The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth properties, is considered a dynamic conceptual entity in the cognitive sphere (Aerts, Broekaert, & Smets, [Foundations of Science 1999, 4, 115–132; International Journal of Theoretical Physics, 2000, 38, 3231–3239]; Aerts and colleagues[Dialogue in Psychology, 1999, 10; Proceedings of Fundamental Approachs to Consciousness, Tokyo ’99; Mind in Interaction]. Basically, the intrinsic contextuality of (...) the truth-value of the Liar Paradox is appropriately covered by the abstracted quantum mechanical approach. The formal details of the model are explicited here for the generalized case. We prove the possibility of constructing a quantum model of the m-sentence generalizations of the Liar Paradox. This includes (i) the truth–falsehood state of the m-Liar Paradox can be represented by an embedded 2m-dimensional quantum vector in a (2m) m -dimensional complex Hilbert space, with cognitive interactions corresponding to projections, (ii) the construction of a continuous ‘time’ dynamics is possible: typical truth and falsehood value oscillations are described by Schrödinger evolution, (iii) Kirchoff and von Neumann axioms are satisfied by introduction of ‘truth-value by inference’ projectors, (iv) time invariance of unmeasured state. (shrink)
We show that Bell inequalities can be violated in the macroscopic world. The macroworld violation is illustrated using an example involving connected vessels of water. We show that whether the violation of inequalities occurs in the microworld or the macroworld, it is the identification of nonidentical events that plays a crucial role. Specifically, we prove that if nonidentical events are consistently differentiated, Bell-type Pitowsky inequalities are no longer violated, even for Bohm's example of two entangled spin 1/2 quantum particles. We (...) show how Bell inequalities can be violated in cognition, specifically in the relationship between abstract concepts and specific instances of these concepts. This supports the hypothesis that genuine quantum structure exists in the mind. We introduce a model where the amount of nonlocality and the degree of quantum uncertainty are parameterized, and demonstrate that increasing nonlocality increases the degree of violation, while increasing quantum uncertainty decreases the degree of violation. (shrink)
We support the authors' claims, except that we point out that also quantum structure different from quantum probability abundantly plays a role in human cognition. We put forward several elements to illustrate our point, mentioning entanglement, contextuality, interference, and emergence as effects, and states, observables, complex numbers, and Fock space as specific mathematical structures.
In this paper we concentrate on the nature of the liar paradox asa cognitive entity; a consistently testable configuration of properties. We elaborate further on a quantum mechanical model (Aerts, Broekaert and Smets, 1999) that has been proposed to analyze the dynamics involved, and we focus on the interpretation and concomitant philosophical picture. Some conclusions we draw from our model favor an effective realistic interpretation of cognitive reality.
We put forward the hypothesis that there exist three basic attitudes towards inconsistencies within world views: (1) The inconsistency is tolerated temporarily and is viewed as an expression of a temporary lack of knowledge due to an incomplete or wrong theory. The resolution of the inconsistency is believed to be inherent to the improvement of the theory. This improvement ultimately resolves the contradiction and therefore we call this attitude the ‘regularising’ attitude; (2) The inconsistency is tolerated and both contradicting elements (...) in the theory are retained. This attitude integrates the inconsistency and leads to a paraconsistent calculus; therefore we will call it the paraconsistent attitude. (3) In the third attitude, both elements of inconsistency are considered to be false and the ‘real situation’ is considered something different that can not be described by the theory constructively. This indicates the incompleteness of the theory, and leads us to a paracomplete calculus; therefore we call it the paracomplete attitude. We illustrate these three attitudes by means of two ‘paradoxical’ situations in quantum mechanics, the wave-particle duality and the situation of non locality. (shrink)
Einstein Meets Magritte: An Interdisciplinary Reflection presents insights of the renowned key speakers of the interdisciplinary Einstein meets Magritte conference (1995, Brussels Free University). The contributions elaborate on fundamental questions of science, with regard to the contemporary world, and push beyond the borders of traditional approaches. All of the articles in this volume address this fundamental theme, but somewhere along the road the volume expanded to become much more than a mere expression of the conference's dynamics. The articles not only (...) deal with several scientific disciplines, they also confront these fields with the full spectrum of contemporary life, and become new science. As such, this volume presents a state-of-the-art reflection of science in the world today, in all its diversity. The contributions are accessible to a large audience of scientists, students, educators, and everyone who wants to keep up with science today. (shrink)
