Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify nonuniformly computable functions on Baire space from the viewpoint of learning theory and piecewise computability. For instance, we show that mind-change-bounded learnability is equivalent to finite View the MathML source2-piecewise computability 2 denotes the difference of two View the MathML sourceΠ10 sets), error-bounded learnability is equivalent to finite View (...) the MathML sourceΔ20-piecewise computability, and learnability is equivalent to countable View the MathML sourceΠ10-piecewise computability . Second, we introduce disjunction-like operations such as the coproduct based on BHK-like interpretations, and then, we see that these operations induce Galois connections between the Medvedev degree structure and associated Medvedev/ Muchnik-like degree structures. Finally, we interpret these results in the context of the Weihrauch degrees and Wadge-like games. (shrink)

It is known that infinitely many Medvedev degrees exist inside the Muchnik degree of any nontrivial Π10 subset of Cantor space. We shed light on the fine structures inside these Muchnik degrees related to learnability and piecewise computability. As for nonempty Π10 subsets of Cantor space, we show the existence of a finite-Δ20-piecewise degree containing infinitely many finite-2-piecewise degrees, and a finite-2-piecewise degree containing infinitely many finite-Δ20-piecewise degrees 2 denotes the difference of two Πn0 sets), whereas the greatest degrees in (...) these three “finite-Γ-piecewise” degree structures coincide. Moreover, as for nonempty Π10 subsets of Cantor space, we also show that every nonzero finite-2-piecewise degree includes infinitely many Medvedev degrees, every nonzero countable-Δ20-piecewise degree includes infinitely many finite-piecewise degrees, every nonzero finite-2-countable-Δ20-piecewise degree includes infinitely many countable-Δ20-piecewise degrees, and every nonzero Muchnik degree includes infinitely many finite-2-countable-Δ20-piecewise degrees. Indeed, we show that any nonzero Medvedev degree and nonzero countable-Δ20-piecewise degree of a nonempty Π10 subset of Cantor space have the strong anticupping properties. Finally, we obtain an elementary difference between the Medvedev degree structure and the finite-Γ-piecewise degree structure of all subsets of Baire space by showing that none of the finite-Γ-piecewise structures is Brouwerian, where Γ is any of the Wadge classes mentioned above. (shrink)

Let f be a computable function from finite sequences of 0ʼs and 1ʼs to real numbers. We prove that strong f-randomness implies strong f-randomness relative to a PA-degree. We also prove: if X is strongly f-random and Turing reducible to Y where Y is Martin-Löf random relative to Z, then X is strongly f-random relative to Z. In addition, we prove analogous propagation results for other notions of partial randomness, including non-K-triviality and autocomplexity. We prove that f-randomness relative to a (...) PA-degree implies strong f-randomness, hence f-randomness does not imply f-randomness relative to a PA-degree. (shrink)

In this paper, we perform theoretical analysis and experiments on the Simplex Crossover (SPX), which we have proposed. Real-coded GAs are expected to be a powerful function optimization technique for real-world applications where it is often hard to formulate the objective function. However, we believe there are two problems which will make such applications difficult; 1) performance of real-coded GAs depends on the coordinate system used to express the objective function, and 2) it costs much labor to adjust parameters so (...) that the GAs always find an optimum point efficiently. The result of our theoretical analysis and experiments shows that a performance of SPX is independent of linear coordinate transformation and that SPX always optimizes various test function efficiently when theoretical value for expansion rate, which is a parameter of SPX, is applied. We also show that BLX-α is equivalent to degenerate form of SPX. Experiments show that we have something misunderstood effect of epistasis on performance degradation of real-coded GAs. (shrink)

We consider weak theories of concatenation, that is, theories for strings or texts. We prove that the theory of concatenation WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}^{-\varepsilon}}$$\end{document}, which is a weak subtheory of Grzegorczyk’s theory TC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{TC}^{-\varepsilon}}$$\end{document}, is a minimal essentially undecidable theory, that is, the theory WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}^{-\varepsilon}}$$\end{document} is essentially undecidable and if one omits an axiom scheme from WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}^{-\varepsilon}}$$\end{document}, then the resulting theory is no longer essentially undecidable. Moreover, we give a positive answer to Grzegorczyk and Zdanowski’s conjecture that ‘The theory TC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{TC}^{-\varepsilon}}$$\end{document} is a minimal essentially undecidable theory’. For the alternative theories WTC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}}$$\end{document} and TC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{TC}}$$\end{document} which have the empty string, we also prove that the each theory without the neutrality of ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon}$$\end{document} is to be such a theory too. (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)

Kierstead showed that every computable marriage problem has a computable matching under the assumption of computable expanding Hall condition and computable local finiteness for boys and girls. The strength of the marriage theorem reaches or if computable expanding Hall condition or computable local finiteness for girls is weakened. In contrast, the provability of the marriage theorem is maintained in even if local finiteness for boys is completely removed. Using these conditions, we classify the strength of variants of marriage theorems in (...) the context of reverse mathematics. Furthermore, we introduce another condition that also makes the marriage theorem provable in, and investigate the sequential and Weihrauch strength of marriage theorems under that condition. (shrink)

私たちは、暴力的な存在なのか?人間にとって、暴力とは何か?その不可避性と、回避/克服の可能性をともに見すえつつ思考をつむぐ、「暴力の哲学/倫理学」の試み。.

