Paradoxes in scientific cognition and nonclassical logics

I. Some Programmatic Comments. 1. Logic, Epistemology and the Unity of Science: An Encyclopedic Project in the Spirit of Neurath and Diderot Shahid Rahman and John Symons. 2. An International Encyclopedia of the Unified Sciences translated by John Symons and Ramon Alvarado) Otto Neurath. II. Game Theory and Independence Friendly Logic as a Unifying Framework. 3. Towards a Unity of the Human Behavioral Sciences Herbert Gintis. 4. Some Coloured Remarks on the Foundations of Mathematics in the 20th Century Gerhard Heinzmann. 5. Logical Versus Nonlogical Concepts: An Untenable Dualism? Jaakko Hintikka. 6. Semantic Games in Logic and Epistemology Ahti-Veikko Pietarinen. 7. IF Logic, Game-Theoretical Semantics and New Prospects for Philosophy of Science Ahti-Veikko Pietarinen and Gabriel Sandu. III. Unity and Plurality in Science and in Logic. 8. Concepts Structured through Reduction: A Structuralist Resource Illuminates the Consolidation-Long-Term Potentiation (LTP) Link John Bickle. 9. The Unity of Science and the Unity of Being: A Sketch of a Formal Approach C. Ulises Moulines. 10. Logical Pluralism and the Preservation of Warrant Greg Restall. 11. In Defence of the Dog: Response to Restall Stephen Read. 12. Normic Laws, Non-monotonic Reasoning, and the Unity of Science Gerhard Schurz. 13. The Puzzling Role of Philosophy in Life Sciences: Bases for a Joint Program for Philosophy and History of Science Juan Manuel Torres. 14. The Creative Growth of Mathematics Jean Paul Van Bendegem. 15. Quantum Logic and the Unity of Science John Woods and Kent Peacock. IV. The Logic of the Knowledge-Seeking Activities. 16. Belief Contraction, Anti-formulae and Resource Overdraft: Part II Deletion in Resource Unbounded Logics Dov Gabbay, Odinaldo Rodrigues and John Woods. 17. Reasoning about Knowledge in Linear Logic: Modalities and Complexity Mathieu Marion and Mehrnouche Sadrzadeh. 18. A Solution to Fitch's Paradox of Knowability Helge Ruckert. 19. Theories of Knowledge and Ignorance Wiebe van der Hoek, Jan Jaspars and Elias Thijsse. 20. Action-Theoretic Aspects of Theory Choice Heinrich Wansing. 21. Some Computational Constraints in Epistemic Logic Timothy Williamson. IV. Contributions from Non-Classical Logics. 22. The Need for Adaptive Logics in Epistemology Diderik Batens. 23. Logics for Qualitative Reasoning Paulo Veloso and Walter Carnielli. 24. Logic of Dynamics and Dynamics of Logic: Some Paradigm Examples Bob Coecke, David J. Moore and Sonja Smets. 25. Complementarity and Paraconsistency Newton C. A. Da Costa and Decio Krause. 26. Law, Logic, Rhetoric: a Procedural Model of Legal Argumentation Arno Lodder. 27. Essentialist Metaphysics in a Scientific Framework Ulrich Nortmann. Index.

Resumen

Background: This article explores the connections between the concept of anviksiki in Hindu philosophy and theories in cognitive science, and how these principles can be applied in modern education. Anviksiki, which focuses on critical thinking and deep reflection, is considered to have strong relevance to cognitive science concepts such as information processing, perception, and decision-making. Methods: The method used in this research is literature study and comparative analysis, by reviewing various literatures that discuss Hindu philosophy and cognitive science in depth. The analysis shows that anviksiki can provide an additional perspective in understanding how humans think and process information, especially in the context of moral and ethical reflection. Finding: In education, the principle of anviksiki that emphasises self-reflection and critical thinking can enrich students' learning process. This concept supports active learning methods that allow students to construct their own understanding, in a way that is in line with Piaget's theory of constructivism. In addition, cognitive science provides practical insights into information processing and memory, which can be used to design more effective teaching strategies. Conclusion: The conclusion of this study confirms that anviksiki can be integrated with cognitive science to create a holistic approach to education, which enriches intellectual, ethical and reflective aspects. By combining Hindu wisdom and cognitive science insights, education can support the development of balanced individuals, who are able to think critically and understand the moral consequences of their decisions. This research reveals that Anviksiki, as a philosophy of critical thinking in the Hindu tradition, has strong relevance to concepts in modern cognitive science, particularly in analytic approaches, logic, and deductive methods. Thus, the heritage of Hindu thought not only demonstrates traditional wisdom but also presents a philosophical foundation that supports contemporary cognitive exploration. Novelty/Originality of this article: This research offers a new perspective by bridging the ancient philosophy of Anviksiki with modern cognitive science, demonstrating the continuity of concepts in the critical thinking process involving logical analysis and deductive methods. It provides new insights in understanding the contribution of the Hindu tradition of thought to the development of cognitive theory today.

