Proof-theory has traditionally been developed based on linguistic (symbolic) representations of logical proofs. Recently, however, logical reasoning based on diagrammatic or graphical representations has been investigated by logicians. Euler diagrams were introduced in the eighteenth century. But it is quite recent (more precisely, in the 1990s) that logicians started to study them from a formal logical viewpoint. We propose a novel approach to the formalization of Euler diagrammatic reasoning, in which diagrams are defined not in terms of regions as in (...) the standard approach, but in terms of topological relations between diagrammatic objects. We formalize the unification rule, which plays a central role in Euler diagrammatic reasoning, in a style of natural deduction. We prove the soundness and completeness theorems with respect to a formal set-theoretical semantics. We also investigate structure of diagrammatic proofs and prove a normal form theorem. (shrink)

We introduce a simple inference system based on two primitive relations between terms, namely, inclusion and exclusion relations. We present a normalization theorem, and then provide a characterization of the structure of normal proofs. Based on this, inferences in a syllogistic fragment of natural language are reconstructed within our system. We also show that our system can be embedded into a fragment of propositional minimal logic.

Recently Lafont [6] showed the finite model property for the multiplicative additive fragment of linear logic (MALL) and for affine logic (LLW), i.e., linear logic with weakening. In this paper, we shall prove the finite model property for intuitionistic versions of those, i.e. intuitionistic MALL (which we call IMALL), and intuitionistic LLW (which we call ILLW). In addition, we shall show the finite model property for contractive linear logic (LLC), i.e., linear logic with contraction, and for its intuitionistic version (ILLC). (...) The finite model property for related substructural logics also follow by our method. In particular, we shall show that the property holds for all of FL and GL - -systems except FL c and GL - c of Ono [11], that will settle the open problems stated in Ono [12]. (shrink)

Proof-theoretical notions and techniques, developed on the basis of sentential/symbolic representations of formal proofs, are applied to Euler diagrams. A translation of an Euler diagrammatic system into a natural deduction system is given, and the soundness and faithfulness of the translation are proved. Some consequences of the translation are discussed in view of the notion of free ride, which is mainly discussed in the literature of cognitive science as an account of inferential efficacy of diagrams. The translation enables us to (...) formalize and analyze free ride in terms of proof theory. The notion of normal form of Euler diagrammatic proofs is investigated, and a normalization theorem is proved. Some consequences of the theorem are further discussed: in particular, an analysis of the structure of normal diagrammatic proofs; a diagrammatic counterpart of the usual subformula property; and a characterization of diagrammatic proofs compared with natural deduction proofs. (shrink)

In 2018 the World Heath Organization decided to re-examine the classification of gender identity disorder and exclude it from being defined as a mental illness. This re-examination means that sex a...

To investigate the relationship between logical reasoning and majority voting, we introduce logic with groups Lg in the style of Gentzen’s sequent calculus, where every sequent is indexed by a group of individuals. We also introduce the set-theoretical semantics of Lg, where every formula is interpreted as a certain closed set of groups whose members accept that formula. We present the cut-elimination theorem, and the soundness and semantic completeness theorems of Lg. Then, introducing an inference rule representing majority voting to (...) Lg, we introduce logic with majority voting Lv. Formalizing the discursive paradox in judgment aggregation theory, we show that Lv is inconsistent. Based on the premise-based and conclusion-based approaches to avoid the paradox, we introduce logic with majority voting for axioms Lva, where majority voting is applied only to non-logical axioms as premises to construct a proof in Lg, and logic with majority voting for conclusions Lvc, where majority voting is applied only to the conclusion of a proof in Lg. We show that both Lva and Lvc are syntactically complete and consistent, and we construct collective judgments based on the provability in Lva and Lvc, respectively. Then, we discuss how these systems avoid the discursive paradox. (shrink)

This book provides an overview of behavioral decision theory and related research findings. In brief, behavioral decision theory is a general term for descriptive theories to explain the psychological knowledge related to decision-making behavior. It is called a theory, but actually it is a combination of various psychological theories, for which no axiomatic systems, such as the utility theory widely used in economics, have been established; it is often limited to qualitative knowledge. However, as suggested in the studies of H. (...) A. Simon, who won the Nobel Prize for Economics in 1978, and D. Kahneman, who won the prize in 2002, the psychological methodology and knowledge of behavioral decision theory have been applied widely in such fields as economics, business administration, and engineering, and are expected to become more useful in the future. This book explains various behavioral decision theories related to decision-making processes. Numerous models have been proposed to explain the psychological processes related to such a selection of decision strategies, and this book also introduces some new models that are useful to explain decision-making processes. The book concludes with speculation about the future of modern behavioral decision theories while referring to their relation to fields associated with neuroscience, such as neuroeconomics, that have been developed in recent years. In addition, each chapter includes a bibliography that can be referred to when studying more details related to behavioral decision theory. Reading this book requires no advanced expertise; nonetheless, an introductory knowledge of psychology, business administration, and economics, and approximately a high school graduate’s level of mathematics should facilitate the reader’s comprehension of the content. (shrink)

