This book provides a general survey of the main concepts, questions and results that have been developed in the recent interactions between quantum information, quantum computation and logic. Divided into 10 chapters, the books starts with an introduction of the main concepts of the quantum-theoretic formalism used in quantum information. It then gives a synthetic presentation of the main “mathematical characters” of the quantum computational game: qubits, quregisters, mixtures of quregisters, quantum logical gates. Next, the book investigates the puzzling entanglement-phenomena (...) and logically analyses the Einstein–Podolsky–Rosen paradox and introduces the reader to quantum computational logics, and new forms of quantum logic. The middle chapters investigate the possibility of a quantum computational semantics for a language that can express sentences like “Alice knows that everybody knows that she is pretty”, explore the mathematical concept of quantum Turing machine, and illustrate some characteristic examples that arise in the framework of musical languages. The book concludes with an analysis of recent discussions, and contains a Mathematical Appendix which is a survey of the definitions of all main mathematical concepts used in the book. (shrink)

Unlike the standard Quantum Computational Logic, where the carrier of information is conventionally assumed to be only the last qubit over a sequence of many qubits, here we propose an extended version of the QCL where the number and the position of the target qubits are arbitrary.

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)

We propose a new interpretation of objective deterministic chances in statistical physics based on physical computational complexity. This notion applies to a single physical system (be it an experimental set--up in the lab, or a subsystem of the universe), and quantifies (1) the difficulty to realize a physical state given another, (2) the 'distance' (in terms of physical resources) from a physical state to another, and (3) the size of the set of time--complexity functions that are compatible with the physical (...) resources required to reach a physical state from another. (shrink)

In this article, we address fallacious analogical reasoning and the Metaphoric Fallacy to a Deductive Inference (MFDI), recently discussed by B. Lightbody and M. Berman (2010). We claim that the authors’ proposal to introduce a new fallacy is only partly justified. We also argue that, in some relevant cases, fallacious analogical reasoning involving metaphors is only affected by the use of quaternio terminorum.

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.

Knowledge representation is a central issue for Artificial Intelligence and the Semantic Web. In particular, the problem of representing n-ary relations in RDF-based languages such as RDFS or OWL by no means is an obvious one. With respect to previous attempts, we show why the solutions proposed by the well known W3C Working Group Note on n-ary relations are not satisfactory on several scores. We then present our abstract model for representing n-ary relations as directed labeled graphs, and we show (...) how this model gives rise to a new ontological pattern for the representation of such relations in the Semantic Web. To this end, we define PROL. PROL is an ontological language designed to express any n-ary fact as a parametric pattern, which turns out to be a special RDF graph. The vocabulary of PROL is defined by a simple RDFS ontology. We argue that the parametric pattern may be particularly beneficial in the context of the Semantic Web, in virtue of its high expressive power, technical simplicity, and faithful meaning rendition. Examples are also provided. (shrink)

Quantum theory is perhaps our best confirmed theory for a description of the physical properties of nature. On top of demonstrating great empirical effectiveness, many technological developments in the 20th century (such as the interpretation of the periodic table of elements, CD players, holograms, and quantum state teleportation) were only made possible with Quantum theory.Despite its success in the past decades, even today it still remains without a universally accepted interpretation.This book provides an interdisciplinary perspective on the question; 'What is (...) Quantum Mechanics talking about?', a question which continues to be one of the most fascinating and important questions in science.Using an interdisciplinary approach to foundational problems in Quantum Mechanics (QM), ranging from philosophical questions about the interpretation of QM to technical problems in quantum computation, this book explores quantum mechanics from different perspectives (physical, logical, philosophical and mathematical), by researchers from Europe, North America, and South America. (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)

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)

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)

In this Introduction we lay out the context of a ‘Continental philosophy of biology’ and suggest why Georges Canguilhem’s place in such a philosophy is important. There is not one single program for Continental philosophy of biology, but Canguilhem’s vision, which he referred to at one stage as ‘biological philosophy’, is a significant one, located in between the classic holism-reductionism tensions, significantly overlapping with philosophy of medicine, philosophy of technology and other themes moving away from the more common existential and (...) phenomenological motifs of post-war European thought. Chapters examine (among other themes) his relation to Lebensphilosophie, to authors such as Kant, Nietzsche and Marjorie Grene, and to current theoretical biology. (shrink)

