Building on Nietzsche’s view of power, Foucault developed an original analysis of power by making use of concepts like “disciplinary power,” “bio-power,” “governmentality,” etc.; however, existing studies have not sufficiently examined his reading of Nietzsche’s works on this topic. Therefore, in order to clarify the connection between the two, this article examines Foucault’s reading of Nietzsche in detail. Firstly, this article examines the notion of “force” which Foucault recognized is at the center of Nietzsche’s view of power, and will explicitly (...) shows its conceptual determinations. In doing so, this paper will also clarify related notions such as “event,” “body” and “history,” and thus bring to light the general principle of force. In addition, Foucault focused on the point at which Nietzsche—using these principles—radically reinterpreted a central concept of human intellectual activity, namely knowledge. Therefore, this article secondly examines how knowledge is formed under the principle of force, and explicitly shows the general mechanism of knowledge. Finally, the article explains that Nietzsche’s view of power is understood by Foucault as the duality between force and knowledge; in other words, as an ontology of force. (shrink)

Although dual-process or divided-mind models of self-control dominate the literature, they suffer from empirical and conceptual challenges. We propose an alternative approach, suggesting that self-control can be characterized by a fragmented part versus integrated whole dynamic. Whereas responses to events derived from fragmented parts of the mind undermine self-control, responses to events derived from integrated wholes enhance self-control. We review empirical evidence from psychology and related disciplines that support this model. We, moreover, discuss the implications of this work for psychology, (...) neuroscience, economics, and philosophy. In particular, we highlight how this model addresses many of the conceptual and empirical short-comings of divided-mind models. We suggest that understanding self-control as the interplay between fragmented parts versus integrated wholes, moreover, provides novel insights and testable new hypotheses. (shrink)

We consider locally o-minimal structures possessing tame topological properties shared by models of DCTC and uniformly locally o-minimal expansions of the second kind of densely linearly ordered abelian groups. We derive basic properties of dimension of a set definable in the structures including the addition property, which is the dimension equality for definable maps whose fibers are equi-dimensional. A decomposition theorem into quasi-special submanifolds is also demonstrated.

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)

If no property of a system of many particles discriminates among the particles, they are said to be indistinguishable. This indistinguishability is equivalent to the requirement that the many-particle distribution function and all of the dynamic functions for the system be symmetric. The indistinguishability defined in terms of the discrete symmetry of many-particle functions cannot change in the continuous classical statistical limit in which the number density n and the reciprocal temperature β become small. Thus, microscopic particles like electrons must (...) remain indistinguishable in the classical statistical limit although their behavior can be calculated as if they move following the classical laws of motion. In the classical mechanical limit in which quantum cells of volume (2πħ)3 are reduced to points in the phase space, the partition functionTr{exp(−βĤ) for N identical bosons (fermions) approaches (2πħ)−3N(N!) ∫ ... ∫ d3r1 d3p1 ... d3rN d3pN exp(−βH). The two factors, (2πħ)−3N and (N!)−1, which are often added in anad hoc manner in many books on statistical mechanics, are thus derived from the first principles. The criterion of the classical statistical approximation is that the thermal de Broglie wavelength be much shorter than the interparticle distance irrespective of any translation-invariant interparticle interaction. A new derivation of the Maxwell velocity distribution from Boltzmann's principle is given with the assumption of indistinguishable classical particles. (shrink)

The provability problem in intuitionistic propositional second-order logic with existential quantifier and implication (∃,→) is proved to be undecidable in presence of free type variables (constants). This contrasts with the result that inutitionistic propositional second-order logic with existential quantifier, conjunction and negation is decidable.

