In this paper, we discuss semantical properties of the logic \(\textbf{GL}\) of provability. The logic \(\textbf{GL}\) is a normal modal logic which is axiomatized by the the Löb formula \( \Box (\Box p\supset p)\supset \Box p \), but it is known that \(\textbf{GL}\) can also be axiomatized by an axiom \(\Box p\supset \Box \Box p\) and an \(\omega \) -rule \((\Diamond ^{*})\) which takes countably many premises \(\phi \supset \Diamond ^{n}\top \) \((n\in \omega )\) and returns a conclusion \(\phi \supset (...) \bot \). We show that the class of transitive Kripke frames which validates \((\Diamond ^{*})\) and the class of transitive Kripke frames which strongly validates \((\Diamond ^{*})\) are equal, and that the following three classes of transitive Kripke frames, the class which validates \((\Diamond ^{*})\), the class which weakly validates \((\Diamond ^{*})\), and the class which is defined by the Löb formula, are mutually different, while all of them characterize \(\textbf{GL}\). This gives an example of a proof system _P_ and a class _C_ of Kripke frames such that _P_ is sound and complete with respect to _C_ but the soundness cannot be proved by simple induction on the height of the derivations in _P_. We also show Kripke completeness of the proof system with \((\Diamond ^{*})\) in an algebraic manner. As a corollary, we show that the class of modal algebras which is defined by equations \(\Box x\le \Box \Box x\) and \(\bigwedge _{n\in \omega }\Diamond ^{n}1=0\) is not a variety. (shrink)

It is well established that gratitude favours prosocial tendencies in neutral and amicable social interactions. Less is clear, however, about the role of gratitude in threatening situations that br...

Examining the interconnections between genes and culture is crucial for a more complete understanding of psychological processes. Genetic predispositions may predict different outcomes depending on one's cultural context, and culture may predict different outcomes depending on genetic predispositions - that is, genes and culture interact. Less is understood, however, about how genes and culture interact, or the psychological mechanisms through which gene–culture interactions occur. In this Element, Joni Y. Sasaki and Heewon Kwon review key findings and theories in gene–culture (...) interaction research. They then go on to discuss current issues and future directions in gene–culture research that may illuminate the path toward an explanatory framework. (shrink)

In the natural deduction system for classical propositional logic given by G. Gentzen, there are some inference rules with assumptions discharged by the rule. D. Prawitz calls such inference rules improper, and others proper. Improper inference rules are more complicated and are often harder to understand than the proper ones. In the present paper, we distinguish between proper and improper derivations by using sequent systems. Specifically, we introduce a sequent system \(\vdash_{\bf Sc}\) for classical propositional logic with only structural rules, (...) and prove that \(\vdash_{\bf Sc}\) does not allow improper derivations in general. For instance, the sequent \(\Rightarrow p \to q\) cannot be derived from the sequent \(p \Rightarrow q\) in \(\vdash_{\bf Sc}\). In order to prove the failure of improper derivations, we modify the usual notion of truth valuation, and using the modified valuation, we prove the completeness of \(\vdash_{\bf Sc}\). We also consider whether an improper derivation can be described generally by using \(\vdash_{\bf Sc}\). (shrink)

This paper describes the situation of philosophy in Japan with respect to the question of internationalism. For more than a hundred years, Japan took Western culture as its model and European philosophy as the authentic philosophy. This tendency was paradoxically strengthened by the post‐war humanism. It gave us Japanese philosophers a clear discipline to work in but cut us off from our own native culture, history, and philosophical traditions. In wishing to recover this loss, I argue that it is necessary (...) to distinguish between two forms of internationalism: humanistic and merely fashionable. The latter in fact derives from domestic reasons. (shrink)

The simple substitution property provides a systematic and easy method for proving a theorem by an axiomatic way. The notion of the property was introduced in Hosoi [4] but without a definite name and he showed three examples of the axioms with the property. Later, the property was given it's name as above in Sasaki [7].Our main result here is that the necessary and sufficient condition for a logicL on a finite slice to have the simple substitution property is (...) thatL is finite. Here the necessity part is essentially new, for the sufficiency part has been proved in Hosoi and Sasaki [5]. Also the proof of sufficiency part is improved here. (shrink)