Probably very few people today would believe that, prior to Japan's modernization during the Meiji period, the Japanese were not able to run. It seems commonsensical that human beings should be able to perform the same body movements such as running—since, of course, we are human beings regardless of whether we live in modern countries. However, it appears, in fact, that people in the Edo Period did not run in the sense of how we run today. There was no need, (...) for example, for farmers to run in the midst of their daily agricultural activities.In addition, it has been also pointed out that, although some premodern Japanese, such as samurai or official messengers... (shrink)

To compare two randomness notions with each other, we ask whether a given randomness notion can be defined via another randomness notion. Inspired by Yu's pioneering study, we formalize our question using the concept of relativization of randomness. We give some solutions to our formalized questions. Also, our results include the affirmative answer to the problem asked by Yu in a discussion with the second author, i.e., whether Schnorr randomness relative to the halting problem is equivalent to Martin‐Löf randomness relative (...) to all low 1‐generic reals. (shrink)

ナショナリズムと親和的関係にある日本通史への欲望を拒否するために、山崎闇斎学派や武士道の語りにおけるナショナルな視線を相対化し、他者性を帯びた「江戸」の自国意識や対中国認識に注目することで、歴史の断面 を記述することの可能性を探る。.

いま、この危機と混迷の時代に、憲法学者・樋口陽一が、基本に立ち戻り、戦後日本を代表する英知・加藤周一と丸山眞男の「憲法論」と「思想」を再読し、その本質を語り尽くす。.

How (Not) to Be Secular is what Jamie Smith calls "your hitchhiker's guide to the present" -- it is both a reading guide to Charles Taylor's monumental work A Secular Age and philosophical guidance on how we might learn to live in our times. Taylor's landmark book A Secular Age (2007) provides a monumental, incisive analysis of what it means to live in the post-Christian present -- a pluralist world of competing beliefs and growing unbelief. Jamie Smith's book is a (...) compact field guide to Taylor's insightful study of the secular, making that very significant but daunting work accessible to a wide array of readers. Even more, though, Smith's How (Not) to Be Secular is a practical philosophical guidebook, a kind of how-to manual on how to live in our secular age. It ultimately offers us an adventure in self-understanding and maps out a way to get our bearings in today's secular culture, no matter who "we" are -- whether believers or skeptics, devout or doubting, self-assured or puzzled and confused. This is a book for any thinking person to chew on. (shrink)

Practical deliberation often involves conditional judgements about what will (likely) happen if certain alternatives are pursued. It is widely assumed that the conditionals useful in deliberation are counterfactual or subjunctive conditionals. Against this, I argue that the conditionals of deliberation are indicatives. Key to the argument is an account of the relation between 'straightforward' future-directed conditionals like ' If the house is not painted, it will soon look quite shabby' and * "w e r e ' ' e d F (...) D C s like ' If the house were not to be painted, it would soon look quite shabby': an account on which both of these types of FDCs are grouped with the indicatives for semantic treatment and on which, while conditionals of both types are properly used in means/ends deliberations, those of the ' were'ed-up variety are especially well suited for that purpose. (shrink)

'Pataphysics: The Poetics of an Imaginary Science is a survey that attempts to describe a hypothetic philosophy--the avant-garde pseudo-science imagined by Alfred Jarry. 'Pataphysics is a supplement to metaphysics, accenting it, then replacing it, in order to create a philosophic alternative, whose discipline can study cases, not of conception, but of exception: variance , alliance , and deviance . 'Pataphysics synthesizes the romantic schism between a literal, scientized discourse and a figural, poeticized discourse, and my thesis suggests that this revision (...) of the signifier "science" by 'pataphysics is symptomatic of a postmodern transition in science from a paradigm of absolutism to a paralogy of relativism. Structured as a descriptive explication, which emphasizes a theoretical perspective, this survey is divided into five chapters: the first chapter recounts the history of the conflict between science and poetry ; the second chapter examines the avant-garde pseudo-science of 'pataphysics itself ; and finally, the last three chapters discuss the influence of 'pataphysics upon the poetics of its subsequent successors . While my thesis focuses upon theories of textual poetics rather than poetry itself , my thesis does nevertheless strive to be as conceptually encyclopedic as 'pataphysics itself: instead of normalizing 'pataphysics within one theoretical perspective, this survey alludes intermittently to 'pataphysical enterprises that constitute exceptions to such a genealogy of Jarryites. What is at stake is the status of poetry in a world of science. How might poetry reclaim its own viable truth? How might science benefit from its own poetic irony? For the postmodern condition, such questions have already opened up a novel space for speculative imagination; hence, this survey presents itself as a kind of primer for a future of possible research. (shrink)