In one of his last writings, Life: Experience and Science, Michel Foucault argued that twentieth-century French philosophy could be read as dividing itself into two divergent lines: on the one hand, we have a philosophical stream which takes individual experience as its point of departure, conceiving it as irreducible to science. On the other hand, we have an analysis of knowledge which takes into account the concrete productions of the mind, as are found in science and human practices. In order (...) to account for this division, Foucault opposed epistemologists such as Cavaillès and Canguilhem to phenomenologists such as Merleau-Ponty and Sartre but, also, and more particularly, he opposed Poincaré to Bergson. The latter was presented by Foucault as being the key-figure of the ?philosophy of experience? at the beginning of the twentieth century. Fifteen years later, in his Deleuze and in the Logics of Worlds, Alain Badiou again uses this dual structure in his interpretation of the past hundred years of French thought. He employs a series of oppositional couples: himself and Deleuze, Lautmann and Sartre, and, finally, Brunschvicg and Bergson. On the one hand a ?mathematical Platonism? and on the other a ?philosophy of vital interiority.? This Manichean reading of philosophy, and the strategic use of the figure of Bergson has, itself, a long tradition. It was also proposed by Althusser who, following Bachelard, opposed his standpoint to any form of ?empiricism.? Althusser developed his thought from a tradition of Marxist thinkers and ideologists, which included Politzer's and Nizan's critique of bourgeois philosophy and, even before that, neo-Kantians such as the philosophers of the Revue de métaphysique et de morale. The aim of this essay is to deconstruct and to put into its precise context of production this series of genealogies which entails the mobilization of Bergsonism and of the name ?Bergson.? By doing so, I hope to weight the importance of Bergsonism in twentieth-century French philosophy, in both its ?positive? and its ?negative? aspect. The essay will proceed regressively, taking into account figures such as Althusser, Badiou, Deleuze, Foucault, Canguilhem, Cavaillès, Sartre, Merleau-Ponty, but also Polizer, Brunschvicg and Alain. The conclusion of the essay is an attempt at reading the ?Bergson renaissance? in the light of new discoveries in genetics and the cognitive sciences and to tie it to the renewal of studies in the history of French philosophy. (shrink)

In the literature there are two well-established but opposite readings of Arendt: as an agonistic theorist and as a deliberative one. In between these two positions a smaller number of scholars have argued that in Arendt these two dimensions can to a large extent be reconciled. This paper follows this third path but tries to bring it one step further. In particular, it defends the idea that those scholars who have proposed this third reading of Arendt have fallen short of (...) revealing the degree to which deliberation and agonism are, for her, interwoven. Through an original reading of Arendt’s views on judgment, persuasion, distinction and Eichmann’s banality, the paper clarifies why, for her, agonism and deliberation are not only compatible but actually mutually dependent. In other words, it clarifies why she believes that there can be no deliberation without agonism and no agonism without deliberation. (shrink)

Coherent-ambiguity aversion is defined within the smooth-ambiguity model as the combination of choice-ambiguity and value-ambiguity aversion. Five ambiguous decision tasks are analyzed theoretically, where an individual faces two-stage lotteries with binomial, uniform, or unknown second-order probabilities. Theoretical predictions are then tested through a 10-task experiment. In tasks 1–5, risk aversion is elicited through both a portfolio choice method and a BDM mechanism. In tasks 6–10, choice-ambiguity aversion is elicited through the portfolio choice method, while value-ambiguity aversion comes about through the (...) BDM mechanism. The behavior of over 75 % of classified subjects is in line with the KMM model in all tasks 6–10, independent of their degree of risk aversion. Furthermore, the percentage of coherent-ambiguity-averse subjects is lower in the binomial than in the uniform and in the unknown treatments, with only the latter difference being significant. The most part of coherent-ambiguity-loving subjects show a high risk aversion. (shrink)

