Science does not exist in vacuum; it arises and works in context. Ground-breaking achievements transforming the scientific landscape often stem from philosophical thought, just as symbolic logic and computer science were born from the early analytic philosophy, and for the very reason they impact our global worldview as a coherent whole as well as local knowledge production in different specialised domains. Here we take first steps in elucidating rich philosophical contexts in which Samson Abramsky’s far-reaching work centring around categorical science (...) as a new kind of science may be placed, explicated, and articulated. We argue, inter alia, that Abramsky’s work, as a whole, may be construed as demonstrating the categorical unity of science, or rather the sciences, in a mathematically rigorous, down-to-earth manner, which has been a salient feature of his work. At the same time we trace his intellectual history, leading from duality, to intensionality, and to contextuality, and place it in a broader context of philosophy beyond the analytic-continental divide, namely towards the reintegration of them as in the post-analytic tradition. Besides, we address issues in philosophy of category theory, such as the foundational autonomy of category theory and the (presumably two) dogmas of set-theoretical foundationalism, which Abramsky actually touch upon in one of his few philosophically inclined works. As to philosophy of category theory, we also address categorical structuralism as higher-order structuralism, categorical epistemology as elucidating higher-order meta-laws, and categorical ontology as allowing for reduction of ontological commitment via structural realism, the structuralist resolution of Benaceraff’s dilemma, and the pluralistic multiverse view of science as opposed to the set-theoretical reductionist ‘universe’ view. We conclude by speculating about the existence of the Oxford School of (Pluralistic) Unified Science as opposed to the Vienna Circle of (Monistic) Unified Science and to the Stanford School of (Pluralistic) Disunified Science; Categorical Unified Science may potentially allow us to reconcile the two camps on the unity and disunity of science whilst doing justice to both of them. Categorical unity arguably allows for unification via epistemological and ontological networking, and via knowledge transfer thus enabled, rather than unification via the reduction of everything and every truth to a single foundationalist framework, whilst taking at face value disunity, plurality, and diversity, and their significance in science and in human civilisation as a whole. (shrink)

Wittgenstein’s philosophy of mathematics is often devalued due to its peculiar features, especially its radical departure from any of standard positions in foundations of mathematics, such as logicism, intuitionism, and formalism. We first contrast Wittgenstein’s finitism with Hilbert’s finitism, arguing that Wittgenstein’s is perspicuous or surveyable finitism whereas Hilbert’s is transcendental finitism. We then further elucidate Wittgenstein’s philosophy by explicating his natural history view of logic and mathematics, which is tightly linked with the so-called rule-following problem and Kripkenstein’s paradox, yielding (...) vital implications to the nature of mathematical understanding, and to the nature of the certainty and objectivity of mathematical truth. Since the incompleteness theorems, foundations of mathematics have mostly lost their philosophical driving force, and anti-foundationalism has become prevalent and pervasive. Yet new foundations have nevertheless emerged and come into the scene, namely categorical foundations. We articulate the foundational significance of category theory by explicating three forms of foundations, i.e., global foundations, local foundations, and conceptual foundations. And we explore the possibility of categorical unified science qua pluralistic unified science, arguing for the categorical unity of science on both mathematical and philosophical grounds. We then turn to an issue in conceptual foundations of mathematics, namely the nature of the concept of space. We elucidate Wittgenstein’s intensional conception of space in relation to Brouwer’s theory of space continua and to the modern conception of space as point-free structure in category theory and algebraic geometry. We finally give a bird’s-eye view of mathematical philosophy from a Wittgensteinian perspective, and further sheds new light on Wittgenstein’s constructive structuralism and his view of incompleteness and contradictions in mathematics. (shrink)

