Classically, weak König's lemma and Brouwer's fan theorem for detachable bars are equivalent. We give a direct constructive proof that the former implies the latter.

In this essay I present the philosophy of Nishida Kitarō, the father of the Kyoto School tradition, as an alternative version of transcendental philosophy. While following the steps of Kant and Husserl in important ways, Nishida attempts to take the transcendental approach even further, finally leaving us with a different view of reality that is neither realist nor idealist, but, rather, radically realist. I call this radical transcendental position, “awakened realism”. Due to word limitations, I can only set the stage (...) for further discussion on what kind of implication this may have for transcendental philosophy. But if I succeed in making my presentation clear enough, it should naturally ignite discussion on how far we can radicalize transcendental philosophy without making it into something else. (shrink)

Several studies have shown that our visual system may construct a “summary statistical representation” over groups of visual objects. Although there is a general understanding that human observers can accurately represent sets of a variety of features, many questions on how summary statistics, such as an average, are computed remain unanswered. This study investigated sampling properties of visual information used by human observers to extract two types of summary statistics of item sets, average and variance. We presented three models of (...) ideal observers to extract the summary statistics: a global sampling model without sampling noise, global sampling model with sampling noise, and limited sampling model. We compared the performance of an ideal observer of each model with that of human observers using statistical efficiency analysis. Results suggest that summary statistics of items in a set may be computed without representing individual items, which makes it possible to discard the limited sampling account. Moreover, the extraction of summary statistics may not necessarily require the representation of individual objects with focused attention when the sets of items are larger than 4. (shrink)

Working in the weakening of constructive Zermelo-Fraenkel set theory in which the subset collection scheme is omitted, we show that the binary refinement principle implies all the instances of the exponentiation axiom in which the basis is a discrete set. In particular binary refinement implies that the class of detachable subsets of a set form a set. Binary refinement was originally extracted from the fullness axiom, an equivalent of subset collection, as a principle that was sufficient to prove that the (...) Dedekind reals form a set. Here we show that the Cauchy reals also form a set. More generally, binary refinement ensures that one remains in the realm of sets when one starts from discrete sets and one applies the operations of exponentiation and binary product a finite number of times. (shrink)

ZusammenfassungIm Mittelpunkt des Beitrags steht die Übertragung ausgewählter Kapitel aus den 1955 niedergelegten autobiographischen Erinnerungen des japanischen Bakteriologen Taichi Kitashima, in denen Kitashima stark persönlich gefärbt über seinen Aufenthalt in Marburg berichtet. Wie andere japanische Mediziner seiner Generation verbrachte Kitashima mehrere Jahre in Deutschland, um dort bei dem Serumforscher Emil von Behring zu arbeiten und sich weiterzubilden. Der Kontakt war über Kitashimas Lehrer Shibasaburô Kitasato zustande gekommen, mit dem Behring in Berlin über Fragen der Immunologie geforscht hatte. Im „Kommentar“ wird (...) diskutiert, inwieweit die von Kitashima in der zeitlichen Distanz von 50 Jahren getroffene Einschätzung des Deutschlandaufenthalts als „vergeudete Zeit“ als zutreffend anzusehen ist, welche Vorteile ihm aus den europäischen Kontakten, zu denen auch Begegnungen im Pariser Pasteur-Institut gehörten, erwuchsen und aus welchen Gründen sie im Nationalsozialismus wiederbelebt wurden. (shrink)

The Dedekind cuts in an ordered set form a set in the sense of constructive Zermelo—Fraenkel set theory. We deduce this statement from the principle of refinement, which we distill before from the axiom of fullness. Together with exponentiation, refinement is equivalent to fullness. None of the defining properties of an ordering is needed, and only refinement for two—element coverings is used. In particular, the Dedekind reals form a set; whence we have also refined an earlier result by Aczel and (...) Rathjen, who invoked the full form of fullness. To further generalise this, we look at Richman's method to complete an arbitrary metric space without sequences, which he designed to avoid countable choice. The completion of a separable metric space turns out to be a set even if the original space is a proper class; in particular, every complete separable metric space automatically is a set. (shrink)

This book provides linguists with a clear, critical, and comprehensive overview of theoretical and experimental work on information structure. Leading researchers survey the main theories of information structure in syntax, phonology, and semantics as well as perspectives from psycholinguistics and other relevant fields. Following the editors' introduction the book is divided into four parts. The first, on theories of and theoretical perspectives on information structure, includes chapters on topic, prosody, and implicature. Part 2 covers a range of current issues in (...) the field, including focus, quantification, and sign languages, while Part 3 is concerned with experimental approaches to information structure, including processes involved in its acquisition and comprehension. The final part contains a series of linguistic case studies drawn from a wide variety of the world's language families. This volume will be the standard guide to current work in information structure and a major point of departure for future research. (shrink)

We systematically study several principles and give a principle which is weaker than disjunctive Markov’s principle. We also show that the principle is underivable and strictly weaker than MP∨ in certain extensions of the system EL of elementary analysis.

