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)

Louveau showed that if a Borel set in a Polish space happens to be in a Borel Wadge class $$\Gamma $$, then its $$\Gamma $$ -code can be obtained from its Borel code in a hyperarithmetical manner. We extend Louveau’s theorem to Borel functions: If a Borel function on a Polish space happens to be a $$ \underset{\widetilde{}}{\varvec{\Sigma }}\hbox {}_t$$ -function, then one can find its $$ \underset{\widetilde{}}{\varvec{\Sigma }}\hbox {}_t$$ -code hyperarithmetically relative to its Borel code. More generally, we prove (...) extension-type, domination-type, and decomposition-type variants of Louveau’s theorem for Borel functions. (shrink)

There are close similarities between the Weihrauch lattice and the zoo of axiom systems in reverse mathematics. Following these similarities has often allowed researchers to translate results from one setting to the other. However, amongst the big five axiom systems from reverse mathematics, so far $\mathrm {ATR}_0$ has no identified counterpart in the Weihrauch degrees. We explore and evaluate several candidates, and conclude that the situation is complicated.

We give a partial answer to an important open problem in descriptive set theory, the Decomposability Conjecture for Borel functions on an analytic subset of a Polish space to a separable metrizable space. Our techniques employ deep results from effective descriptive set theory and recursion theory. In fact it is essential to extend several prominent results in recursion theory (e.g. the Shore-Slaman Join Theorem) to the setting of Polish spaces. As a by-product we give both positive and negative results on (...) the Martin Conjecture on the degree preserving Borel functions between Polish spaces. Additionally we prove results about the transfinite version as well as the computable version of the Decomposability Conjecture. (shrink)

We introduce the notion of a convex tree. We show that the binary expansion for real numbers in the unit interval ) is equivalent to weak König lemma ) for trees having at most two nodes at each level, and we prove that the intermediate value theorem is equivalent to \ for convex trees, in the framework of constructive reverse mathematics.

We show that there is a computable procedure which, given an ∀∃-sentence ${\varphi}$ in the language of the partially ordered sets with a top element 1 and a bottom element 0, computes whether ${\varphi}$ is true in the Medvedev degrees of ${\Pi^0_1}$ classes in Cantor space, sometimes denoted by ${\mathcal{P}_s}$.

This article presents a unified theory of irony which claims, with the help of Fauconnier’s (1985) mental space theory, that an ironical utterance refers to the mental space of a mutually manifest expectation. According to this view, what a typical ironical speaker does is to say without any distinct space builders that something is the case in the mental space of expectation in order to make it mutually manifest that it is not so in the initial reality space. This expectation (...) space theory of irony integrates the explanatory power of Sperber and Wilson’s (1986) echoic interpretation theory with the descriptive power of the view of irony as relevant inappropriateness. (shrink)

異文化コミュニケーションのスキル、仕事の現場、技術者倫理など、グローバルエンジニアを志す人に必要な情報をまとめた一冊。.

We prove the Decomposability Conjecture for functions of Baire class $2$ from a Polish space to a separable metrizable space. This partially answers an important open problem in descriptive set theory.

Consider a randomness notion C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}. A uniform test in the sense of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} is a total computable procedure that each oracle X produces a test relative to X in the sense of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}. We say that a binary sequence Y is C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}-random uniformly relative to (...) X if Y passes all uniform C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} tests relative to X. Suppose now we have a pair of randomness notions C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} and D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{D}}$$\end{document} where C⊆D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C} \subseteq \mathcal{D}}$$\end{document}, for instance Martin-Löf randomness and Schnorr randomness. Several authors have characterized classes of the form Low which consist of the oracles X that are so feeble that C⊆DX\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C} \subseteq \mathcal{D}^X}$$\end{document}. Our goal is to do the same when the randomness notion D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{D}}$$\end{document} is relativized uniformly: denote by Low \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\star}$$\end{document} the class of oracles X such that every C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}-random is uniformly D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{D}}$$\end{document}-random relative to X. We show that X∈Low⋆\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\in Low ^\star}$$\end{document} if and only if X is c.e. tt-traceable if and only if X is anticomplex if and only if X is Martin-Löf packing measure zero with respect to all computable dimension functions. We also show that X∈Low⋆\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\in Low^\star}$$\end{document} if and only if X is computably i.o. tt-traceable if and only if X is not totally complex if and only if X is Schnorr Hausdorff measure zero with respect to all computable dimension functions. (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)