Wittgenstein’s philosophy of mathematics is often devalued due to its peculiar features, especially its radical departure from any of standard positions in foundations of mathematics, such as logicism, intuitionism, and formalism. We first contrast Wittgenstein’s finitism with Hilbert’s finitism, arguing that Wittgenstein’s is perspicuous or surveyable finitism whereas Hilbert’s is transcendental finitism. We then further elucidate Wittgenstein’s philosophy by explicating his natural history view of logic and mathematics, which is tightly linked with the so-called rule-following problem and Kripkenstein’s paradox, yielding (...) vital implications to the nature of mathematical understanding, and to the nature of the certainty and objectivity of mathematical truth. Since the incompleteness theorems, foundations of mathematics have mostly lost their philosophical driving force, and anti-foundationalism has become prevalent and pervasive. Yet new foundations have nevertheless emerged and come into the scene, namely categorical foundations. We articulate the foundational significance of category theory by explicating three forms of foundations, i.e., global foundations, local foundations, and conceptual foundations. And we explore the possibility of categorical unified science qua pluralistic unified science, arguing for the categorical unity of science on both mathematical and philosophical grounds. We then turn to an issue in conceptual foundations of mathematics, namely the nature of the concept of space. We elucidate Wittgenstein’s intensional conception of space in relation to Brouwer’s theory of space continua and to the modern conception of space as point-free structure in category theory and algebraic geometry. We finally give a bird’s-eye view of mathematical philosophy from a Wittgensteinian perspective, and further sheds new light on Wittgenstein’s constructive structuralism and his view of incompleteness and contradictions in mathematics. (shrink)

Teaching has been one of the central themes in educational research. Not only empirical researchers of education but also philosophers of education inquire into the activity. Philosophers used to analyse the concept of teaching. The merely analytic approach, however, is no longer the main one in educational research. Will philosophical consideration of teaching, then, never contribute to our educational activity or any other activities in our life at all? In order to explore the possibilities for philosophical consideration of teaching, I (...) will examine three philosophers' distinction between teaching and telling. The philosophers are Israel Scheffler, Karatani Kojin, and Ludwig Wittgenstein. I will conclude that Wittgenstein deconstructs the distinction between teaching and telling, and that he requires us to change our attitude to the recognition of the others. (shrink)

This paper discusses what constitutes good teaching, taking as its cue the ‘aesthetic’ concept treated in everyday aesthetics and ‘internal good’ accounted by McIntyre. Teaching is viewed as practice, not merely as a basic action, due to its epistemological nature as everyday work. What everyday aesthetics teaches us is that even in the practice of teaching, sensory experiences such as comfort, familiarity, discomfort, ordinariness, etc. can be viewed as aesthetic experience. This kind of aesthetic experience constitute intuition supporting ’good teaching’ (...) that confirmed by examining Dreyfus et al. This ‘good teaching’ sensitivity is not specific to the individual practitioner, but is considered to be an ‘in-practice value (internal good?)’ (McIntyre) shared by the community of practice. From the aesthetic perspective, this value could be called ‘aesthetic value in practice’. In the teaching community of practice, ‘good teaching’ is both ‘beautiful teaching’ and ‘ethically good’ teaching. Teaching should be seen as a relational practice, and for this reason, The Ethico-Aesthetics of Teaching should be constructed. (shrink)

It has long been thought that transmembrane cell‐surface receptors, such as receptor tyrosine kinases and cytokine receptors, among others, are activated by ligand binding through ligand‐induced dimerization of the receptors. However, there is growing evidence that prior to ligand binding, various transmembrane receptors have a preformed, yet inactive, dimeric structure on the cell surface. Various studies also demonstrate that during transmembrane signaling, ligand binding to the extracellular domain of receptor dimers induces a rotation of transmembrane domains, followed by rearrangement and/or (...) activation of intracellular domains. The paper here describes transmembrane cell‐surface receptors that are known or proposed to exist in dimeric form prior to ligand binding, and discusses how these preformed dimers are activated by ligand binding. (shrink)

This paper explores relationships between many-valued logic and fuzzy topology from the viewpoint of duality theory. We first show a fuzzy topological duality for the algebras of Łukasiewicz n -valued logic with truth constants, which generalizes Stone duality for Boolean algebras to the n -valued case via fuzzy topology. Then, based on this duality, we show a fuzzy topological duality for the algebras of modal Łukasiewicz n -valued logic with truth constants, which generalizes Jónsson-Tarski duality for modal algebras to the (...) n -valued case via fuzzy topology. We emphasize that fuzzy topological spaces naturally arise as spectrums of algebras of many-valued logics. (shrink)

There are still on-going debates on what exactly is wrong with Prior’s pathological “tonk.” In this article I argue, on the basis of categorical inferentialism, that two notions of inconsistency ought to be distinguished in an appropriate account of tonk; logic with tonk is inconsistent as the theory of propositions, and it is due to the fallacy of equivocation; in contrast to this diagnosis of the Prior’s tonk problem, nothing is actually wrong with tonk if logic is viewed as the (...) theory of proofs rather than propositions, and tonk perfectly makes sense in terms of the identity of proofs. Indeed, there is fully complete semantics of proofs for tonk, which allows us to link the Prior’s old philosophical idea with contemporary issues at the interface of categorical logic, computer science, and quantum physics, and thereby to expose commonalities between the laws of Reason and the laws of Nature, which are what logic and physics are respectively about. I conclude the article by articulating the ideas of categorical logical positivism and pluralistic unified science as its goal, including the unification of realist and antirealist conceptions of meaning by virtue of the categorical logical basis of metaphysics. (shrink)

10.1093/mind/fzl659p. 688, line 10:for So if is a theorem of M read So if ϕ is a theorem of Mp. 688, line 13:for where ϕ* is the result of indexing the terms of ϕ* to Mread where ϕ* is the result of indexing the terms of ϕ to M.