The main purpose of this book is to offer to philosophers and students abroad who show a great interest in Japanese philosophy and the philosophy of the Kyoto school major texts of the leading philosophers. This interest has surely developed out of a desire to obtain from the thought of these philosophers, who stood within the interstice between East and West, a clue to reassessing the issues of philosophy from the ground up or to drawing new creative possibilities.The present condition (...) seems to be, however, that the material made available to further realize this kind of intellectual dialogue is far too scarce. This book is intended to be of some help in this regard.The book presents selected texts of representative philosophers of the Kyoto school such as Nishida Kitaro, Tanabe Hajime, Miki Kiyoshi, Nishitani Keiji, and others who best illustrate the characteristics of this school, and works that together portray its image as a whole. Those who are interested in Japanese philosophy or specifically the philosophy of the Kyoto School can survey a comprehensive representation from this book.These texts are, of course, quite difficult and cannot be well understood without sufficient preliminary knowledge. Expository essays have therefore been included after each text to provide guidance. In each of these commentaries a scholar of our time with deep understanding of the philosopher in question has provided an account of his life, intellectual journey, and the significance of the text included here.From this book will emerge a new dialogue of ideas that in turn will engender new developments in philosophy, thereby further expanding the network of philosophical thought worldwide. (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)

When I deliver an introductory lecture on Japanese Philosophy, I always raise the following question: Is it appropriate to modify the word philosophy with an adjective such as Japanese? Philosophy is, after all, a discipline that addresses universal problems, and so transcends the restrictions implied in geographical descriptors. However, as Kuki Shūzō argues in his essay “Tokyo and Kyoto,” I think that this is only part, and not the whole truth of the matter.One’s thinking takes place within the framework of (...) one’s cultural heritage, and the different nuances of each of the words one uses can influence how one thinks. It is for this reason that every philoso­phy has its own unique character. As Otto Pöggeler suggests, there is something about the thought of Japanese philosophers such as Nishida Kitarō and Nishitani Keiji that does not fit easily into the framework of “philosophy” in the Western tradition. This is a conse­quence of the fact that they did not simply passively adopt, but rather attempted to critically challenge Western philosophy. I suppose that their grounding in Japanese and other Eastern traditions contributed to their critical challenge of Western philosophy. And I submit that there is a strong tendency in traditional East Asian thought to not simply grasp things within a presupposed framework of “knowledge,” but rather, since “knowledge” itself is understood to be a certain kind of restriction, to return to its roots.Needless to say, neither Nishida’s nor Nishitani’s thought is merely a philosophical reiteration of such traditional East Asian teachings. Nevertheless, we can say that the East Asian idea that knowledge is at root something restrictive lives on in their thinking. The radical­ity of Nishida’s and Nishitani’s thought can be understood to lie in the manner in which they cast light on the limits of the “knowledge” pursued by Western philosophy, problematizing the basis on which this knowledge is established as well as the framework it sets up.I think that the “character” of this or that philosophy arises from such different ways of seeing things and different attitudes toward “knowledge.” It is crucial to point out, however, that the gaps resulting from these differences need not become hindrances for philosophical thinking. Indeed, I think that the existence of such gaps, rather than hindering “dialogues” between different philosophies, is precisely what enables them to be meaningful. This is also what I have in mind when I stress the importance of dialogue in my lectures on Japanese philoso­phy. It is, after all, the creative dialogue engendered in this manner that enables philosophy to progress along its path of radical inquiry. (shrink)

New equations of motion for a Bloch electron [momentum p=h k,energy ε n(p),zone number n, charge -e]: $$m_j \frac{{dv_j }}{{dt}} = - e(E + v \times B)_j $$ are proposed, where v≡∂εn(p)/∂p is the velocity, and {mj}are the principal masses m j − 1=∂2εn/∂p j 2 along the normal and the two principal axes of curvatures at each point of the constant-energy surface represented by ε=εn(p).Their advantages over the prevalent equations of motion where the left-hand-side is replaced by hk j (...) are demonstrated by examining de Haas-van Alphen oscillations and orientation-dependent cyclotron resonance peaks. (shrink)

There has been a long-standing controversy in the context of language evolution on whether the original function of human language was internal thought or external communication. However, given the fact that language clearly serves both functions, internalization and externalization must have been co-evolutionarily acted in the emergence of human language. This article proposes a theoretical hypothesis about this co-evolutionary relationship of internalization and externalization, which especially explains the emergence of the human lexicon. To discuss the evolution of language from a (...) comprehensive perspective, this article proposes a promising model that integrates two approaches with different standpoints: generative grammar and cognitive linguistics. This paper also examines the definition and nature of the lexicon and lexical items based on this integrated model. The hypothesis presented here demonstrates that the co-evolutionary work of internalization and externalization has been involved in two processes in the development of the lexicon: the establishment of syntactic objects (lexical items) and the improvement of creativity responsible for the expansion of lexicon size. The main conclusion is that these processes have formed a positive feedback loop and provided our lexicon with complex and unique properties. (shrink)

This paper discusses sufficient conditions for a definably complete expansion of a densely linearly ordered abelian group to have uniformly locally o‐minimal open cores of the first/second kind and strongly locally o‐minimal open core, respectively.

