"Tanabe's agenda was not religious but philosophical in that he tried to integrate Eastern and Western insights in order to acquire a cross-cultural philosophical vision for the post-war world community.... This book shows his superior philosophical originality.... It is high time that Tanabe's thought should be introduced to the West."—Joseph Kitagawa, University of Chicago.

This article introduces English translations of Tanabe’s two essays entitled “Moral Freedom” and “On Moral Freedom Revisited.” In these essays, Tanabe tries to understand the unity of the contradictory division between freedom and necessity, while remaining truthful to the moral experience. Freedom is ultimately characterized as ideality that we ought to realize in reality, while the stage of religion constitutes the ultimate end of such moral struggles. Tanabe does not clearly work out how the continuity of the freedom-necessity discontinuity is (...) possible in these essays. Nevertheless, we can gain insight into the early stages of Tanabe’s practical metaphysics that culminate in his mature works on the philosophy of religion. The translators’ introduction will highlight these points and also provide a brief description of the historical background in which the publication of these texts took place in 1917. (shrink)

The history of the Vedanta school is well known since the time of Sankaracarya on, and its prehistory before Sankara is quite obscure. However, from the time of compilation of major Upanisads to Sankara there is a period of thousand years, and the tradition of Upanisads was not lost; there appeared many philosophers and dogmaticians, although their thoughts are not clearly known. The author has made clear the details of the pre-Sankara Vedanta philosophy, utilizing not only Sanskrit materials, but also (...) Pali, Prakrit (Jain), as well as Tibetan and Chinese sources. In this respect this is quite a unique work. For this work the author was awarded the Imperial Prize by the Academy of Japan. Some sections of this work were already published in Indian as well as European and American journals in English. This work is a complete English translation of the entire book. The English translation was done with the financial aid by the Harvard-Yenching Institute, and the final touch was given by Mr. Trevor Leggett, the British writer, who is well-versed in Sanskrit as well as in Japanese. (shrink)

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.

This paper presents the first English translation of one of Tanabe’s early essays on Kant. Tanabe marks the occasion of the first translation of the Critique of Practical Reason into Japanese by providing his reflections on Kant’s theory of freedom in this essay. This creative essay by Tanabe represents the hallmark Kyoto School interpretation of Kant. Tanabe weaves his account of Kant with elements from other philosophers in an attempt to think systematically about the nature of freedom. He agrees with (...) Kant that morality itself “rises and falls” with the idea of freedom; however, Tanabe also tries to rescue some of the pitfalls he sees in Kant’s theory by reconstructing Kant’s account. In this brief, but rich essay, Tanabe unfolds one of the more creative aspects of his philosophy through Kant. (shrink)

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.

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.

This paper offers an explanation of how collaboration leads to abstract and flexible problem solving. We asked the individual and paired subjects to indicate 3/4 of 2/3 of the area of a square sheet of paper and found that (1) they primarily folded or partitioned the paper rather than algorithmically calculating the answer, (2) they strongly tendened to backtrack and confirm their proto‐plans on externalized traces such as creases on the paper, and (3) only the paired subjects shifted to the (...) mathematical strategy in their second trials. Based on these results, we propose that two factors, individuals' activeness in choosing and confirming the initial strategies and the frequent role exchange between task‐doing and monitoring in collaborative situations, interact in collaboration to generate various solutions differing in the degree of abstraction, which are then reflected upon by the participants to lead them to abstraction. (shrink)

Dans son premier article, Tanabe soutient que le jugement n’est pas seulement un acte secondaire de la pensée : il est aussi l’acte par lequel l’objet est posé et sur lequel la connaissance se fonde, lorsqu’un acte d’attention se tourne vers le contenu de l’expérience pure. Dans celle-ci, objet et sujet sont encore indistincts. Ce jugement thétique fondamental diffère des autres jugements en ceci qu’en lui, il n’y a pas de décalage entre exigence et reconnaissance. Il est donc toujours affirmatif (...) et ne devient pas clairement conscient. Tanabe entend éviter ainsi l’idéalisme subjectif. (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 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 deal with a restricted form WC-N' of the weak continuity principle, a version BT' of Baire's theorem, and a boundedness principle BD-N. We show, in the spirit of constructive reverse mathematics, that WC-N'. BT' + ¬LPO and BD-N + ¬LPO are equivalent in a constructive system, where LPO is the limited principle of omniscience.

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)

In order to represent legal knowledge adequately, it is vital to create a formal device that can freely construct an individual concept directly from a predicate expression. For this purpose, a Compound Predicate Formula (CPF) is formulated for use in legal expert systems. In this paper, we willattempt to explain the nature of CPFs by rigorous logical foundation, i.e., establishing their syntax and semantics precisely through the use of appropriate examples. We note the advantages of our system over other such (...) systems and discuss the significance of CPFs with regard to the formalization of legal reasonings using examples from the United Nations Convention for the International Sale of Goods. (shrink)

This article introduces the first English translation of one of Tanabe’s early essays on metaphysics. It questions the relation of the universal to the particular in context of logic, phenomenology, Neo-Kantian epistemology, and classical metaphysics. Tanabe provides his reflections on the nature of the concept of universality and its constitutive relation to phenomenal particulars through critical analyses of the issue as it is discussed across various schools of philosophy including: British Empiricism, the Marburg School, the Austrian School, the Kyoto School, (...) and Platonism. In this essay, Tanabe reveals his ability to think metaphysically the ground for the possibility of reasoning and dares to voice his own thought beyond references to the most prominent thinkers of his time from distinct intellectual traditions in both the east and the west. This essay, therefore, demonstrates that his strong tendency to move beyond the received epistemology and phenomenology of the European intellectual tradition to metaphysics was already present in the early days of his academic life and thereby marks a more general contribution of the Kyoto School of Philosophy to distinct European schools of thought in the early twentieth century. (shrink)

We show that in elementary analysis (EL) the contrapositive of countable choice is equivalent to double negation elimination for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma_{2}^{0}}$$\end{document}-formulas. By also proving a recursive adaptation of this equivalence in Heyting arithmetic (HA), we give an instance of the conservativity of EL over HA with respect to recursive functions and predicates. As a complement, we prove in HA enriched with the (extended) Church thesis that every decidable predicate is recursive.

In this paper, we deal with a relationship among the law of excluded middle, the double negation elimination and the independence of premiss rule ) for intuitionistic predicate logic. After giving a general machinery, we give, as corollaries, several examples of extensions of \ and \ which are closed under \ but do not derive the independence of premiss axiom.

We extend Bishopʼs concept of function spaces to the concept of pre-function spaces. We show that there is an adjunction between the category of neighbourhood spaces and the category of Φ-closed pre-function spaces. We also show that there is an adjunction between the category of uniform spaces and the category of Ψ-closed pre-function spaces.

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)

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.