Specification acquisition in the system design process has been improved since the middle of the 1980s when the upper CASE tools appeared. On the contrary the quality of requirement acquisition in the upper processes of system design has not been enhanced as much as specification acquisition. Understanding the user's requirements is indispensable as one of the basic conditions for building systems that can really satisfy users.This article discusses obtaining requirement knowledge, in terms of human-centred design. The focus is on the (...) process of requirement acquisition, where there is room for one to make full use of human knowledge in a dynamic manner. (shrink)

Human interaction has two principle functions: building and maintaining relationships with others and exchanging information. The function of building and maintaining relationships with others relates to interpersonal coordination; this behavior pattern is expected to predict the outcome of social relationships, such as between therapists and patients. It is unclear, however, whether the exchange of information is associated with interpersonal coordination. In the present study, we tested a hypothesis of whether body movement synchrony occurs in a natural conversation and whether this (...) synchrony has a positive correlation with the degree of information exchange. Fifty participants were engaged in a conversation task; each had different roles in the conversation. We measured their body movements during this conversation using an optical motion capture system. Similar to methods that can be found in previous research, we calculated body movements and quantified their synchrony applying the methods previously reported that automatically quantified their body movements. Moreover, we determined the participants’ degree of information exchange concerning the conversation using a questionnaire. We observed that the body movement synchrony of pairs who talked with each other was significantly higher than that of pairs who did not talk with each other, and that this synchrony was positively associated with the degree of information exchange. These results suggest that body movement synchrony predicted information exchange. (shrink)

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)

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)

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)

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)

This paper argues for a virtue-based account of questioning. First, it delineates the unreflective yet rational aspects of questioning and demonstrates that “good” questions – that is, properly focused, pertinent questions – can be obtained not only in reflective but also in unreflective processes. This paper then argues that the unreflective yet rational mode of inquirers in questioning can be characterized by an automatic response to good questions and cues for relevant doubt and further questions, the active and standby modes (...) of responsiveness, and emotional stress on cues for relevant doubt and further questions. Finally, this article outlines how these features can fully be explicated in terms of exercising a sensitivity to good questions as a virtue. (shrink)

Emotional processing without conscious awareness plays an important role in human social interaction. Several behavioral studies reported that subliminal presentation of photographs of emotional facial expressions induces unconscious emotional processing. However, it was difficult to elicit strong and robust effects using this method. We hypothesized that dynamic presentations of facial expressions would enhance subliminal emotional effects and tested this hypothesis with two experiments. Fearful or happy facial expressions were presented dynamically or statically in either the left or the right visual (...) field for 20 (Experiment 1) and 30 (Experiment 2) ms. Nonsense target ideographs were then presented, and participants reported their preference for them. The results consistently showed that dynamic presentations of emotional facial expressions induced more evident emotional biases toward subsequent targets than did static ones. These results indicate that dynamic presentations of emotional facial expressions induce more evident unconscious emotional processing. (shrink)

The number of competing-brands changes by new product's entry. The new product introduction is endemic among consumer packaged goods firm and is an integral component of their marketing strategy. As a new product's entry affects markets, there is a pressing need to develop market response model that can adapt to such changes. In this paper, we develop a dynamic model that capture the underlying evolution of the buying behavior associated with the new product. This extends an application of a dynamic (...) linear model, which is used by a number of time series analyses, by allowing the observed dimension to change at some point in time. Our model copes with a problem that dynamic environments entail: changes in parameter over time and changes in the observed dimension. We formulate the model with framework of a state space model. We realize an estimation of the model using modified Kalman filter/fixed interval smoother. We find that new product's entry (1) decreases brand differentiation for existing brands, as indicated by decreasing difference between cross-price elasticities; (2) decreases commodity power for existing brands, as indicated by decreasing trend; and (3) decreases the effect of discount for existing brands, as indicated by a decrease in the magnitude of own-brand price elasticities. The proposed framework is directly applicable to other fields in which the observed dimension might be change, such as economic, bioinformatics, and so forth. (shrink)

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。.

