The debate about constructivism in physics has led to different kinds of questions that can be conventionally framed in two classes. One concerns the mathematics that is considered for the theoretical development of physics. The other is concerned with the experimental parts of physical theories. It is unnecessary to observe that the intersection between our two classes of problems is far from being empty. In this paper we will mainly deal with topics belonging to the second class. However, let us (...) briefly mention some important problems that have been debated in the framework of our first class. For instance, the following: to what extent do the undecidability and incompleteness results of classical mathematics affect fragments of physical theories, in such way as to have a “real physical meaning”? are the mathematical arguments that seem to be essential for physics justifiable in the framework of traditional mathematical constructivism?The first question has recently been investigated by Pitowski, Penrose, da Costa, Doria, Mundici, Svozil and others. As expected by most logicians, one can construct undecidable sentences whose physical meaning seems to be hardly questionable. This happens both in classical and in quantum mechanics. (shrink)

Constructibility and complexity play central roles in recent research in computer science, mathematics and physics. For example, scientists are investigating the complexity of computer programs, constructive proofs in mathematics and the randomness of physical processes. But there are different approaches to the explication of these concepts. This volume presents important research on the state of this discussion, especially as it refers to quantum mechanics. This `foundational debate' in computer science, mathematics and physics was already fully developed in 1930 in the (...) Vienna Circle. A special section is devoted to its real founder Hans Hahn, referring to his contribution to the history and philosophy of science. The documentation section presents articles on the early Philipp Frank and on the Vienna Circle in exile. Reviews cover important recent literature on logical empiricism and related topics. (shrink)

The total and the sharp character of orthodox quantum logic has been put in question in different contexts. This paper presents the basic ideas for a unified approach to partial and unsharp forms of quantum logic. We prove a completeness theorem for some partial logics based on orthoalgebras and orthomodular posets. We introduce the notion of unsharp orthoalgebra and of generalized MV algebra. The class of all effects of any Hilbert space gives rise to particular examples of these structures. Finally, (...) we investigate the relationship between unsharp orthoalgebras, generalized MV algebras, and orthomodular lattices. (shrink)

Fuzzy intuitionistic quantum logics (called also Brouwer-Zadeh logics) represent to non standard version of quantum logic where the connective not is split into two different negation: a fuzzy-like negation that gives rise to a paraconsistent behavior and an intuitionistic-like negation. A completeness theorem for a particular form of Brouwer-Zadeh logic (BZL 3) is proved. A phisical interpretation of these logics can be constructed in the framework of the unsharp approach to quantum theory.

This volume includes recent contributions to the philosophy of science from a historical point of view and of the highest topicality: the range of the topics covers all fields in the philosophy of the science provided by authors from around the world focusing on ancient, modern and contemporary periods in the development of the science philosophy. This proceedings is for the scientific community and students at graduate level as well as postdocs in this interdisciplinary field of research.

Two different generalizations of Brouwer–Zadeh posets (BZ posets) are introduced. The former (called pre-BZ poset) arises from topological spaces, whose standard power set orthocomplemented complete atomic lattice can be enriched by another complementation associating with any subset the set theoretical complement of its topological closure. This complementation satisfies only some properties of the algebraic version of an intuitionistic negation, and can be considered as, a generalized form of a Brouwer negation. The latter (called degenerate BZ poset) arises from the so-called (...) special effects on a Hilbert space. It is shown that the standard Brouwer negation for effect operators produces a degenerate BZ poset with respect to the order induced from the partial sum operation. (shrink)

The reconstruction of ensemble d–f of the Akhmîm Papyrus, better known as the Strasbourg Papyrus, which attests approximately eighteen of the over seventy new lines of Empedocles’ physical poem, has drawn the attention of scholars over recent years. Thanks to the good condition of the papyrus and the coincidence with two Empedoclean lines, already known from the indirect tradition, ensemble d–f 1–10a presents a well-restored text and an intelligible sense. In contrast, because of the damaged state of the papyrus, the (...) restoration of d–f 10b–18 is more complicated. These lines seem to describe a life-generative process, but what process was Empedocles talking about? Some resemblances between these papyrus lines and the lines of another Empedoclean fragment, DK 31 B 62, have suggested to scholars, notably to A. Martin and O. Primavesi in 1999 and M. Rashed in 2011, that the lines of the papyrus depict, just like DK 31 B 62, the generation of whole-natured beings. Other scholars, however, such as R. Janko in 2004 and A. Laks and G.W. Most in 2016, show more caution and leave the possibility open that Empedocles is here talking about the generation of something else. (shrink)