We present in this paper an alternative of modeling physical systems through a non-Classical logic namely the Paraconsistent Logic (PL) whose main feature is the revocation of the principle of non-contradiction. The Paraconsistent Annotated Logic with annotation of two values (PAL2v) is a type of PL and has in its theoretical structure the main feature of dealing with contradictions offering flexibility in drawing conclusions. Several works about applications of PAL2v have shown that such logic is able to provide us with an adequate treatment to uncertainties. Based on the foundations of the PAL2v we presented the ParaQuantum logic (PQL) with the goal of performing analysis of signals from information sources which model physical systems. The formalization of the concepts of the logics PQL, that it is represented in a Lattice, requires the considering of Paraquantum logical states ψ which are propagated through variations of the evidence Degrees µ and λ which come out from measurements performed in Observable Variables in the physical world. When we analyze the lattice of the PQL, we obtain equations which quantify values of physical quantities from where we obtain the effects of propagation of the Paraquantum logical states ψ. In this paper, we introduce the Paraquantum Factor of quantization hψ whose value is associated with a special logical state on the lattice which is identified with the Planck constant h. We conclude through these studies that the Paraquantum Logical Model based on the ParaQuantum logics PQL can link the several fields of the physical sciences by means of quantization of values. It is an innovative approach of formulating natural phenomena.

In this paper we examine up to which point Modern logic can be qualified as non-Aristotelian. After clarifying the difference between logic as reasoning and logic as a theory of reasoning, we compare syllogistic with propositional and first-order logic. We touch the question of formal validity, variable and mathematization and we point out that Gentzen’s cut-elimination theorem can be seen as the rejection of the central mechanism of syllogistic – the cut-rule having been first conceived as a modus Barbara by Hertz. We then examine the non-Aristotelian aspect of some non-classical logics, in particular paraconsistent logic. We argue that a paraconsistent negation can be seen as neo-Aristotelian since it corresponds to the notion of subcontrary in Boethius’ square of opposition. We end by examining if the comparison promoted by Vasiliev between non-Aristotelian logic and non-Euclidian geometry makes sense.

Para-consistent logic is a non-classical logic whose foundations allow the treatment of contradictions without invalidating the conclusions. This paper presented an attempt of using Annotated Para-consistent Analysis (APA) for supporting eXplained Artificial Intelligence (XAI) on Neural-Networks. For the study case, it was presented a situation where a binary classification model was able to correctly recognize one label but not the other with the form of the principle of explosion (p\(\wedge \lnot \)p). By plotting the linear output max-min scaled data into the paraconsistent reticulate, it was possible to properly understand that the selected architectures were being able to predict. This result is early support for using APA for Neural-Network XAI, corroborating with this paper hypothesis.

The issue of what consequences to draw from the existence of non-classical logical systems has been the subject of an interesting debate across a diversity of fields. In this paper the matter of alternative logics is considered with reference to a specific belief system and its propositions :the Azande are said to maintain beliefs about witchcraft which, when expressed propositionally, appear to be inconsistent. When the Azande have been presented with such inconsistencies, they either fail to see them as such or else accept them as non-problematical. Is our knowledge of logical truths a relative and culturally determined phenomenon, or is there some (transcendent) criterion that allows us to adjudicate between alternative logical systems? The authors propose an approach for resolving disputes about the status of Azande reasoning which assumes a paraconsistent framework, thus providing a new perspective on this debate