Neoliberal reforms have changed the conduct of academic research in, and beyond, science, technology and society. Social science scholars have undertaken critical studies regarding the negative consequences of neoliberalism, such as the globalization of poverty and the inattention to rights and fairness. However, science and technology studies (STS), which should take a critical approach to science and technology, has generally not addressed the problem of neoliberalism. Rather, some currents in STS may be viewed as supportive of neoliberal transformations. 1 Why (...) is this so? To address this question, Japanese public policy will provide a case study. In Japan, public policy changed, affected by neoliberal reforms in the 1990s. Consequently, a broad area of Japanese social sciences was altered regarding how to be engaged in public policy. STS in Japan was formed at this time and shifted to neoliberal public policy. As a result STS, as well as many other social sciences, transformed their critical function. These circumstances seem to have overlapped and caused STS in Japan to be uncritical of neoliberalism. (shrink)

A Polish space is not always homeomorphic to a computably presented Polish space. In this article, we examine degrees of non-computability of presenting homeomorphic copies of compact Polish spaces. We show that there exists a $\mathbf {0}'$ -computable low $_3$ compact Polish space which is not homeomorphic to a computable one, and that, for any natural number $n\geq 2$, there exists a Polish space $X_n$ such that exactly the high $_{n}$ -degrees are required to present the homeomorphism type of $X_n$. (...) Along the way we investigate the computable aspects of Čech homology groups. We also show that no compact Polish space has a least presentation with respect to Turing reducibility. (shrink)

In this article, we study an analogue of tt-reducibility for points in computable metric spaces. We characterize the notion of the metric tt-degree in the context of first-level Borel isomorphism. Then, we study this concept from the perspectives of effective topological dimension theory and of effective fractal dimension theory.

Some philosophers have thought that life could only be meaningful if there is no God. For Sartre and Nagel, for example, a God of the traditional classical theistic sort would constrain our powers of self-creative autonomy in ways that would severely detract from the meaning of our lives, possibly even evacuate our lives of all meaning. Some philosophers, by contrast, have thought that life could only be meaningful if there is a God. God and the Meanings of Life is interested (...) in exploring the truth in both these schools of thought, seeking to discover what God could and couldn't do to make life meaningful (as well as what he would and wouldn't do). Mawson espouses a version of the 'amalgam' or 'pluralism' thesis about the issue of life's meaning – in essence, that there are a number of different legitimate meanings of 'meaning' (and indeed 'life') in the question of life's meaning. According to Mawson, God, were he to exist, would help make life meaningful in some of these senses and hinder in some others. He argues that whilst there could be meaning in a Godless universe, there could be other sorts of meaning in a Godly one and that these would be deeper. (shrink)

We investigate computability theoretic and descriptive set theoretic contents of various kinds of analytic choice principles by performing a detailed analysis of the Medvedev lattice of $\Sigma ^1_1$ -closed sets. Among others, we solve an open problem on the Weihrauch degree of the parallelization of the $\Sigma ^1_1$ -choice principle on the integers. Harrington’s unpublished result on a jump hierarchy along a pseudo-well-ordering plays a key role in solving this problem.