Contents: PART 1. MODELS IN SCIENTIFIC PROCESSES. Joseph AGASSI: Why there is no theory of models. Ma??l??gorzata CZARNOCKA: Models and symbolic nature of knowledge. Adam GROBLER: The representational and the non-representational in models of scientific theories. Stephan HARTMANN: Models as a tool for the theory construction; some strategies of preliminary physics. William HERFEL: Nonlinear dynamical models as concrete construction. Elzbieta KA??L??USZY??N??SKA: Styles of thinking. Stathis PSILLOS: The cognitive interplay between theories and models: the case of 19th century optics. PART 2. (...) TOOLS OF SCIENCE. Nancy D. CARTWRIGHT, Towfic SHOMAR, Maricio SUAREZ: The tool-box of science. Javier ECHEVERRIA: The four contexts of scientific activity. Katline HAVAS: Continuity and change; kinds of negation in scientific progress. Matthias KAISER: The independence of scientific phenomena. W??l??adys??l??aw KRAJEWSKI: Scientific meta-philosophy. Ilkka NIINILUOTO: The emergence if scientific specialities: six models. Leszek NOWAK: Antirealism, realism and idealization. Rinat M. NUGAYEV: Classic, modern and postmodern scientific unification. Veikko RANTALA: Translation and scientific change. Gerhard SCHURZ: Theories and their applications - a case of nonmonotonic reasoning. Witold STRAWI??N??SKI: The unity of science today. Vardan TOROSIAN: Are the ethic and logic of science compatible. PART 3. UNSHARP APPROACHES IN SCIENCE. Ernest W. ADAMS: Problems and prospects in a theory of inexact first-order theories. Wolfgang BALZER and Gerhard ZOUBEK: On the comparison of approximative empirical claims. Gianpierro CATTANEO, Maria Luisa DALLA CHIARA, Roberto GIUNTINI: The unsharp approaches to quantum theory. Theo A.F. KUIPERS: Falsification versus efficient truth approximation. Bernhard LAUTH: Limiting decidability and probability. Jaros??l??aw PYKACZ: Many-valued logics in foundations of quantum mechanics. Roman R. ZAPATRIN: Logico-algebraic approach to spacetime quantization. (shrink)

Le volume rassemble 25 études concernant la cosmologie médiévale, abordée à travers ses diverses composantes, à l’intérieur d’une fourchette chronologique allant de Calcidius jusqu’au XIVe siècle. Dix contributions sont consacrées à des questions de cosmologie hébraïque et islamique, traitant en particulier de Gersonide (R. Gatti), Maïmonide (L. Pepi), Avicenne (C. Di Martino, O. Lizzini), Sohravardî (I. Panzeca), Qûnawî (P. Spallino), les Frères de la Pureté (C. Baffioni) ainsi qu’aux interférences qui existent entre moyen âge islamique et latin : la grande (...) question de la cosmologie alchimique (M. Pereira), des textes traduits comme le De secretis naturae (P. Travaglia), la doctrine de la grande année dans Thebit et Pietro d’Abano (F. Seller). Les travaux de E.S. Mainoldi et de R. Gambino consacrent une large place à l’influence de la patristique grecque sur la pensée occidentale. D’autres études présentent le développement de la pensée cosmologique et scientique latine à partir de Calcidius (C. Militello), par l’intermédiaire d’Adélard de Bath (P. Palmeri), de Guillaume de Conches (G. Pellegrino) et d’autres documents divers (A. Tarabochia Canavero) jusqu’à l’avènement de l’aristotélisme physique, en particulier dans les commentaires universitaires aux Météorologiques (G. Fioravanti), au De caelo (C.A. Musatti, A. Vella) et chez Dante (M. Gallarino, P. Falzone). Quant à la littérature scientifique en langue vulgaire, elle est représentée par Restoro d’Arezzo (U. Villani-Lubelli) et Raymond Lull (J.Gayà). La communication de G. Alliney est dédiée à des questions de méthode historiographique, tandis que la contribution magistrale de Tullio Gregory sur “Cosmogonie et cosmologies chrétiennes” reconstitue de manière idéale l’ensemble des liens constituant les coordonnées générales de l’ensemble de la problématique abordée sous ses différentes facettes par les auteurs du volume. (shrink)

Paraconsistent quantum logics are weak forms of quantum logic, where the noncontradiction and the excluded-middle laws are violated. These logics find interesting applications in the operational approach to quantum mechanics. In this paper, we present an axiomatization, a Kripke-style, and an algebraic semantical characterization for two forms of paraconsistent quantum logic. Further developments are contained in Giuntini and Greuling's paper in this issue.

Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. The basic algebraic properties of this system have been studied in Dalla Chiara et al. (Foundations of Physics 39(6):559–572, 2009), where we have introduced the notion of Shi-Aharonov quantum computational structure. In this paper we propose an algebraic abstraction from the Hilbert-space quantum computational structures, by introducing the notion of Toffoli-Hadamard algebra. From an intuitive (...) point of view, such abstract algebras represent a natural quantum generalization of both classical and fuzzy-like structures. (shrink)

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)

The characteristic holistic features of the quantum theoretic formalism and the intriguing notion of entanglement can be applied to a field that is far from microphysics: logical semantics. Quantum computational logics are new forms of quantum logic that have been suggested by the theory of quantum logical gates in quantum computation. In the standard semantics of these logics, sentences denote quantum information quantities: systems of qubits (quregisters) or, more generally, mixtures of quregisters (qumixes), while logical connectives are interpreted as special (...) quantum logical gates (which have a characteristic reversible and dynamic behavior). In this framework, states of knowledge may be entangled, in such a way that our information about the whole determines our information about the parts; and the procedure cannot be, generally, inverted. In spite of its appealing properties, the standard version of the quantum computational semantics is strongly “Hilbert-space dependent”. This certainly represents a shortcoming for all applications, where real and complex numbers do not generally play any significant role (as happens, for instance, in the case of natural and of artistic languages). We propose an abstract version of quantum computational semantics, where abstract qumixes, quregisters and registers are identified with some special objects (not necessarily living in a Hilbert space), while gates are reversible functions that transform qumixes into qumixes. In this framework, one can give an abstract definition of the notions of superposition and of entangled pieces of information, quite independently of any numerical values. We investigate three different forms of abstract holistic quantum computational logic. (shrink)

A vivid and comprehensive picture of the current state of research in all directions of logic and philosophy of science. The book presents a wide combination of papers containing relevant technical results in the foundations of science and papers devoted to conceptual analyses, deeply rooted in advanced present-day research. Audience: The volume is attractive both for specialists in foundational questions and scholars interested in general epistemology.

In recent times, a particular attention has been devoted to thesignificance of Quantum Theory for other disciplines. The articlescollected in this issue discuss some interesting cases,characterized by an interaction between Quantum Theory andother fields. Some basic notrons of the mathematical formalismof the theory are here summarized.

How are abstract concepts and musical themes recognized on the basis of some previous experience? It is interesting to compare the different behaviors of human and of artificial intelligences with respect to this problem. Generally, a human mind that abstracts a concept (say, table) from a given set of known examples creates a table-Gestalt: a kind of vague and out of focus image that does not fully correspond to a particular table with well determined features. A similar situation arises in (...) the case of musical themes. Can the construction of a gestaltic pattern, which is so natural for human minds, be taught to an intelligent machine? This problem can be successfully discussed in the framework of a quantum approach to pattern recognition and to machine learning. The basic idea is replacing classical data sets with quantum data sets, where either objects or musical themes can be formally represented as pieces of quantum information, involving the uncertainties and the ambiguities that characterize the quantum world. In this framework, the intuitive concept of Gestalt can be simulated by the mathematical concept of positive centroid of a given quantum data set. Accordingly, the crucial problem “how can we classify a new object or a new musical theme (we have listened to) on the basis of a previous experience?” can be dealt with in terms of some special quantum similarity-relations. Although recognition procedures are different for human and for artificial intelligences, there is a common method of “facing the problems” that seems to work in both cases. (shrink)

In contemporary science uncertainty is often represented as an intrinsic feature of natural and of human phenomena. As an example we need only think of two important conceptual revolutions that occurred in physics and logic during the first half of the twentieth century: (1) the discovery of Heisenberg’s uncertainty principle in quantum mechanics; (2) the emergence of many-valued logical reasoning, which gave rise to so-called ‘fuzzy thinking’. I discuss the possibility of applying the notions of uncertainty, developed in the framework (...) of quantum mechanics, quantum information and fuzzy logics, to some problems of political and social sciences. (shrink)

There has been a great deal of interaction among game theorists, philosophers and logicians in certain foundational problems concerning rationality, the formalization of knowledge and practical reasoning, and models of learning and deliberation. This volume brings together the work of some of the pre-eminent figures in their respective disciplines, all of whom are engaged in research at the forefront of their fields. Together they offer a conspectus of the interaction of game theory, logic and epistemology in the formal models of (...) knowledge, belief, deliberation and learning, and in the relationship between Bayesian decision theory and game theory, as well as between bounded rationality and computational complexity. (shrink)