In this article we question the utility of the distinction between conceptual and nonconceptual content in cognitive science, and in particular, in the empirical study of visual perception. First, we individuate some difficulties in characterizing the notion of "concept" itself both in the philosophy of mind and cognitive science. Then we stress the heterogeneous nature of the notion of nonconceptual content and outline the complex and ambiguous relations that exist between the conceptual/nonconceptual duality and other pairs of notions, such as top---down/bottom-up and modular/nonmodular. Finally we look in greater detail at the proposal developed by Jacob and Jeannerod (Ways of seeing. The scopes and limits of visual cognition. Oxford, UK: Oxford University Press, 2003), who apply the notion of nonconceptual content to empirical research on visual perception. After reconstructing their point of view on concepts, we try to reject their major arguments in support of the conceptual/nonconceptual distinction, i.e. the compositionality of thought and the fineness of grain of percepts.

Mathematical logic is a discipline used in sciences and humanities with different point of view. Although in tertiary level computer science education it has a solid place, it does not hold also for secondary level education. We present a heterogeneous study both theoretical based and empirically based which points out the key role of logic in computer science, computer science education and knowledge representation. We focus on the key contrast of semantics and syntax, the resolution principle as a leading inference technique (giving also interesting non-clausal generalization of the rule). Further we discuss the possibilities of inclusion the non-classical (many-valued) logics in education together with the original generalization of the non-clausal resolution rule into fuzzy logic. The last part describes partial results of the research concerning the secondary education in the Czech Republic especially in the mathematical logic field. The generalization of the presented ideas entails the article.

Paradoxes have played an important role both in philosophy and in mathematics and paradox resolution is an important topic in both fields. Paradox resolution is deeply important because if such resolution cannot be achieved, we are threatened with the charge of debilitating irrationality. This is supposed to be the case for the following reason. Paradoxes consist of jointly contradictory sets of statements that are individually plausible or believable. These facts about paradoxes then give rise to a deeply troubling epistemic problem. Specifically, if one believes all of the constitutive propositions that make up a paradox, then one is apparently committed to belief in every proposition. This is the result of the principle of classical logical known as ex contradictione (sequitur) quodlibet – that anything and everything follows from a contradiction, and the plausible idea that belief is closed under logical or material implication (i.e. the epistemic closure principle). But, it is manifestly and profoundly irrational to believe every proposition and so the presence of even one contradiction in one's doxa appears to result in what seems to be total irrationality. This problem is the problem of paradox-induced explosion. In this paper it will be argued that in many cases this problem can plausibly be avoided in a purely epistemic manner, without having either to resort to non-classical logics for belief (e.g. paraconsistent logics) or to the denial of the standard closure principle for beliefs. The manner in which this result can be achieved depends on drawing an important distinction between the propositional attitude of belief and the weaker attitude of acceptance such that paradox constituting propositions are accepted but not believed. Paradox-induced explosion is then avoided by noting that while belief may well be closed under material implication or even under logical implication, these sorts of weaker commitments are not subject to closure principles of those sorts. So, this possibility provides us with a less radical way to deal with the existence of paradoxes and it preserves the idea that intelligent agents can actually entertain paradoxes.

Abstract. Many research works have been oriented to the formulation of different algorithms for estimating the paths in indoor environments from three-dimensional representations of space. The architectural configuration, the actions that take place within it, and the location of some objects in the space influence the paths along which is it possible to move, as they may cause visibility problems. To overcome the visibility issue, different methods have been proposed which allow to identify the visible areas and from a certain point of view, but often they do not take into account the user’s visual perception of the environment and not allow estimating how much may be complicated to follow a certain path. In the field of space syntax and cognitive science, it has been attempted to describe the characteristics of a building or an urban environment by the isovists and visibility graphs methods; some numerical properties of these representations allow to describe the space as for how it is perceived by a user. However, most of these studies are directed to analyze the environment in a two-dimensional space. In this paper we propose a method to evaluate in a quantitative way the complexity of a certain path within an environment represented by a three-dimensional point cloud, by the combination of some of the previously mentioned techniques, considering the space visible from a certain point of view, depending on the moving agent (pedestrian , people in wheelchairs, UAV, UGV, robot).