1. Kō to shi no shisōshi -- 2. Kō to shi no shakai kagaku -- 3. Nihon ni okeru kō to shi -- 4. Ō-Bei ni okeru kō to shi -- 5. Kokka to ningen to kōkyōsei -- 6. Keizai kara mita kōshi mondai -- 7. Chūkan shūdan ga hiraku kōkyōsei -- 8. Kagaku gijutsu to kōkyōsei -- 9. chikyū kankyō to kōkyōsei -- 10. 21-seiki kōkyō tetsugaku no chihei -- 14. Rīdāshippu kara kangaeru kōkyōsei.

『不思議の国のアリス』の数学観から、古代ギリシャから現代への懐疑主義思想との格闘をたどって、数学的知識の成立根拠を探る。.

Hobbs (2010) introduced ‘clause-internal coherence’ (CIC) to describe inferences in, e.g., ‘A jogger was hit by a car,’ where the jogging is understood to have led to the car-hitting. Cohen & Kehler (2021) argue that well-known pragmatic tools cannot account for CIC, motivating an enrichment account familiar from discourse coherence research. An outstanding question is how to compositionally derive CIC from coherence relations. This paper takes strides in answering this question. It first provides experimental support for the existence of CIC (...) via offline evidence that attributive (non-)deverbal adjectives can trigger the same causal inferences within clauses that their predicative counterparts can trigger across clauses, albeit more weakly. To explain the experimental results, we use tools in Segmented Discourse Representation Theory (SDRT), which allows us to show that causal inferences can be derived in various ways, depending on whether deverbal adjectives are used attributively or predicatively. If the former, they are presupposition triggers and the coherence relations Elaboration/Continuation compete with Background; if the latter, Explanation/Result compete with Background. These different competitions -- cashed out in terms of interaction between default axioms -- correlate with the difference in the relative salience of the causal inferences. (shrink)

While the artistic traditions of the various countries of East, Southeast and South Asia display distinctive aesthetic features, this volume examines the qualities of each area, and seeks commonalities that define the aesthetics of a broader Asian civilization. Contributors includes specialists in philosophy, literature, art history, religion and the comparative study of cultures. Some of them are writing from within their own cultural traditions while others approach their subjects as outside observers. The book is divided into five sections, dealing with (...) Japanese, Korean, Chinese, Indian and Southeast Asian aesthetics. Individual chapters provide in-depth investigations of specific traditions, embracing both classical as well as modern aesthetic forms. The author suggest that Japanese culture is characterized by an openness to diverse cultural influences, Korean culture by "peninsularity," Chinese culture by parallels with the West, Indian culture by "rasa", and Southeast Asian culture by dilemmas of modernization. The volume as a whole integrates these studies, clarifying essential elements of each aesthetic culture and drawing on this material to characterize an Asian civilization that transcends individual countries and cultures. (shrink)

Volume 20, Issue 8, August 2020, Page 32-36.

In the natural deduction system for classical propositional logic given by G. Gentzen, there are some inference rules with assumptions discharged by the rule. D. Prawitz calls such inference rules improper as opposed to proper ones. Improper inference rules are more complicated than proper ones and more difficult to understand. In 2022, we provided a sequent system based solely on the application of proper rules. In the present paper, on the basis of our system from 2022, we classify improper inference (...) rules. (shrink)

Il s’agit ici de mettre en évidence une propriété de la beauté, à la fois subtile et évidente, mais largement ignorée de l’esthétique occidentale : la capacité du beau à embellir ce qui l’entoure. L’analyse s’appuie sur le commentaire d’un waka d’Akiko Yosano et étudie les proximités et les différences de cette beauté embellissante et de concepts philosophiques européens qui s’en rapprochent : l’éclat selon Platon, l’aura selon W. Benjamin, et le cérémonial, selon H. Kuhn.