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)

We can easily discriminate self-produced from externally generated sensory signals. Recent studies suggest that the prediction of the sensory consequences of one’s own actions made by forward model can be used to attenuate the sensory effects of self-produced movements, thereby enabling a differentiation of the self-produced sensation from the externally generated one. The present study showed that attenuation of sensation occurred both when participants themselves performed a goal-directed action and when they observed experimenter performing the same action, although they clearly (...) reported that the tones were produced by other during action observation and by themselves during their own action. These results suggest that sensory prediction of action modulates ongoing auditory processing irrespective of who produces the sounds and that the explicit judgment of agency does not necessarily rely on the same mechanisms on which implicit perceptual measures such as sensory attenuation rely. (shrink)

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.

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.

We introduce a new axiom called inductive dichotomy, a weak variant of the axiom of inductive definition, and analyze the relationships with other variants of inductive definition and with related axioms, in the general second order framework, including second order arithmetic, second order set theory and higher order arithmetic. By applying these results to the investigations on the determinacy axioms, we show the following. (i) Clopen determinacy is consistency-wise strictly weaker than open determinacy in these frameworks, except second order arithmetic; (...) this is an enhancement of Schweber–Hachtman separation of open and clopen determinacy into the consistency-wise separation. (ii) Hausdorff–Kuratowski hierarchy of differences of opens is faithfully reflected by the hierarchy of consistency strengths of corresponding parameter-free determinacies in the aforementioned frameworks; this result is valid also in second order arithmetic only except clopen determinacy. (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)

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.

... because the thing-in-itself has no abnormality. Anything unusual will appear, after I myself see it: Abnormality belongs not to the thing-in-itself, but to myself. Kuo P'u (276-324), Shan-hai ching (Scriptures of the Mountains and the Seas).

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。.

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.

Genshi shiroku -- Hakurokudō Shoin keijimon.

1. Seikyō ronkō -- 2-3. Shibunrui -- 4-10. Rangai shorui -- 11-12. Genshi shiroku -- 13-14. Fukureki.

Crew Pairing is one of the most important and difficult problems for airline companies. Nets to fuel costs, the crew costs constitute the largest cost of airlines, and the crew costs depend on the quality of the solution to the pairing problem. Conventional systems have been used to solve a daily model, which handles only regular flights with many simplifications, so a lot of corrections are needed to get a feasible solution and the quality of the solution is not so (...) high. A fully dated model, which handles regular flights and irregular flights simultaneously, is extremely hard and has not been solved directly hitherto. The number of irregular flights tend to increase in Europe and Japan, hence the resolution of the practical fully dated pairing system is desired. This paper presents a new approach which solves directly the fully dated crew pairing by Genetic Algorithms. GA is improved with stochastic processes to attack the fully dated model, and many heuristics are included in the decoding mecanism of the GA. For several hundred flights per day for fully dated 2 months scheduling period, the system found better or equivalent solutions to the human scheduler’s without any simplification from 5 to 20 times faster. (shrink)

Schedule planning is one of the most crucial issues for any airline company, because the profit of the company directly depends on the efficiency of the schedule. This paper presents a novel scheduling method which solves problems related to time scheduling, fleet assignment and maintenance routing simultaneously by Genetic Algorithms. Every schedule constraint is embeded in the fitness function, which is described as an object oriented model and works as a simulater developing itself over time, and whose solution is executable (...) without human correction. The schedular is able to solve the problems involving several hundred flights in a few hours, and the solutions are superior or equivalent to those by human experts in terms of the estimated profit. (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)

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)

We introduce a new simple way of defining the forcing method that works well in the usual setting under FA, the Foundation Axiom, and moreover works even under Aczel's AFA, the Anti-Foundation Axiom. This new way allows us to have an intuition about what happens in defining the forcing relation. The main tool is H. Friedman's method of defining the extensional membership relation ∈ by means of the intensional membership relation ε .Analogously to the usual forcing and the usual generic (...) extension for FA-models, we can justify the existence of generic filters and can obtain the Forcing Theorem and the Minimal Model Theorem with some modifications. These results are on the line of works to investigate whether model theory for AFA-set theory can be developed in a similar way to that for FA-set theory.Aczel pointed out that the quotient of transition systems by the largest bisimulation and transition relations have the essentially same theory as the set theory with AFA. Therefore, we could hope that, by using our new method, some open problems about transition systems turn out to be consistent or independent. (shrink)

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.

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)

This article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditionalω. Namely, the equivalence between normal transfinite recursion scheme and newdependent transfinite recursionscheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universeVof sets is treated as the given (...) totality. (shrink)

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)

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。.