Although Wittgenstein’s influence on logic and foundations of mathematics is well recognized, nonetheless, his legacy concerning other sciences is much less elucidated, and in this article we aim at shedding new light on physics, artificial intelligence, and cognitive science from a Wittgensteinian perspective. We focus upon three issues amongst other things: the Chosmky versus Norvig debate on the nature of language; a Neo-Kantian parallelism between Bohr’s philosophy of physics and Hilbert’s philosophy of mathematics; the relationships between cognitive contextuality and physical (...) contextuality as shown by recent Bell-type results. The Chosmky versus Norvig debate may be seen as a battle between Wittgenstein’s earlier and later conceptions of meaning, i.e., picture theory and use theory. From a Wittgensteinian point of view, quantum physics may be seen as a physical version of the Linguistic Turn. The parallelism between Bohr’s philosophy of classical concepts and Hilbert’s philosophy of finitism builds upon transcendental philosophy in the Kantian tradition, both Bohr and Hilbert having been influenced by Neo-Kantian thinkers, such as Hertz, whose sign theory is actually a common root of Wittgenstein’s picture theory and Hilbert’s axiomatics. Wittgenstein is considered a root of contextualism in contemporary philosophy. Contextuality has different manifestations in physics and cognitive science, and contextuality studies across the sciences are rapidly developing in cutting-edge research. We elucidate both analogies and disanalogies between contextuality of reality and contextuality of reason in terms of the nature of probabilities involved. In passing, we also give a reformulation of Penrose’s quantum mind thesis. (shrink)

Although Wittgenstein’s influence on logic and foundations of mathematics is well recognized, nonetheless, his legacy concerning other sciences is much less elucidated, and in this article we aim at shedding new light on physics, artificial intelligence, and cognitive science from a Wittgensteinian perspective. We focus upon three issues amongst other things: the Chosmky versus Norvig debate on the nature of language; a Neo-Kantian parallelism between Bohr’s philosophy of physics and Hilbert’s philosophy of mathematics; the relationships between cognitive contextuality and physical (...) contextuality as shown by recent Bell-type results. The Chosmky versus Norvig debate may be seen as a battle between Wittgenstein’s earlier and later conceptions of meaning, i.e., picture theory and use theory. From a Wittgensteinian point of view, quantum physics may be seen as a physical version of the Linguistic Turn. The parallelism between Bohr’s philosophy of classical concepts and Hilbert’s philosophy of finitism builds upon transcendental philosophy in the Kantian tradition, both Bohr and Hilbert having been influenced by Neo-Kantian thinkers, such as Hertz, whose sign theory is actually a common root of Wittgenstein’s picture theory and Hilbert’s axiomatics. Wittgenstein is considered a root of contextualism in contemporary philosophy. Contextuality has different manifestations in physics and cognitive science, and contextuality studies across the sciences are rapidly developing in cutting-edge research. We elucidate both analogies and disanalogies between contextuality of reality and contextuality of reason in terms of the nature of probabilities involved. In passing, we also give a reformulation of Penrose’s quantum mind thesis. (shrink)

The frame problem is a fundamental challenge in AI, and the Lucas-Penrose argument is supposed to show a limitation of AI if it is successful at all. Here we discuss both of them from a unified Gödelian point of view. We give an informational reformulation of the frame problem, which turns out to be tightly intertwined with the nature of Gödelian incompleteness in the sense that they both hinge upon the finitarity condition of agents or systems, without which their alleged (...) limitations can readily be overcome, and that they can both be seen as instances of the fundamental discrepancy between finitary beings and infinitary reality. We then revisit the Lucas-Penrose argument, elaborating a version of it which indicates the impossibility of information physics or the computational theory of the universe. It turns out through a finer analysis that if the Lucas-Penrose argument is accepted then information physics is impossible too; the possibility of AI or the computational theory of the mind is thus linked with the possibility of information physics or the computational theory of the universe. We finally reconsider the Penrose’s Quantum Mind Thesis in light of recent advances in quantum modelling of cognition, giving a structural reformulation of it and thereby shedding new light on what is problematic in the Quantum Mind Thesis. Overall, we consider it promising to link the computational theory of the mind with the computational theory of the universe; their integration would allow us to go beyond the Cartesian dualism, giving, in particular, an incarnation of Chalmers’ double-aspect theory of information. (shrink)