In this paper I urge friends of truth-value gaps and truth-value gluts—proponents of paracomplete and paraconsistent logics—to consider theories not merely as sets of sentences, but as pairs of sets of sentences, or what I call ‘bitheories,’ which keep track not only of what holds according to the theory, but also what fails to hold according to the theory. I explain the connection between bitheories, sequents, and the speech acts of assertion and denial. I illustrate the usefulness of bitheories by showing how they make available a technique for characterising different theories while abstracting away from logical vocabulary such as connectives or quantifiers, thereby making theoretical commitments independent of the choice of this or that particular non-classical logic. Examples discussed include theories of numbers, classes and truth. In the latter two cases, the bitheoretical perspective brings to light some heretofore unconsidered puzzles for friends of naive theories of classes and truth.

This paper concerns an alternative logic, called “quantum logic”, the general framework of which is presented by Peter Mittelstaedt in his contribution “Does Quantum Physics require a New Logic?”. Starting with the pragmatic possibilities of the speaker of a language about the properties of a quantum-physical system who is also an observer of the system, a proof process semantics can be developed and a formal language can be constituted, the internal structure of which gives raise to the “new” quantum logic.

From the Publisher: Biomedicine has become one of the best-modeled domains from several perspectives - artificial intelligence, psychology, and the social sciences; yet few studies have combined these points of view. In this book, the interdisciplinary strengths of cognitive science offer fresh insights into biomedical problem solving. Cognitive Science in Medicine presents current research that focuses on issues and results in applying techniques from cognitive science to problems in biomedicine. It includes material by researchers who have worked in both areas and is unique in linking models of physician knowledge with models of physician behavior. David Evans discusses issues of cognitive science in medicine in his introduction; and in a chapter with Cindy Gadd and Harry Pople, deals with the problem of managing coherence and context in medical problem-solving discourse. Vimla Patel, Evans, and Guy Groen provide experimental data that illuminates the role of biomedical knowledge in clinical reasoning; and Patel, Evans, and David Kaufman offer a cognitive science framework for analysis of clinical interviews. Other contributors and subjects include Clark Glymour on the empirical and representational issues in cognitive and medical science; Alan Lesgold on multilevel models of expertise; Arthur Elstein, James Dodd, and Gerald B. Holzman on the analysis of estrogen replacement decisions among residents; Kenneth R. Hammond, Elizabeth Frederick, Nichole Robillard, and Doreen Victor on the features of the student-teacher dialog in medicine; Naomi Rodolitz and William J. Clancey on tutoring for strategic knowledge; Paul J. Feltovich, Rand J. Spiro, and Richard L. Coulson on the foundationsof misunderstanding in established medical knowledge; John K. Vries, Evans, and Peretz Shoval on the development of semantic networks for medical information retrieval; and John Bruer, with a preface on the implications of cognitive-scientific studies for medical education. David A. Evans is Assistant Professor of Linguistics and Computer Science at Carnegie-Mellon University and Vimla L. Patel is Associate Professor of Medicine and Educational Psychology at McGill University. A Bradford Book.

In this article we present a theoretical framework and some models for assisting the conception of tactile communication devices. In order to propose relevant concepts and successful innovative products, designers need to anticipate as early as possible the user experience that will emerge from actual use of the product they are developing. The way the designer imagines the qualities of the product has strong consequences for the possible experience that will be available to the user. However, it is very difficult to accurately anticipate the actual experience of the user; and the lack of knowledge concerning the final user is particularly drastic in the case of high-technology applications, where the potentialities of the technology are hugely superior to the acceptability of the final users. In order to remedy this difficulty, this article presents research from the fields of design, cognitive science and Virtual Reality, in order to understand how lived experience is constituted by the use of a technological device. The aim of this research is to provide guidelines for anticipating user experience in the design process. We found that there are two kinds of perception over time: perceiving the other as part of environment, versus perceiving the activity of other perceiving me. It is by switching between these two kinds of perception that it becomes possible for one subject to understand the position from which the other subject perceives the scene. We call this process the constitution of a « point of view ». From this ability to constitute a system of points of view, the feeling of sharing a common space with another intentional being can emerge. Finally, we present the application of these considerations to the design of devices for interindividual interaction.