Throughout the biological and biomedical sciences there is a growing need for, prescriptive ‘minimum information’ (MI) checklists specifying the key information to include when reporting experimental results are beginning to find favor with experimentalists, analysts, publishers and funders alike. Such checklists aim to ensure that methods, data, analyses and results are described to a level sufficient to support the unambiguous interpretation, sophisticated search, reanalysis and experimental corroboration and reuse of data sets, facilitating the extraction of maximum value from data sets (...) them. However, such ‘minimum information’ MI checklists are usually developed independently by groups working within representatives of particular biologically- or technologically-delineated domains. Consequently, an overview of the full range of checklists can be difficult to establish without intensive searching, and even tracking thetheir individual evolution of single checklists may be a non-trivial exercise. Checklists are also inevitably partially redundant when measured one against another, and where they overlap is far from straightforward. Furthermore, conflicts in scope and arbitrary decisions on wording and sub-structuring make integration difficult. This presents inhibit their use in combination. Overall, these issues present significant difficulties for the users of checklists, especially those in areas such as systems biology, who routinely combine information from multiple biological domains and technology platforms. To address all of the above, we present MIBBI (Minimum Information for Biological and Biomedical Investigations); a web-based communal resource for such checklists, designed to act as a ‘one-stop shop’ for those exploring the range of extant checklist projects, and to foster collaborative, integrative development and ultimately promote gradual integration of checklists. (shrink)
Presented here is the German translation of Jan Patočka’s fragment Nitro a svět which was written in the 1940s and belongs to the so called „Strahov Papers“. The fragment reflects Patočka’s early attempts towards a thinking of subjectivity and the world. Thereby Patočka’s approach is phenomenological, but also integrates motives of German Idealism. The critical impact of the fragment lies in its orientation against the scientific biologism of its times.
We reproduce here forty previously unpublished letters sent by Jan Patočka to the Polish philosopher Krzysztof Michalski between 1973 and 1976. The letters to Michalski reveal his key role in motivating Patočka to formulate his ideas concerning the philosophy of history and present them first in a series of underground lectures in Prague and finally on paper in his last samizdat book, the Heretical Essays on the Philosophy of History.
To get distracted, to enclose and to give oneself. The Gesture of Transcendence in Jan Patočka The problem of transcendence can be traced throughout the whole work of Jan Patočka. The appeal to transcend our bonds to mere objectivity is a constant issue of his thought. It finds a new substantiation in the 1960s in his studies focusing on the meaning of the other as human being. The relation to the other person offers a special "occasion" or "place" of transcendence (...) and poses the challenge to transcend one's own particular setting. While in the mid-1960s Patočka maintains his earlier dramatic vocabulary to describe the process of transcendence, in the late 1960s his idiom becomes less vehement. Yet, it is precisely within this more "sober" framework that he symbolizes the process of transcendence with an emphatic turn to a "myth of the divine man" and its key metaphor of resurrection. To transcend means, for Patočka, always to liberate oneself from a state of self-distraction between things. However, in his late lectures, he briefly refers to a deeper layer, suggesting that this self-distraction has its "roots" in a self-enclosure or self-isolation, in the exclusive concentration on our own interests and in the illusion of our self-sufficiency. Transcendence, then, means to overcome this self-enclosure by means of a self-forgetting love. Are these rarely mentioned "roots" perhaps implicitly present in all Patočka's accounts of transcendence? (shrink)
This paper describes the work of the Polish logician Jan Kalicki (1922?1953). After a biographical introduction, his work on logical matrices and equational logic is appraised. A bibliography of his papers and reviews is also included.
Jan Łukasiewicz a élaboré un programme de recherche portant sur l’histoire de la logique. À son avis, la logique mathématique contemporaine (modern) est en continuité directe avec la logique formelle du passé. En conséquence, une interprétation correcte et fidèle des idées anciennes exige une application des outils logiques contemporains. Autrement dit, de bonnes études historiques sur la logique doivent consister à examiner la logique d’autrefois à travers les lunettes logiques contemporaine...
A unifying framework of probabilistic reasoning Content Type Journal Article Category Book Review Pages 1-4 DOI 10.1007/s11016-011-9573-x Authors Jan Sprenger, Tilburg Center for Logic and Philosophy of Science, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.
