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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)

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Modern technology has radically altered the conditions for human action, endowing us with tremendous power to affect the future. Patterns of action that appear positive in their short-term effects must sometimes be judged unsustainable. Hans Jonas and Thomas Berry are among those who emphasize the necessity of transforming ethics in light of these considerations. In a Whiteheadian framework, this needed transformation is rooted in the nature of things.

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The aim of this paper is to examine the role of imagination in environmental ethics and introduce an imaginative dimension as an essential part of environmental ethics. Imagination constitutes a basic condition for ethical thinking and action. Matters of environmental ethics have revealed the indispensable role of imagination in ethics. I’ll advance an imagination-based environmental ethics by developing Hans Jonas’ ethical thought. From his viewpoint, various effects of our action on nature and future generations, generally out of our sight, have (...) become an ethical concern. This necessitates the exercise of imagination because we must “imagine” those distant effects to act in an environmentally responsible way. Jonas’ “heuristics of fear” is an imaginative approach necessary for responsible action. Further, I reinterpret the role of imagination as motivating our “will to know.” In conclusion, I suggest the importance of environmental education as cultivating ecological imagination from the standpoint of environmental ethics. (shrink)

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L'ipséité du moi, qui pense soi-même, constitue l'épreuve de la pensée. Chaque fois que Kant fonde ses théories sur des conceptions de l'ipséité, il remet lui-même en question ses fondements. Il destitue le sujet en tant que « je pense » en examinant son pouvoir de se déterminer, au moment même où il va fonder son éthique de la loi sur la liberté du sujet. Par la suite c'est son concept de liberté éthique que Kant remet en question, repérant le (...) fondement de la transgression de la loi dans la liberté par laquelle le sujet se détermine par la loi. Pourquoi Kant pense-t-il l'ipséité du sujet libre comme étant mise en épreuve? Comment le sujet libre se constitue-t-il lui-même dans l'épreuve de son ipséité? C'est sous le thème de l'auto-détermination par la loi que nous abordons l'auto-constitution dans l'épreuve de soi. (shrink)

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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)

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文明の衰亡は必然なのか?衰退から逃れる道はないのか?本書ではローマ帝国、ビザンチン帝国、大英帝国、アメリカ、中国そして江戸時代の日本など独自の世界を確立した大国の興亡の光景を描き出し、その「文明衰退の 理」を歴史の教訓から導き出す。史上、外敵の侵入で滅んだ国はない。衰退はその国の「内なる原因」によってなされたと著者は論ずる。世界史的・文明史的視点から、日本の衰退と再生を洞察する「衰退学」の集大成であ る。.

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独自の視点から思想の可能性をつかみ出し、現代の倫理として編み直す。鶴見哲学の中心へ、気鋭の哲学者による決定的論考。.

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This paper examines some aspects of the grammar of measurement based on data from non-split and split measure phrase (MP) constructions in Japanese. I claim that the non-split MP construction involves measurement of individuals, while the split MP construction involves measurement of events as well as of individuals. This claim is based on the observation that, while both constructions are subject to some semantic restrictions in the nominal domain, only the split MP construction is sensitive to restrictions in the verbal (...) domain (namely, incompatibility with single-occurrence events and with individual-level predicates, and (un)availability of collective readings). It is shown that these semantic restrictions can be explained by a uniform semantic constraint on the measure function, namely, Schwarzschild’s [(2002). The grammar of measurement. The Proceedings of Semantics and Linguistics Theory, 24, 241–306] monotonicity constraint. In particular, I argue that, in the two constructions at issue, the measure function is subject to the monotonicity constraint, and that we observe different semantic restrictions depending on whether the measure function applies to a nominal or a verbal domain. (shrink)

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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)

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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)

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現代哲学の最先端を踏まえ、フッサール以来の現象学の根源的問題をたどりなおし、全く新しい生命の哲学、「媒体性の現象学」を世界に先駆けて提唱する。.