The possibility of a Derridian theory of the university lies not in the discussion of the “as if” in “The University without Condition” but, rather, in a theoretical crack that Derrida's book promised to elucidate—between the “as if” and the “perhaps,” the performative and the event, transcendence and immanence. Moreover, we see a kind of rupture between this book and numerous texts from the 1970s and 80s, which are collected and published under the title of Right to Philosophy. Here lies (...) a real philosophical stake. We see between the early Derrida and the later Derrida not only an ethico-political turn but also, so to speak, a radical transition from the problematic of institution or case law (jurisprudence) to the axiomatic of law (loi) by aggravation of the transcendental. (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)

We define and investigate a uniformly locally o-minimal structure of the second kind in this paper. All uniformly locally o-minimal structures of the second kind have local monotonicity, which is a local version of monotonicity theorem of o-minimal structures. We also demonstrate a local definable cell decomposition theorem for definably complete uniformly locally o-minimal structures of the second kind. We define dimension of a definable set and investigate its basic properties when the given structure is a locally o-minimal structure which (...) admits local definable cell decomposition. (shrink)

Consider a definably complete uniformly locally o-minimal expansion of the second kind of a densely linearly ordered abelian group. Let $f:X \rightarrow R^n$ be a definable map, where X is a definable set and R is the universe of the structure. We demonstrate the inequality $\dim ) \leq \dim $ in this paper. As a corollary, we get that the set of the points at which f is discontinuous is of dimension smaller than $\dim $. We also show that the (...) structure is definably Baire in the course of the proof of the inequality. (shrink)

We first show that the projection image of a discrete definable set is again discrete for an arbitrary definably complete locally o‐minimal structure. This fact together with the results in a previous paper implies a tame dimension theory and a decomposition theorem into good‐shaped definable subsets called quasi‐special submanifolds. Using this fact, we investigate definably complete locally o‐minimal expansions of ordered groups when the restriction of multiplication to an arbitrary bounded open box is definable. Similarly to o‐minimal expansions of ordered (...) fields, Łojasiewicz's inequality, Tietze's extension theorem and affiness of pseudo‐definable spaces hold true for such structures under the extra assumption that the domains of definition and the pseudo‐definable spaces are definably compact. Here, a pseudo‐definable space is a topological space having finite definable atlases. We also demonstrate Michael's selection theorem for definable set‐valued functions with definably compact domains of definition. (shrink)

We define a discrete closure operator for definably complete locally o‐minimal structures. The pair of the underlying set of and the discrete closure operator forms a pregeometry. We define the rank of a definable set over a set of parameters using this fact and call it ‐dimension. A definable set X is of dimension equal to the ‐dimension of X. The structure is simultaneously a first‐order topological structure. The dimension rank of a set definable in the first‐order topological structure also (...) coincides with its dimension. (shrink)

Of all the nations in the East, the Chinese have had and still have the keenest awareness of the function of history, influencing, to a lesser extent, Japan, Korea, Vietnam, etc.The best evidence of this is the fact that events which occurred in China have been continuously recorded by the Chinese, chronologically and with accuracy as to dates, with greater and greater precision as time went on, up to today. We know that the First Emperor of the Ch'in Empire, the (...) founder of United China, died on the 7th day of the 7th month of the 37th year of his reign, i.e., 210 B.C., just as we know that Sun Yat-sen died on March 12, 1925. We also know that the date of the T'ang Emperor Hsüantsung's retreat from his capital to avoid rebellious troops was the 13th day of the 6th month of the 15th year of T'ien-pao (if transferred to the Julian Calendar, July 14, 756 A.D.), just as we know that the date of the Empress Dowager's retreat from Peking to avoid the Boxers was August 15, 1900. Furthermore, we know that on that unfortunate morning in 756 it was raining. (shrink)