A non-classical subsystem of orthomodular quantum logic is proposed. This system employs two basic operations: the Sasaki hook as implication and the _and-then_ operation as conjunction. These operations successfully satisfy modus ponens and the deduction theorem. In other words, they form an adjunction in terms of category theory. Two types of semantics are presented for this logic: one algebraic and one physical. The algebraic semantics deals with orthomodular lattices, as in traditional quantum logic. The physical semantics is given as a (...) procedure for deriving a final segment of a series of yes-no experiments. (shrink)

The concept of quantum logic is extended so that it covers a more general set of propositions that involve non-trivial probabilities. This structure is shown to be embedded into a multi-modal framework, which has desirable logical properties such as an axiomatization, the finite model property and decidability.

It can be intuitively understood that sets and their elements in mathematics reflect the atomistic way of thinking in physics: Sets correspond to physical properties, and their elements correspond to particles that have these properties. At the same time, quantum statistics and quantum field theory strongly support the view that quantum particles are not individuals. Some of the problems faced in modern physics may be caused by such discrepancy between set theory and physical theory. The question then arises: Is it (...) possible to reconstruct the concept of set as a collection of objects that model quantum particles rather than as a mere collection of individuals? David Deutsch has argued that identical entities can be diverse in their attributes, and that this nature, what he calls fungibility, must lie at the heart of quantum physics. In line with this idea, a set theory with fungible elements is established, and the collection of such sets is shown to be endowed with an ortholattice structure, which is better known as quantum logic. (shrink)

The logical structure derived from the algebra of generalised projection operators on a module is investigated. With the assumption of the operators being linear, the associated logic becomes Boolean, while without the assumption, the logic does not admit negation: the concept of linearity of projection operators on a module corresponds to that of negation in Boolean logic. The logic of nonlinear operators is formalised and its soundness and completeness results are proved.

Quantum logic is only applicable to microscopic phenomena while classical logic is exclusively used for everyday reasoning, including mathematics. It is shown that both logics are unified in the framework of modal interpretation. This proposed method deals with classical propositions as latently modalized propositions in the sense that they exhibit manifest modalities to form quantum logic only when interacting with other classical subsystems.

The paper presents a new argument for epistemic permissivism. The version of permissivism that we defend is a moderate version that applies only to explicit doxastic attitudes. Drawing on Yalcin’s framework for modeling such attitudes, we argue that two fully rational subjects who share all their evidence, prior beliefs, and epistemic standards may still differ in the explicit doxastic attitudes that they adopt. This can happen because two such subjects may be sensitive to different questions. Thus, differing intellectual interests can (...) yield failures of uniqueness. This is not a merely pragmatic phenomenon. (shrink)

田辺は自己の生を包摂する時代の趨勢と真摯に対峙し、廣松は「近代」の陥穽を注視し絶えず他者との協働を考察し続けた。この二人の視座から「啓蒙の弁証法」の陥穽に落ちた日本社会と日本人の「生の姿」を考えていく 。.

Recent work on the application of neural networks to language modeling has shown that models based on certain neural architectures can capture syntactic information from utterances and sentences even when not given an explicitly syntactic objective. We examine whether a fully data-driven model of language development that uses a recurrent neural network encoder for utterances can track how child language utterances change over the course of language development in a way that is comparable to what is achieved using established language (...) assessment metrics that use language-specific information carefully designed by experts. Given only transcripts of child language utterances from the CHILDES Database and no pre-specified information about language, our model captures not just the structural characteristics of child language utterances, but how these structures reflect language development over time. We establish an evaluation methodology with which we can examine how well our model tracks language development compared to three known approaches: Mean Length of Utterance, the Developmental Sentence Score, and the Index of Productive Syntax. We discuss the applicability of our model to data-driven assessment of child language development, including how a fully data-driven approach supports the possibility of increased research in multilingual and cross-lingual issues. (shrink)

Interventions performed on a pregnant woman's body can affect the fetus in multiple ways. Such effects can be harmful to beneficial to the fetus. Unfortunately, the effects of new drugs and compoun...

丸山眞男の政治思想史と廣松渉の哲学は「現代の人間世界における人間性の運命とは」を「問う」たのであった。今、だからこそ惰性となった現実主義を「醒めた目」で捉える必要がある。つまり、丸山と廣松の両者のよう に「“鉄のように堅い殻”」の歴史内部で退動する「弁証法的緊張」を把握しなくてはならない。二人が生涯を賭けた思想史と哲学の探求は、人間の歴史的現実に対する私たち自身の課題なのである。.