Estrogen receptor α (ERα) is a ligand‐dependent transcription factor that regulates the expression of estrogen‐responsive genes. Approximately 70% of patients with breast cancer are ERα positive. Estrogen stimulates cancer cell proliferation and contributes to tumor progression. Endocrine therapies, which suppress the ERα signaling pathway, significantly improve the prognosis of patients with breast cancer. However, the development of de novo or acquired endocrine therapy resistance remains a barrier to breast cancer treatment. Therefore, understanding the regulatory mechanisms of ERα is essential to (...) overcome the resistance to treatment. This review focuses on the regulation of ERα expression, including copy number variation, epigenetic regulation, transcriptional regulation, and stability, as well as functions from the point of view post‐translational modifications. (shrink)

This work examines Japanese government policies that impact on the environment in order to determine whether they incorporate a sufficient ethical substance. In the enquiry into the ethics of the policies, Kagawa-Fox explores how Western philosophers combined their theories to develop a 'Western environmental ethics code'; she also reveals the existence of a unique 'Japanese environmental ethics code' built on Japan's cultural traditions, religious practices, and empirical experiences. The discovery of the distinctive Japanese code is not only important for what (...) it discloses as a new philosophy, but most importantly how it can be used to analyse the ethical framework of the Japanese policies. In spite of the positive contributions that Japan has shown towards the global environment, the government has failed to show a corresponding moral obligation to the world ecology in its global environmental policy. The policies examined in the three case studies comprising whaling, nuclear energy, and forestry, have also been found wanting in ecological ethical considerations, both from a Western and Japanese perspective. The main reason for this is that the integrity of the policies has been compromised by Japanese vested interest groups; business and political interests ensure that the policies are primarily focused on maintaining sustainable economic growth. Whilst Japan's global environmental policy initiatives are the key to its economic survival into the 21st century, and these initiatives may achieve their aim, they do however fail the Japanese code of environmental ethics."--Publisher's description. (shrink)

The impact of _Harukanaru Sanga ni_ upon its publication in 1947 was immediate and dramatic- -the impetus, many have argued, for a post-war peace movement in Japan that has lasted over half a century. Now the text is available for the first time in English as _In the Far Away Mountains and Rivers_, a heart-wrenching and thought-provoking collection of letters, journal entries, and essays written by University of Tokyo students as they were drafted to fight in World War II. Many (...) of these students faced certain death as pilots in the kamikaze squads. Many of them deplored the war, and many were simply motivated by a sense of duty to their families and their country. They turned to poetry, philosophy, and religion—all in an attempt to make sense of the universal tragedy of war. (shrink)

Many existence propositions in constructive analysis are implied by the lesser limited principle of omniscience LLPO; sometimes one can even show equivalence. It was discovered recently that some existence propositions are equivalent to Bouwer's fan theorem FAN if one additionally assumes that there exists at most one object with the desired property. We are providing a list of conditions being equivalent to FAN, such as a unique version of weak König's lemma. This illuminates the relation between FAN and LLPO. Furthermore, (...) we give a short and elementary proof of the fact that FAN is equivalent to each positive valued function with compact domain having positive infimum. (shrink)

Uniform sequential continuity, a property classically equivalent to sequential continuity on compact sets, is shown, constructively, to be a consequence of strong continuity on a metric space. It is then shown that in the case of a separable metric space, uniform sequential continuity implies strong continuity if and only if one adopts a certain boundedness principle that, although valid in the classical, recursive and intuitionistic setting, is independent of Heyting arithmetic.

The purpose of this paper is an axiomatic study of the interrelations between certain continuity properties. We deal with principles which are equivalent to the statements "every mapping is sequentially nondiscontinuous", "every sequentially nondiscontinuous mapping is sequentially continuous", and "every sequentially continuous mapping is continuous". As corollaries, we show that every mapping of a complete separable space is continuous in constructive recursive mathematics (the Kreisel-Lacombe-Schoenfield-Tsejtin theorem) and in intuitionism.