Ethics education for professionals has become popular in Japan over the last two decades. Many professional schools now require students to take an applied ethics or professional ethics course. In contrast, very few courses of professional ethics for teaching exist or have been taught in Japan. In order to obtain suggestions for teacher education, this paper reviews and examines practices of ethics education for engineers and nurses in Japan that have been successfully implemented. The paper concludes that difficulties in professional (...) ethics education in Japan are caused by the fact that both teachers and students lack experience in leading and participating in discussion‐based classes and misunderstand the effectiveness of a case‐based pedagogy. It also suggests that we need to offer teachers systematic opportunities to be trained to be proficient in enabling students to be active and critical in class. (shrink)

We pursue the idea that predicate logic is a “fibred algebra” while propositional logic is a single algebra; in the context of intuitionism, this algebraic understanding of predicate logic goes back to Lawvere, in particular his concept of hyperdoctrine. Here, we aim at demonstrating that the notion of monad-relativised hyperdoctrines, which are what we call fibred algebras, yields algebraisations of a wide variety of predicate logics. More specifically, we discuss a typed, first-order version of the non-commutative Full Lambek calculus, which (...) has extensively been studied in the past few decades, functioning as a unifying language for different sorts of logical systems (classical, intuitionistic, linear, fuzzy, relevant, etc.). Through the concept of Full Lambek hyperdoctrines, we establish both generic and set-theoretical completeness results for any extension of the base system; the latter arises from a dual adjunction, and is relevant to the tripos-to-topos construction and quantale-valued sets. Furthermore, we give a hyperdoctrinal account of Girard’s and Gödel’s translation. (shrink)

SummaryParadigmatology as a science of structures of reasoning which vary from culture to culture, from profession to profession, and sometimes from individual to individual is outlined, and communication difficulties between paradigms are discussed. Three paradigms are used as examples: hierarchical, unilateral, homogenistic, universalistic, categorical, classificational, deductive, rank‐ordering, competitive paradigm with predetermined universe; individualistic, isolationists, random, nominalistic, atomistic, statistical, probabilistic, egocentric paradigm with thermodynamically and informationally decaying universe; mutualistic, reciprocally interactive, heterogeneity‐creating, network‐structured, relational, contextual, complementary, symbiotic paradigm with self‐generating and self‐organizing (...) universe based on mutual causality and post‐Shannon information theory.Paradigmatologie et son Application à la Communication entre des Domaines de Spécialisation différents, entre des Professions et entre des Cultures. (shrink)

Ethics education for professionals has become popular in Japan over the last two decades. Many professional schools now require students to take an applied ethics or professional ethics course. In contrast, very few courses of professional ethics for teaching exist or have been taught in Japan. In order to obtain suggestions for teacher education, this paper reviews and examines practices of ethics education for engineers and nurses in Japan that have been successfully implemented. The paper concludes that difficulties in professional (...) ethics education in Japan are caused by the fact that both teachers and students lack experience in leading and participating in discussion-based classes and misunderstand the effectiveness of a case-based pedagogy. It also suggests that we need to offer teachers systematic opportunities to be trained to be proficient in enabling students to be active and critical in class. (shrink)

人の始期から終期の「生」について、生殖医療、再生医療、ゲノム医療などの先端医療を紹介し、バイオエシックス教育の実際をみる。.