Notwithstanding the recent prominence of the term “problem” in the humanities, few scholars have analysed its history. This essay tries to partially fill that lack, principally covering the period from late modernity through to the 1960s, in order to understand the role that the term plays in “Continental” philosophy, with special emphasis on the writings of Gilles Deleuze. This analysis focuses on the strategies employed by different agents to define “philosophical” problems, or “philosophical” ways of posing problems. The term, originally (...) used in antiquity by knowledge-producers located in an autonomous position, implied an idea of cognition oscillating between production and reproduction. Once the term escaped the context of geometry, it was involved in symbolic struggles that radicalized during modernity. The Kantians placed “philosophy” in a supposedly neutral position of science treating “the problem of all the problems” and invented a new genre, the “history of philosophy,” focusing on the analysis of “philosophical problems.” This approach had great institutional success in the German and French universities and clashed, during the twentieth century, with another usage of philosophy as a practice of “dissolution of problems,” developed in the United Kingdom and the Austro-Habsburg Empire. (shrink)

We analyze the results from three different risk attitude elicitation methods. First, the broadly used test by Holt and Laury, HL, second, the lottery-panel task by Sabater-Grande and Georgantzis, SG, and third, responses to a survey question on self-assessment of general attitude towards risk. The first and the second task are implemented with real monetary incentives, while the third concerns all domains in life in general. Like in previous studies, the correlation of decisions across tasks is low and usually statistically (...) non-significant. However, when we consider only subjects whose behavior across the panels of the SG task is compatible with constant relative risk aversion, the correlation between HL and self-assessed risk attitude becomes significant. Furthermore, the correlation between HL and SG also increases for CRRA-compatible subjects, although it remains statistically non-significant. (shrink)

Artefacts do not always do what they are supposed to, due to a variety of reasons, including manufacturing problems, poor maintenance, and normal wear-and-tear. Since software is an artefact, it should be subject to malfunctioning in the same sense in which other artefacts can malfunction. Yet, whether software is on a par with other artefacts when it comes to malfunctioning crucially depends on the abstraction used in the analysis. We distinguish between “negative” and “positive” notions of malfunction. A negative malfunction, (...) or dysfunction, occurs when an artefact token either does not or cannot do what it is supposed to. A positive malfunction, or misfunction, occurs when an artefact token may do what is supposed to but, at least occasionally, it also yields some unintended and undesirable effects. We argue that software, understood as type, may misfunction in some limited sense, but cannot dysfunction. Accordingly, one should distinguish software from other technical artefacts, in view of their design that makes dysfunction impossible for the former, while possible for the latter. (shrink)

In this paper Giuseppe Bianco analyzes the ideological and epistemological coordinates and the space of possibilities proper to the cluster of philosophy students of which Tournier was part between 1943 and 1948; to do so he reconstructs their evolution in a context dominated by the currents of Neo-Scholasticism, Personalism, phenomenology, Marxism, and Existentialism. Finally, he focuses on the importance of Jean-Paul Sartre for these young people, underlining their particular interpretation of his work.

Even more than for other treatments, great importance must be given to informed consent in the case of electroconvulsive therapy. In a percentage of cases, the symbolic connotation of the treatment, even if mostly and intrinsically negative, may actually be a determining factor in the patient’s motives for giving consent. On an ethical and medicolegal level, the most critical point is that concerning consent to the treatment by a psychotic subject with a severely compromised ability to comprehend the nature and (...) objective of the proposed therapy, but who nonetheless expresses his consent, for reasons derived from delusional thoughts. In fact, this situation necessarily brings to light the contradiction between an explicit expression of consent, a necessary formality for the commencement of therapy, and the validity of this consent, which may be severely compromised due to the patient’s inability to comprehend reality and therefore to accept the proposal of treatment, which is intrinsic to this reality. With the use of an electric current, the symbolic experience associated with anaesthesia, and the connection to convulsions, ECT enters the collective consciousness. In relation to this, ECT is symbolic of these three factors and hooks on to the thoughts, fears, feelings and expectations of delusional patients. These are often exemplified in the violent intervention of the persecutor in the patient with schizophrenia, the expected punishment for the ’error’ committed for which the depressed patient blames himself and the social repression of the maniacal patient’s affirmation of his inflated self-esteem. (shrink)