We will overview the results in an informal approach to constructive reverse mathematics, that is reverse mathematics in Bishop’s constructive mathematics, especially focusing on compactness properties and continuous properties.

We will overview the results in an informal approach to constructive reverse mathematics, that is reverse mathematics in Bishop’s constructive mathematics, especially focusing on compactness properties and continuous properties.

The purpose of this paper is an axiomatic study of the interrelations between certain continuity properties. We show that every mapping is sequentially continuous if and only if it is sequentially nondiscontinuous and strongly extensional, and that "every mapping is strongly extensional", "every sequentially nondiscontinuous mapping is sequentially continuous", and a weak version of Markov's principle are equivalent. Also, assuming a consequence of Church's thesis, we prove a version of the Kreisel-Lacombe-Shoenfield-Tsĕitin theorem.

We investigate separation properties for neighbourhood spaces in some details within a framework of constructive mathematics, and define corresponding separation properties for quasi-apartness spaces. We also deal with separation properties for spaces with inequality.

We present statements equivalent to some fragments of the principle of non-deterministic inductive definitions (NID) by van den Berg (2013), working in a weak subsystem of constructive set theory CZF. We show that several statements in constructive topology which were initially proved using NID are equivalent to the elementary and finitary NIDs. We also show that the finitary NID is equivalent to its binary fragment and that the elementary NID is equivalent to a variant of NID based on the notion (...) of biclosed subset. Our result suggests that proving these statements in constructive topology requires genuine extensions of CZF with the elementary or finitary NID. (shrink)

The subject of Western environmental ethics has been widely written about and discussed but the same can not be said of 'Japanese' environmental ethics. This discipline has not been covered in any branch of Japanese philosophy nor has there been sufficient pressure exerted by ecologists on Japanese thinkers and writers to explain how the Japanese code addresses environmental concerns. Although some Japanese scholars have in the past articulated their ideas on working with the natural world, the field covering the spirit (...) and core of Japanese environmental ethics remains largely unexplored. This paper examines and compares the discipline of Japanese environmental ethics, a 'bottom up process', with that of the Western model, a 'top down process'. It defines, and presents a new insight into environmental ethics from the Japanese perspective where the concept of 'living with nature' is more sensitive towards the environment than is the Western one of 'taming nature'. (shrink)

We show, within the framework of Bishop's constructive mathematics, that (sequential) completeness of the locally convex space $\mathcal{D} (\mathbb{R})$ of test functions is equivalent to the principle BD-N which holds in classical mathemtatics, Brouwer's intuitionism and Markov's constructive recursive mathematics, but does not hold in Bishop's constructivism.

In this note, we prove that certain theories of (many‐sorted) intuitionistic predicate logic are closed under the independence of premiss rule (IPR). As corollaries, we show that and extended by some non‐classical axioms and non‐constructive axioms are closed under IPR.

Consider the problem which set V of propositional variables suffices for whenever, where, and ⊢c and ⊢i denote derivability in classical and intuitionistic implicational logic, respectively. We give a direct proof that stability for the final propositional variable of the (implicational) formula A is sufficient; as a corollary one obtains Glivenko's theorem. Conversely, using Glivenko's theorem one can give an alternative proof of our result. As an alternative to stability we then consider the Peirce formula. It is an easy consequence (...) of the result above that adding a single instance of the Peirce formula suffices to move from classical to intuitionistic derivability. Finally we consider the question whether one could do the same for minimal logic. Given a classical derivation of a propositional formula not involving ⊥, which instances of the Peirce formula suffice as additional premises to ensure derivability in minimal logic? We define a set of such Peirce formulas, and show that in general an unbounded number of them is necessary. (shrink)

We aim at developing a systematic method of separating omniscience principles by constructing Kripke models for intuitionistic predicate logic $\mathbf {IQC}$ and first-order arithmetic $\mathbf {HA}$ from a Kripke model for intuitionistic propositional logic $\mathbf {IPC}$. To this end, we introduce the notion of an extended frame, and show that each IPC-Kripke model generates an extended frame. By using the extended frame generated by an IPC-Kripke model, we give a separation theorem of a schema from a set of schemata in (...) $\mathbf {IQC}$ and a separation theorem of a sentence from a set of schemata in $\mathbf {HA}$. We see several examples which give us separations among omniscience principles. (shrink)

We show, within the framework of Bishop's constructive mathematics, that (sequential) completeness of the locally convex space $\mathcal{D} (\mathbb{R})$ of test functions is equivalent to the principle BD-N which holds in classical mathemtatics, Brouwer's intuitionism and Markov's constructive recursive mathematics, but does not hold in Bishop's constructivism.