Lawvere hyperdoctrines give categorical algebraic semantics for intuitionistic predicate logic. Here we extend the hyperdoctrinal semantics to a broad variety of substructural predicate logics over the Typed Full Lambek Calculus, verifying their completeness with respect to the extended hyperdoctrinal semantics. This yields uniform hyperdoctrinal completeness results for numerous logics such as different types of relevant predicate logics and beyond, which are new results on their own; i.e., we give uniform categorical semantics for a broad variety of non-classical predicate logics. And (...) we introduce an analogue of Lawvere–Tierney topology and cotopology in the hyperdoctrinal setting, which gives a unifying perspective on different logical translations, in particular allowing for a uniform treatment of Girard’s exponential translation between linear and intuitionistic logics and of Kolmogorov’s double negation translation between intuitionistic and classical logics. In the hyerdoctrinal conception, type theories are categories, logics over type theories are functors, and logical translations between them, then, are natural transformations, in particular Lawvere–Tierney topologies and cotopologies on hyperdoctrines. The view of logical translations as hyperdoctrinal Lawvere–Tierney topologies and cotopologies has not been elucidated before, and may be seen as a novel contribution of the present work. From a broader perspective, this work may be regarded as taking first steps towards interplay between algebraic and categorical logics; it is, technically, a combination of substructural algebraic logic and hyperdoctrinal categorical logic, as the hyperdoctrinal completeness theorem is shown via the integration of the Lindenbaum–Tarski algebra construction with the syntactic category construction. As such this work lays a foundation for further interactions between algebraic and categorical logics. (shrink)

The epistemology which sees intra-specific and intra-group heterogenization, symbiotization, interactive pattern-generating and change as basic principles produces types of theories and research strategies different from the epistemology based on the notions of intra-specific and intra-group uniformity, competition and stabilization. In the uniformistic view, individual variations have been reduced mainly either to statistical deviations from the mean or to dominance relationship. On the other hand in the heterogenistic view, mutual beneficial interactions between qualitatively heterogeneous individuals within a group is regarded as (...) indispensable for the increase of the level of behavioral and biological sophistication and evolution. This article compares five epistemologies including the two mentioned above in the context of the current epistemological transition in science, particularly due to the emergence of non-equilibrium thermodynamics in physics and differentiation-amplifying reciprocal causal models in mathematics and engineering, both of which consider the universe as pattern-generating, information-creating and evolving. (shrink)

What is the future of Philosophy of education? Or as many of scholars and thinkers in this final ‘future-focused’ collective piece from the philosophy of education in a new key Series put it, what are the futures—plural and multiple—of the intersections of ‘philosophy’ and ‘education?’ What is ‘Philosophy’; and what is ‘Education’, and what role may ‘enquiry’ play? Is the future of education and philosophy embracing—or at least taking seriously—and thinking with Indigenous ethicoontoepistemologies? And, perhaps most importantly, what is that (...) ‘Future’? These debates have been located in the work of diverse scholars: from the West, from Global South, from indigenous thinkers. In this collective piece, we purposefully juxtapose diverse takes on the future of these intersections. We have given up the urge to organise, place together, separate with subheadings or connect the paragraphs that follow. Instead, we let these philosophers of education and thinkers who use philosophical texts and ideas to sit together in one long read as potentially ‘strange and unusual bedfellows’. This text urges us to understand how these scholars and thinkers perceive our educational philosophical futures, and how the work and thinking they have done on thinking about what the future of that new key in philosophy of education may look like is embedded in a much deeper and richer literature, and personal experience. (shrink)

Inspired by locale theory, we propose “pointfree convex geometry”. We introduce the notion of convexity algebra as a pointfree convexity space. There are two notions of a point for convexity algebra: one is a chain-prime meet-complete filter and the other is a maximal meet-complete filter. In this paper we show the following: the former notion of a point induces a dual equivalence between the category of “spatial” convexity algebras and the category of “sober” convexity spaces as well as a dual (...) adjunction between the category of convexity algebras and the category of convexity spaces; the latter notion of point induces a dual equivalence between the category of “m-spatial” convexity algebras and the category of “m-sober” convexity spaces. We finally argue that the former notion of a point is more useful than the latter one from a category theoretic point of view and that the former notion of a point actually represents a polytope and the latter notion of a point properly represents a point. We also remark on the close relationships between pointfree convex geometry and domain theory. (shrink)

It behooves us to examine , first, in the work of Rousseau the overlapping of their conception of nature and the foundations of social and political life : it is possible to mention the harmony between man and nature without considerations of politics? Then we examine some aspects of modern subjectivity – feeling of existence , moral conscience , the idea of ​​ happiness, pursuit of the indoor unit.

Basic concepts of communicational elements are explained: culturally institutionalized or individually internalized conscious or unconscious, intentional and unintentional encoding and decoding systems of verbal and nonverbal behavior, metacommunicational cues, various modes of communication , the rôle of situational context and of background information.Examples of complex misunderstandings in interpersonal interactions are given and analysed. This analytical method has been useful in psychiatry as well as in daily life situations.