In this short but meaty book, Peter Unger questions the objective answers that have been given to central problems in philosophy. As Unger hypothesizes, many of these problems are unanswerable, including the problems of knowledge and scepticism, the problems of free will, and problems of causation and explanation. In each case, he argues, we arrive at one answer only relative to an assumption about the meaning of key terms, terms like "know" and like "cause," even while we arrive at an (...) opposite answer relative to quite different assumptions, but equally arbitrary assumptions, about what the key terms mean. (shrink)

This article explores the enduring mysteries of consciousness and the afterlife, two enigmatic topics that have fascinated humanity for ages. Despite extensive scientific efforts, the existence of an afterlife remains unproven, and understanding consciousness remains a significant challenge. The research introduces innovative hypotheses through simple thought experiments with empirical evidence and robust theoretical foundations. It delves into the complexities of consciousness, its relationship with the brain, and the need for interdisciplinary approaches encompassing physics, psychology, and philosophy. Boldly contemplating the probability (...) of a continuous consciousness after death, the study argues that existing evidence strongly supports this idea. Beyond theoretical implications, it envisions practical outcomes, suggesting that insights into these mysteries could enhance human well-being and contribute to a more harmonious world. In summary, this article embarks on a quest to shed light on age-old questions about consciousness and the afterlife. Through fresh methodologies, it aims to provide new perspectives that could reshape our understanding of existence and inspire intellectuals to positive individual and societal advancements. -/- . (shrink)

Neoplatonic allegorical interpretation expounds how literary texts present philosophical ideas in an enigmatic and coded form, offering an alternative path to the divine truths. The Neoplatonist Porphyry’s _On the Cave of the Nymphs_ is one of the most significant allegorical interpretation handed down to us from Antiquity. This monograph, exclusively dedicated to the analysis of _On the Cave of Nymphs_, demonstrates that Porphyry interprets Homer’s verse from Odyssey 13.102-112 to convey his philosophical thoughts, particularly on the material world, relationship between (...) soul and body and the salvation of the soul through the doctrines of Plato and Plotinus. The Homeric cave of the nymphs with two gates is a station where the souls descend into genesis and ascend to the intelligible realm. Porphyry associates Odysseus’ long wanderings with the journey of the soul and its salvation from the irrational to rational through escape from all toils of the material world. (shrink)

are ambiguous. In the mouth of someone who cannot remember whether it was Michael, or rather someone else, who was top scorer, can express the epistemic possibility that Michael led the league in scoring. But from someone who knows that Michael did not even play last season, but is wondering what would have happened if he had, means something quite different. Now where it has this quite different meaning, may still turn out to be the expression of some epistemic possibility. (...) Perhaps where does not express the epistemic possibility of ‘Michael led the league in scoring’, it expresses the epistemic possibility of ‘Michael would have led the league in scoring’. Analysis of this ‘would have’ statement, together with an exploration of the suspicion that the ‘might have’ statement is ambiguous between these two epistemic possibilities, will have to await another occasion. The important point for present purposes is that is ambiguous between an expression of the epistemic possibility of ‘Michael led the league in scoring’ and some quite different reading. (shrink)

What are the criteria for reasonable clinical judgements? The reasonableness of macro-level decision-making has been much discussed, but little attention has been paid to the reasonableness of applying guidelines generated at a macro-level to individual cases. This paper considers a framework for reasonable clinical decision-making that will capture cases where relevant guidelines cannot reasonably be followed. There are three main sections. (1) Individual claims on healthcare from the point of view of concerns about equity are analysed. (2) The demands of (...) responsibility and equity on professional clinical performance are discussed, and how the combination of these demands emerges into seven requirements that constitute the framework is explored. Since this framework is developed to assist in reasonable clinical decision-making, practical implications of all these requirements are also suggested. (3) Challenges concerning the framework are discussed. First, a crucial presumption that the framework relies upon is considered—namely, clinicians’ willingness to justify their decisions as requested. Then how public deliberation may influence clinical decision-making is discussed. Next is a consideration of how clinicians’ need to have confidence in their own judgements in order to perform in a manner worthy of trust would be compatible with adherence to the framework supported by public deliberation. It is concluded that fair distribution in the interplay between macro- and micro-level considerations can be secured by legitimising procedures on each level, by ensuring well-organised and continuing public debate and by basing individual clinical judgements upon well-justified and principled normative bases. (shrink)