This article will attempt to show that from the beginning of the letter of Eusebius of Nicodemia to Paulinus of Tyre, the meaning of ὁμοούσιος should be sought in the opposition on the part of the Council of Nicea to the divisive doctrine of hypostases by Arius and his followers. The assertion of the similarity or identity of nature or ousia between the Father and the Son that ὁμοούσιος suggests is traceable to the teaching of Alexander of Alexandria, but also (...) of Eusthatius of Antioch, so that it could be thought that in Nicea a convergence between the two major opponents of Arius could have taken place, in the same way in which it had occurred over the Antiochene formula of 325. Analysis of the doctrine of ὁμοούσιος by Athanasius confirms that the term was opposed to the divisive interpretation of the hypostases within Arianism. The second part of the article, takes into consideration the study on the interpretation of the Nicene ὁμοούσιος proposed by P. F. Beatrice. The Author argues that Beatrice’s thesis, which attempts to trace the introduction of the term in the Nicene Creed back exclusively to Constantine, with the agreement of Eusebius of Caesarea, is not backed by the documentation at our disposal. (shrink)

This study intends to show how the essential elements in the debate over the divinity of the Son provoked by Arianism are already present within the Alessandrian Church during the first decades of the 3rd century. From the works of Origen it becomes apparent that his teaching on the eternity of the Logos intends to oppose those who asserted a temporal beginning thus separating the Logos from the divinity of the Father, which allows us to define them as radical supporters (...) of the theology of the Logos. Against this doctrine, there is an identified opposition which probably utilized the term ὁμοούσιος to indicate to the contrary the divinity of the Son; nevertheless Origen, while proposing that the Son is generated from the ousia of the Father, does not share this teaching because in his theology the Son remains subordinate to the Father. (shrink)

Henri Bergson (1859–1940), the most prominent member of nineteenth-century French spiritualism, is the first philosopher who explicitly defined philosophy as a practice which consists in posing problems anew and in creating concepts. In this article, I will try to reconstruct the progressive importance acquired by the terms ‘problem’ and ‘concept’ in nineteenth-century French philosophy and how they combined in Bergson’s theories about creativity, invention and novelty. I will argue that Bergson’s conception of philosophy as a creative intellectual practice was the (...) result of a negotiation, inside a pre-existent spiritualist framework, between, on the one hand, neo-Kantianism and, on the other hand, evolutionism which strongly influenced empirical psychology and the emerging social sciences. Bergson’s solution, influenced by the evolution of mathematics and literary theory, was just one of the possible options, and the main alternative to a new form of transcendental philosophy. (shrink)

The moving spotlight account (MS) is a view that combines an eternalist ontology and an A-theoretic metaphysics. The intuition underlying MS is that the present time is somehow privileged and experientially vivid, as if it were illuminated by a moving spotlight. According to MS-theorists, a key reason to prefer MS to B-theoretic eternalism is that our experience of time supports it. We argue that this is false. To this end, we formulate a new family of positions in the philosophy of (...) time, which differ from MS in that, intuitively, they admit a plurality of moving spotlights. We argue that these ‘deviant’ variants of MS cannot be dismissed as conceptually incoherent, and that they are as well-supported by our experience as is MS. One of these variants, however, is consistent with the B-theory. Thus, if our experience of time supports MS, then it supports the B-theory as well. (shrink)

Résumé Cet article cherche à éclairer l’élection de Martial Gueroult (1891-1976) à la chaire d’Histoire et technologie des systèmes philosophiques en 1951, et, indirectement, le succès de son approche « structurale » de l’histoire de la philosophie. Ceux qui occupaient des rôles clés dans la gestion de l’économie disciplinaire des sciences humaines ne devaient pas contredire dans leur travaux les axiomes qui avaient réglé la pratique de l’histoire de la philosophie depuis le début du XIXe siècle tout en faisant montre (...) d’innovation dans ce champ. Dans un premier temps nous résumons la méthode historiographique proposée par Gueroult ; un deuxième temps l’inscrit dans une tradition d’historiographie de la philosophie ; le troisième temps situe sommairement la pratique de l’histoire de la philosophie au Collège de France et à la Sorbonne ; dans de quatrième et cinquième temps nous décrivons les rapporteurs et les candidats lors de l’élection au Collège de France, et les pièces pertinentes ; enfin nous considérons les stratégies adoptées pendant la campagne qui ont pu déterminer le résultat de l’élection. (shrink)