomic, and weakly modular.

There is a large literature on the issue of the lack of properties (i.e. accidents) in quantum mechanics (the problem of “hidden variables”) and also on the indistinguishability of particles. Both issues were discussed as far back as the late 1920’s. However, the implications of these challenges to classical ontology were taken up rather late, in part in the ‘quantum set theory’ of Takeuti (Curr Issues Quant Logic 303–322, 1981), Finkelstein (in Beltrametti EG, Van Fraassen BC (eds) Current issues (...) in quantum logic. Plenum, New York, 1981) and the work of Décio Krause (1992)—and subsequent publications). But the problems created by quantum mechanics go far beyond set theory or the identity of indiscernibles (another subject that has been often discussed)—it extends, I argue, to our accounts of truth. To solve this problem, i.e. to have an approach to truth that facilitates a transition from a classical to a quantum ontology one must have a unified framework for them both. This is done within the context of a pluralist view of truthmaking, where the truthmakers are unified in having a monoidal structure. The structure of the paper is as follows. After a brief introduction, the idea of a monoid is outlined (in Sect. 1) followed by a standard set of axioms that govern the truthmaker relation from elements of the monoid to the set of propositions. This is followed, in Sect. 2, by a discussion of how to have truthmakers for two kinds of necessities: tautologies and analytic truths. The next Sect. 3, then applies these ideas to quantum mechanics. It gives an account of quantum states and shows how these form a monoid. The final section then argues that quantum logic does not, despite what one might initially suspect, stand in the way of an account of quantum truth. (shrink)

These are the proceedings of the Workshop on Quantum Logic held in Erice (Sicily), December 2 - 9, 1979, at the Ettore Hajorana Centre for Scientific Culture. A conference of this sort was originally proposed by Giuliano Toraldo di Francia, who suggested the idea to Antonino Zichichi, and thus laid the foundation for the Workshop. To both of them we express our appreciation and thanks, also on behalf of the other participants, for having made this conference possible. There were approximately (...) fifty participants; their names and institutions are listed in the text. Quantum logic, which has now a history of some forty or more years, has seen remarkable growth during the sixties and seventies. The papers in the present volume presuppose, by and large, some acquaintance with the elements of the subject. These may be found in the well-known books by J.H. Jauch (Foundations of Quantum Hechanics; Reading, 1968), V.S. Varadarajan (Geometry of Quantum Theory: Princeton, 1968), and C. Piron (Foundations of Quantum Theory; New York, 1976). The initial program for the conference listed about twenty-five invited papers. But in the context of a very active and qualified attendance, other contributions were offered. This volume contains all of them. The program listed six main topics: I. Classification or different areas of quantum logic, and open problems. II. Comparison and unification of different approaches to quantum theories; problems of interpretation. III. Formal quantum logic; axiomatics. IV. Hodal interpretations of quantum logic. v vi FOREWORD V. Quantum set theory. (shrink)

This article reports the findings of AI4People, an Atomium—EISMD initiative designed to lay the foundations for a “Good AI Society”. We introduce the core opportunities and risks of AI for society; present a synthesis of five ethical principles that should undergird its development and adoption; and offer 20 concrete recommendations—to assess, to develop, to incentivise, and to support good AI—which in some cases may be undertaken directly by national or supranational policy makers, while in others may be led by other (...) stakeholders. If adopted, these recommendations would serve as a firm foundation for the establishment of a Good AI Society. (shrink)

É bem conhecida a oposição estabelecida por Kant entre experiência possível e dialética, na medida em que esta última é caracterizada como a “lógica da ilusão”. Ao mesmo tempo, o modo de pensar metafísico, que ocorre dialeticamente, em sentido kantiano, é uma tendência inevitável da razão, expressa na exigência formal de completude das categorias. Como o pensar, enquanto exercício livre da razão, é em si mesmo mais amplo do que a atividade de conhecer, própria do entendimento, o pensar contém o (...) conhecimento, embora este se qualifique pelas regras e pelos limites determinantes da objetividade. A pergunta que tentaremos formular é se essa relação continente-conteúdo não poderia configurar também uma dependência da experiência em relação ao raciocínio dialético, que estaria de algum modo indicada na função reguladora das idéias da razão. Nesse caso, a oposição formal entre conhecer e pensar seria inseparável da inclusão estrutural (dependência) da experiência no âmbito da razão. Na raiz do problema estaria talvez a tensão (dialética) entre a aspiração subjetiva de totalidade e as exigências objetivas de limitação e segmentação da experiência e a forma da experiência teria de ser finalmente concebida a partir de um fundo de inteligibilidade problemática. Dialectics and experienceThe separation of possible experience as objective knowledge and dialetics as a non-objective or non-theoretical knowledge is one of the most important aspects of kantian critical philosophy. But Kant also says that the activity of reason, as a pure thinking, has more amplitude than understanding knowledge. So we could say that theoric knowledge would depend on rational ( and non-theoretical) knowledge, as something contained in it. If we accept that, the consequence would be a relation of dependence between the form of objective knowledge and the background of a problematic – even doubtful – inteligible knowledge. (shrink)

El propósito de este texto es ofrecer una visión general de la relación entre nación e historia en los debates que se generaron por parte de los historiadores y otros intelectuales de las ciencias sociales a finales del siglo XIX y durante gran parte del siglo XX. La reflexión central que se plantea consiste entonces en estudiar y mostrar cómo al mismo tiempo que las naciones modernas eran objeto de un proceso de redefinición política, en el escenario intelectual de las (...) ciencias sociales, y en particular de los historiadores, fueron apareciendo también un conjunto de debates y obras que intentaban problematizar y someter a consideración las relaciones que pretendían establecerse entre la nación y la historia como un elemento que las justificaba. (shrink)

Wittgenstein’s concepts shed light on the phenomenon of schizophrenia in at least three different ways: with a view to empathy, scientific explanation, or philosophical clarification. I consider two different “positive” wittgensteinian accounts―Campbell’s idea that delusions involve a mechanism of which different framework propositions are parts, Sass’ proposal that the schizophrenic patient can be described as a solipsist, and a Rhodes’ and Gipp’s account, where epistemic aspects of schizophrenia are explained as failures in the ordinary background of certainties. I argue that (...) none of them amounts to empathic-phenomenological understanding, but they provide examples of how philosophical concepts can contribute to scientific explanation, and to philosophical clarification respectively. (shrink)

An important contribution to the foundations of probability theory, statistics and statistical physics has been made by E. T. Jaynes. The recent publication of his collected works provides an appropriate opportunity to attempt an assessment of this contribution.