We give a variant of the Gödel-Gentzen-negative translation, and a syntactic characterization which entails conservativity result for formulas.

How are the various classically equivalent definitions of compactness for metric spaces constructively interrelated? This question is addressed with Bishop-style constructive mathematics as the basic system – that is, the underlying logic is the intuitionistic one enriched with the principle of dependent choices. Besides surveying today's knowledge, the consequences and equivalents of several sequential notions of compactness are investigated. For instance, we establish the perhaps unexpected constructive implication that every sequentially compact separable metric space is totally bounded. As a by-product, (...) the fan theorem for detachable bars of the complete binary fan proves to be necessary for the unit interval possessing the Heine-Borel property for coverings by countably many possibly empty open balls. (shrink)

This special issue explores the significance of collectivism in modern and contemporary Japanese art. Japanese artists banded together throughout the twentieth century to work in collectives, reflecting and influencing each evolution of their culture. Illuminating the interplay between individual and community throughout Japan’s tumultuous century, the contributors to this issue examine both the practical internal operations of the collectives and the art that they produced. One contributor studies the art societies of prewar imperial Japan, whose juried art salons defined a (...) new _nihonga_ painting tradition. While recent scholarly work on art produced during World War II has tended to neglect the collectivist tradition, this issue covers wartime groups like the Art Unit for Promoting the Munitions Industry and the important questions they pose about the relationship between artists and the state. Art collectives in post-occupation Japan gained prominence working in the experimental vanguard of the global art scene in painting, sculpture, design, and intermedia projects. Adding a crucial dimension to the study of Japanese art and modernism, this issue explores how these groups attempted to accommodate the creative paradox of individualism within collectivism. _Contributors: Maki Kaneko, Kuroda Raiji, John Szostak, Miwako Tezuka, Ming Tiampo, Reiko Tomii, Alicia Volk, Midori Yoshimoto Reiko Tomii_ is an independent art historian and curator in New York. She is coauthor of _Xu Bing_. _Midori Yoshimoto_ is Associate Professor of Art History and curator of two galleries at New Jersey City University. She is the author of _Into Performance: Japanese Women Artists in New York_. (shrink)

We extend the concept of apartness spaces to the concept of quasi-apartness spaces. We show that there is an adjunction between the category of quasi-apartness spaces and the category of neighbourhood spaces, which indicates that quasi-apartness is a more natural concept than apartness. We also show that there is an adjoint equivalence between the category of apartness spaces and the category of Grayson’s separated spaces.

The standard construction of quotient spaces in topology uses full separation and power sets. We show how to make this construction using only the predicative methods available in constructive type theory and constructive set theory.

Political developments in Japan from the latter part of 2000 to the year 2001 were highlighted by the executive transition from unpopular Yoshiro Mori to exceptionally popular Junichiro Koizumu as the nation's leader.

Consistency with the formal Church’s thesis, for short CT, and the axiom of choice, for short AC, was one of the requirements asked to be satisfied by the intensional level of a two-level foundation for constructive mathematics as proposed by Maietti and Sambin From sets and types to topology and analysis: practicable foundations for constructive mathematics, Oxford University Press, Oxford, 2005). Here we show that this is the case for the intensional level of the two-level Minimalist Foundation, for short MF, (...) completed in 2009 by the second author. The intensional level of MF consists of an intensional type theory à la Martin-Löf, called mTT. The consistency of mTT with CT and AC is obtained by showing the consistency with the formal Church’s thesis of a fragment of intensional Martin-Löf’s type theory, called \, where mTT can be easily interpreted. Then to show the consistency of \ with CT we interpret it within Feferman’s predicative theory of non-iterative fixpoints \ by extending the well known Kleene’s realizability semantics of intuitionistic arithmetics so that CT is trivially validated. More in detail the fragment \ we interpret consists of first order intensional Martin-Löf’s type theory with one universe and with explicit substitution rules in place of usual equality rules preserving type constructors -rule which is not valid in our realizability semantics). A key difficulty encountered in our interpretation was to use the right interpretation of lambda abstraction in the applicative structure of natural numbers in order to model all the equality rules of \ correctly. In particular the universe of \ is modelled by means of \-fixpoints following a technique due first to Aczel and used by Feferman and Beeson. (shrink)