Ariga Tetsutaro (1899–1977) war Professor für das Studium des Christentums an der Universität Kyoto und gehörte dort der zweiten Professoren-generation an. Er legte die Grundlagen der Patristik und der Erforschung des Christentums in Japan. In seinem Hauptwerk “Origenes” hatte er den Historismus in der Theologie erforscht, aber nachdem er seinen Dienst als Professor an der staatlichen Universität aufgenommen hatte, die die Trennung von Staat und Religion hochhielt, suchte er nach Wegen, ein ‘Studium des Christlichen’ zu etablieren, das sich von der (...) Theologie unterschied. Dabei dienten ihm Schleiermachers “Kurze Darstellung des theologischen Studiums” und die Tradition des deutschen liberalen Protestantismus als Anhaltspunkte. Anstatt der Theologie, die den Glauben als methodischen Ausgangspunkt hat, und der Religionswissenschaft, die nur die distanzierte Objektivität als Ausgangspunkt wählt, schlug er als neuen Versuch ein Christliches Studium mit akademischem Standpunkt vor, bei dem der Gelehrte eine Forschungshaltung einnimmt, die durch ein Mindestmaß an vernünftiger Kritik und ‘Ur-Sympathie’ gegenüber der Religion geprägt ist. (shrink)

Ariga Tetsutaro (1899–1977) war Professor für das Studium des Christentums an der Universität Kyoto und gehörte dort der zweiten Professoren-generation an. Er legte die Grundlagen der Patristik und der Erforschung des Christentums in Japan. In seinem Hauptwerk “Origenes” hatte er den Historismus in der Theologie erforscht, aber nachdem er seinen Dienst als Professor an der staatlichen Universität aufgenommen hatte, die die Trennung von Staat und Religion hochhielt, suchte er nach Wegen, ein ‘Studium des Christlichen’ zu etablieren, das sich von der (...) Theologie unterschied. Dabei dienten ihm Schleiermachers “Kurze Darstellung des theologischen Studiums” und die Tradition des deutschen liberalen Protestantismus als Anhaltspunkte. Anstatt der Theologie, die den Glauben als methodischen Ausgangspunkt hat, und der Religionswissenschaft, die nur die distanzierte Objektivität als Ausgangspunkt wählt, schlug er als neuen Versuch ein Christliches Studium mit akademischem Standpunkt vor, bei dem der Gelehrte eine Forschungshaltung einnimmt, die durch ein Mindestmaß an vernünftiger Kritik und ‘Ur-Sympathie’ gegenüber der Religion geprägt ist. (shrink)

The $$\varepsilon $$ -elimination method of Hilbert’s $$\varepsilon $$ -calculus yields the up-to-date most direct algorithm for computing the Herbrand disjunction of an extensional formula. A central advantage is that the upper bound on the Herbrand complexity obtained is independent of the propositional structure of the proof. Prior (modern) work on Hilbert’s $$\varepsilon $$ -calculus focused mainly on the pure calculus, without equality. We clarify that this independence also holds for first-order logic with equality. Further, we provide upper bounds analyses (...) of the extended first $$\varepsilon $$ -theorem, even if the formalisation incorporates so-called $$\varepsilon $$ -equality axioms. (shrink)

人間は「生」を得た瞬間から「死」という「滅び」に向かって生きている。そうであるからこそ「生」を尊ぶという考え方が日本の美をつくってきた。日本の美意識の基層をなし、自然に美を見いだした「優美」。演技を七 分にとどめ、完全に演じ切らないことを説いた世阿弥の「幽玄」。慢心する秀吉を戒め、侘びることを説いた利休の「侘び」。旅の途中で寂びつくして命つきることを願った芭蕉の「さび」。西欧文化の影響が背景にある「 きれい」。そして、二一世紀に世界を席巻する「かわいい」とは―。日本の美の潮流を俯瞰し、心のふるさとに耳をすます。.

This paper presents a natural deduction system for orthomodular quantum logic. The system is shown to be provably equivalent to Nishimura’s quantum sequent calculus. Through the Curry–Howard isomorphism, quantum $$\lambda $$ -calculus is also introduced for which strong normalization property is established.