T. A. Cavanaugh's Hippocrates' Oath and Asclepius' Snake: The Birth of the Medical Profession articulates the Oath as establishing the medical profession's unique internal medical ethic - in its most basic and least controvertible form, this ethic mandates that physicians help and not harm the sick. Relying on Greek myth, drama, and medical experience (e.g., homeopathy), the book shows how this medical ethic arose from reflection on the most vexing medical-ethical problem -- injury caused by a physician -- and argues (...) that deliberate iatrogenic harm, especially the harm of a doctor choosing to kill (physician assisted suicide, euthanasia, abortion, and involvement in capital punishment), amounts to an abandonment of medicine as an exclusively therapeutic profession. The book argues that medicine as a profession necessarily involves stating before others what one stands for: the good one seeks and the bad one seeks to avoid on behalf of the sick, and rejects the view that medicine is purely a technique lacking its own unique internal ethic. It concludes noting that medical promising (as found in the White Coat Ceremony through which U. S. medical students matriculate) implicates medical autonomy which in turn merits respect, including honoring professional conscientious objections. (shrink)

This text is designed to help students construct and evaluate arguments.

How do we think about animals? How do we decide what they deserve and how we ought to treat them? Subhuman takes an interdisciplinary approach to these questions, drawing from research in philosophy, neuroscience, psychology, law, history, sociology, economics, and anthropology. Subhuman argues that our attitudes to nonhuman animals, both positive and negative, largely arise from our need to compare ourselves to them.

Exegesis, with text, on the Nyāyasūtra of Gautama, basic aphoristic text of Nyāya.

Kit Fine (2000) breaks with tradition, arguing that, pace Russell (e.g., 1903: 228), relations have neither directions nor converses. He considers two ways to conceive of these new "neutral" relations, positionalism and anti-positionalism, and argues that the latter should be preferred to the former. Cody Gilmore (2013) argues for a generalization of positionalism, slot theory, the view that a property or relation is n-adic if and only if there are exactly n slots in it, and (very roughly) that each slot (...) may be occupied by at most one entity. Slot theory (and with it, positionalism) bears the full brunt of Fine's (2000) symmetric completions and conflicting adicities problems. I fully develop an alternative, plural slot theory (or pocket theory), which avoids these problems, key elements of which are first considered by Yi (1999: 168 ff.). Like the slot theorist, the pocket theorist posits entities (pockets) in properties and relations that can be occupied. But unlike the slot theorist, the pocket theorist denies that at most one entity can occupy any one of them. As a result, she must also deny that the adicity of a property or relation is equal to the number of occupiable entities in it. By abandoning these theses, however, the pocket theorist is able to avoid Fine's problems, resulting in a stronger theory about the internal structure of properties and relations. Pocket theory also avoids a serious drawback of anti-positionalism. (shrink)

_Purpose._ This paper aims to investigate the phenomenon of a human being within the Confucian tradition as well as its interpretations from intercultural perspective. _Theoretical basis._ One of the ways to understand the deepest level of the intercultural dialogue is to reveal the interpretations of a human being in philosophical traditions, since they refer to the formation of personality and identity within a given culture including interpersonal, intergroup, and intercultural relations. Humanism based on the unity of Human and Heaven runs (...) like a red thread through the philosophical teachings of Confucius, Mencius, Xunzi, Zhu Xi, Wang Yangming defining the ideas of human nature, his/her duties, his/her place and roles in society that shaped the Chinese mentality. _Originality._ Quite often, Chinese concepts (for example, human dignity beyond the ideas of democracy and mass political participation, guanxi, mianzi) are incomprehensible to the representatives of the Western civilization, which leads to the challenges in intercultural communication. The interpretation of these ideas in the context of Confucianism allows to understand them from the perspective of Others and expand the set of patterns of cultural perception. This ultimately leads to the awareness that there are many social, political, cultural realities, which we perceive through the lens of our own concepts and attitudes. The participants of an intercultural dialogue realize that each of them has a unique experience, own way of posing a problem and resolving it, and no one is better or worse. _Conclusions._ Confucian philosophy shaped the worldview of Chinese people, defined values, goals, meanings, attitudes, communication models, which affected all spheres of Chinese life and culture. The study of the philosophical heritage of the great Chinese civilization enhances the cultural competence of the intercultural communicators and expands the field of dialogue to the level of global communication. (shrink)