We prove in the framework of Bishop's constructive mathematics that the sequential completion equation image of the space [MATHEMATICAL SCRIPT CAPITAL D] is filter-complete. Then it follows as a corollary that the filter-completeness of [MATHEMATICAL SCRIPT CAPITAL D] is equivalent to the principle BD-ℕ, which can be proved in classical mathematics, Brouwer's intuitionistic mathematics and constructive recursive mathematics of Markov's school, but does not in Bishop's constructive mathematics. We also show that equation image is identical with the filter-completion which was (...) provided by Bishop. (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 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.

篤胤において死の問題は、死後の存在としての霊魂の問題となり、さらには霊魂の行き場所の問題となる。もし人が死後に霊魂となることが確実であり、霊魂の行き着く場所が特定されるのであれば、先に現在の私たちに即 して述べたような死の問題は、「解決」されるに違いない。篤胤はまさにそのことを『霊の真柱』において試み、「幽冥界」という観念を提示することになる。.

新資料から、現代にも通ずる日本独自の豊かな死生観を探求した、江戸後期を代表する思想家としての新たな篤胤像を描き出す意欲作。.

儒教・仏教という知的伝統と、西洋哲学という新たな知が出会った明治。近代化と伝統の間で花開く新たな知の深層を明らかにする!

As I have pointed out in a series of papers, which appeared about fifteen years ago in the Revue de l'histoire des religions, there are numerous resemblances between the ancient myths of the Indo-Europeans, on the one hand, and those of Japan, on the other. These resemblances, relating both to the fundamental structures of the two mythological systems and to a number of curious details, constitute an assemblage which seems too conspicuous to be regarded as either accidental or the result (...) of a similitude of human mentalities, manifesting itself, so it seems, through the creation of a great many similar myths and legends throughout the length and breadth of the surface of our planet. (shrink)

S-Modulin is a frog homolog of recoverin. The function and the underlying mechanism of the action of these proteins are now understood in general. However, there remain some unsolved issues including; two distinct effects of S-modulin; Ca2+-dependent binding of S-modulin to membranes and a possible target protein; S-modulin-like proteins in other neurons. These issues are considered in this commentary.

「近代の超克」から「近代の止揚」への“燎爛たる分裂”。西田幾多郎、三木清、戸坂潤の哲学を「個人‐市民‐大衆」形成論として捉える。.

In dieser Abhandlung versuchen wir die Theorie des Erhabenen bei Kant als eine Logik der reflektierenden Urteilskraft darzustellen, die den Ubergang des Sinnlichen ins Ubersinnliche ermoglicht. Die Urteilskraft bezieht die Spannung der Einbildungskraft vor dem Nicht-Darstellbaren auf das Ubersinnliche, und in dieser Beziehung sieht Kant "eine a priori im Subjekte liegende Zweckmassigkeit". Durch die Vorstellung der gewaltigen Natur kann unsere innere Idee erweckt werden, wenn wir berucksichtigen, "dass auf jene moralischen Anlagen bei jeder schicklichen Veranlassung Rucksicht genommen werden sollte". Durch (...) das Urteil uber das Erhabene erhalten wir eine Veranlassung fur diejenige Reflexion, die innerhalb der Natur auch die ubersinnliche Idee (oder ein gottliches Wesen) denkt. (edited). (shrink)

We show that length initial submodels of S12 can be extended to a model of weak second order arithmetic. As a corollary we show that the theory of length induction for polynomially bounded second order existential formulae cannot define the function division.

We define a theory of two-sort bounded arithmetic whose provably total functions are exactly those in ${\mathcal{F}_{LOGCFL}}$ by way of a generalized quantifier that expresses computations of SAC 1 circuits. The proof depends on Kolokolova’s conditions for the connection between the provable capture in two-sort theories and descriptive complexity.

We define a fragment of Primitive Recursive Arithmetic by replacing the defining axioms for primitive recursive functions by those for functions in some specific complexity class. In this note we consider such theory for AC0. We present a model-theoretical property of this theory, by means of which we are able to characterize its provably total functions. Next we consider the problem of how strong the induction scheme can be in this theory.

We will give a two-sort system which axiomatizes winning strategies for the combinatorial game Node Kayles. It is shown that our system captures alternating polynomial time reasonings in the sense that the provably total functions of the theory corresponds to those computable in APTIME. We will also show that our system is equivalently axiomatized by Sprague–Grundy theorem which states that any Node Kayles position is provably equivalent to some NIM heap.

Despite the tendency to be otherwise, some non-classical logics are known to validate formulas that are invalid in classical logic. A subclass of such systems even possesses pairs of a formula and its negation as theorems, without becoming trivial. How should these provable contradictions be understood? The present paper aims to shed light on aspects of this phenomenon by taking as samples the constructive connexive logic C, which is obtained by a simple modification of a system of constructible falsity, namely (...) N4, as well as its non-constructive extension C3. For these systems, various observations concerning provable contradictions are made, using mainly a proof-theoretic approach. The topics covered in this paper include: how new contradictions are found from parts of provable contradictions; how to characterise provable contradictions in C3 that are constructive; how contradictions can be seen from the relative viewpoint of strong implication; and as an appendix an attempt at generating provable contradictions in C3. (shrink)

日本の固有の宗教神道より説き起こし、日本の仏教、歌人・念仏者・茶人・武人・医者・妙好人・禅僧・真宗僧侶・作家・俳人と多種な人間像を通して、日本人の生き生きとした生命の躍動感を解き明かす。.