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)

中世から近世に移るカオスの中で人びとはどのように生き、社会の中で思想を形成していったか。本書はそこにみられる、近代が切り捨ててきた、人と人とのつながりを真摯に追求する。.

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 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)

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)

"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.

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 volume contains a selection of papers presented at the special workshop "Truth and Objectivity in Law and Morals," held at the 26th World Congress of the IVR. The papers deal with diverse but correlated issues such as the search for truth in and through legal argumentation; the intelligible character of rules inside theories of interpretation which guarantee the coherence and the integrity of law; the role of hermeneutic analysis in the construction of the objectivity of law; the procedural and (...) contextual aspects of objectivity in legal reasoning; the role of objectivity in the distinction between the context of justification and the context of discovery; the problem about truth of normative propositions and legal statements; the incompatibility of non factualism with the traditional account of validity and legality; as well as the possibility of objectivity in morals. (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.

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.

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)

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, 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 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.