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儒教が「国教」となったのはいつか。皇帝と天子は同じものか。曹操はなぜ文学を称揚したか。諸葛亮は何を守ろうとしたのか。「竹林の七賢」は何に抵抗したか。国家の正統性を主張し、統治制度や世界観の裏づけとなる 「正統思想」の意置に儒教が上り、その思想内容が変転していく様を、体系性と神秘思想の鄭玄、合理性と現実主義の王粛、光武帝、王莽、曹操や諸葛亮など、多彩な人物を軸にして、「漢」の成立と衰退、三国、魏晉時代 の歴史を交えながら描き出す。.

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It is proved that $\Pi^1_1$ -indescribability in $P_{\kappa}\lambda$ can be characterized by combinatorial properties without taking care of cofinality of $\lambda$ . We extend Carr's theorem proving that the hypothesis $\kappa$ is $2^{\lambda^{<\kappa}}$ -Shelah is rather stronger than $\kappa$ is $\lambda$ -supercompact.

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This paper addresses the question of whether the preverbal even (VP-even) embedded in a nonfinite clause can take wide scope (e.g., Bill refused to even drink WATER). The paper presents novel evidence for wide scope VP-even that is independent of the presuppositions of even. The evidence is based on examples of antecedent-contained deletion (ACD), where embedded VP-even associates with a nominal constituent (or part of it) that raises out of the embedded clause via quantifier raising. Assuming that even must c-command (...) the focus that it associates with, the case at issue forces VP-even to have wide scope, and further shows that VP-even in NPI-licensing contexts is not necessarily an NPI. (shrink)

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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)

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京都学派の経済哲学者として知られた梯明秀の本格的研究書。梯の戦時下における哲学の再評価と創造的復権をめざして、形而上学批判と根源的自然の復権というまったく新たな視点からその意義と射程を明らかにしようと する力作。.

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In this paper, we introduce systems of nonstandard second-order arithmetic which are conservative extensions of systems of second-order arithmetic. Within these systems, we do reverse mathematics for nonstandard analysis, and we can import techniques of nonstandard analysis into analysis in weak systems of second-order arithmetic. Then, we apply nonstandard techniques to a version of Riemannʼs mapping theorem, and show several different versions of Riemannʼs mapping theorem.

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We define a new theory of concatenation WTC which is much weaker than Grzegorczyk's well-known theory TC. We prove that WTC is mutually interpretable with the weak theory of arithmetic R. The latter is, in a technical sense, much weaker than Robinson's arithmetic Q, but still essentially undecidable. Hence, as a corollary, WTC is also essentially undecidable.

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Early morphogenesis of mouse submandibular gland provides an excellent model for the formation of epithelial lobules as a consequence of epithelial‐mesenchymal interactions. Both proteoglycans and a glycosaminoglycan, high molecular weight components which contain amino‐sugars and hexuronic acids, seem to be important in maintaining the lobular structure through the formation of epithelial basal lamina. Collagen also appears to play a crucial role in this morphogenesis. By visualizing the distribution of collagen fibrils and by changing the concentration of collagen in the gland, (...) we have developed a new hypothesis which emphasizes the mechanical role of mesenchyme in epithelial cleft formation. Precise mechanisms for the involvement of these molecules have not been elucidated, yet it is now clear that knowledge of the function of the extracellular matrix components is a prerequisite for understanding the epithelial‐mesenchymal interactions. (shrink)

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Abstract.A type of subtlety for Pκλ called “strongly subtle” is introduced to show almost ineffability is consistencywise stronger than Shelah property. The following are also shown: is strongly subtle” has rather strong consequences. (ii) The ideal is not strongly subtle} is not λ-saturated, and completely ineffable ideal is not precipitous. (iii) In case that λ<κ=2λ, almost λ-ineffability coincides with λ-ineffability. (iv) It is not provable that κ is λ<κ-ineffable whenever κ is λ-ineffable.

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We study the distributivity of the bounded ideal on Pkλ and answer negatively to a question of Johnson in [13]. The size of non-normal ideals with the partition property is also studied.

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二十世紀初頭、フッサールによって創唱された現象学。経験のなかに知識の原理として機能する原型を探るこの学問は、ハイデガー、サルトル、メルロ=ポンティらに多大な影響を与え、思想・哲学の大きな潮流となる。フ ッサールの哲学を原テクストに則して問い直し、現象学の基本的事象とその本質を解明する、斯界の泰斗の精緻な思索が結晶した珠玉の書。.

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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)

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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)

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