One of the traditional applications of Euler diagrams is as a representation or counterpart of the usual set-theoretical models of given sentences. However, Euler diagrams have recently been investigated as the counterparts of logical formulas, which constitute formal proofs. Euler diagrams are rigorously defined as syntactic objects, and their inference systems, which are equivalent to some symbolic logical systems, are formalized. Based on this observation, we investigate both counter-model construction and proof-construction in the framework of Euler diagrams. We introduce the (...) notion of “counter-diagrammatic proof”, which shows the invalidity of a given inference, and which is defined as a syntactic manipulation of diagrams of the same sort as inference rules to construct proofs. Thus, in our Euler diagrammatic framework, the completeness theorem can be formalized in terms of the existence of a diagrammatic proof or a counter-diagrammatic proof. (shrink)

Methodological nationalism in sociological theory is unfit for the current globalized era, and should be discarded. In light of this contention, the present article discusses Max Weber’s view of language as a way to relativize the frame of the national society. While a “linguistic turn” in sociology since the 1960s has assumed that the sharing of language—linguistic community—stands as an intersubjective foundation for understanding of meaning, Weber saw linguistic community as constructed. From Weber’s rationalist, subjectivist, individualist viewpoint, linguistic community was (...) a result of social actions, not a prior entity as assumed by German metaphysical organicism (and historicist holism). Indeed, Central Europe in Weber’s era was a battlefield of linguistic nationalism(s); in contrast to the national societies of the Cold War period, national borders were unstable and ultimately the multiethnic empires of the region were dismantled after World War I into ethnolinguistic nation-states. Experience of this contemporary reality brought Weber to the core of the relationship between language and politics: A language community is an imaginary one demarcated not by language itself but by conscious opposition against outsiders, with monolingual contexts within borders created artificially by homogenizing policies like linguistic standardization and national education—the first modernity of language. In this way, Weber felt, language can be a means to domination. (shrink)

We present some ideas on logical process descriptions, using relations from the DIO (Drug Interaction Ontology) as examples and explaining how these relations can be naturally decomposed in terms of more basic structured logical process descriptions using terms from linear logic. In our view, the process descriptions are able to clarify the usual relational descriptions of DIO. In particular, we discuss the use of logical process descriptions in proving linear logical theorems. Among the types of reasoning supported by DIO one (...) can distinguish both (1) basic reasoning about general structures in reality and (2) the domain-specific reasoning of experts. We here propose a clarification of this important distinction between (realist) reasoning on the basis of an ontology and rule-based inferences on the basis of an expert’s view. (shrink)

The objective of this paper is to consider some of the philosophical problems on gender in sport in terms of practical philosophy by examining previous studies on sports and gender in Japan. The previous studies of the Journal of Sport and Gender Studies, an institutional journal of the Japan Society for Sport and Gender Studies , and were reviewed to explain the characteristics and the limits of previous sports-gender studies in Japan to establish the parameters for a philosophical discussion of (...) sport-gender studies. A philosophical examination of the issues of affirmative actions, which is the least discussed topic among those listed in ‘JSGS’, is presented. By revealing fundamental problems in research on sports and gender in Japan, this study may potentially contribute to the resolution of multiple issues surrounding women in sports in Japan. Also, by exposing general and omnipresent problems, the study transcends the limited framework of sports in Japan, and can point to those common and overarching gender issues that need to be resolved around the world. (shrink)

明治時代の“知と行動の巨人”の思想に迫る!東洋大学創立者、妖怪博士、近代仏教復興の立役者...と獅子奮迅の活躍を見せた井上円了。その業績を支えた独自の世界観・人生観を原典に基づきながら解明。.

仏教復興への情熱と行動の足跡を丹念にたどり、この偉大な先達が哲学的に究明した仏教思想の全貌をあきらかにする。画期的円了論。.

We extend natural deduction for first-order logic (FOL) by introducing diagrams as components of formal proofs. From the viewpoint of FOL, we regard a diagram as a deductively closed conjunction of certain FOL formulas. On the basis of this observation, we first investigate basic heterogeneous logic (HL) wherein heterogeneous inference rules are defined in the styles of conjunction introduction and elimination rules of FOL. By examining what is a detour in our heterogeneous proofs, we discuss that an elimination-introduction pair of (...) rules constitutes a redex in our HL, which is opposite the usual redex in FOL. In terms of the notion of a redex, we prove the normalization theorem for HL, and we give a characterization of the structure of heterogeneous proofs. Every normal proof in our HL consists of applications of introduction rules followed by applications of elimination rules, which is also opposite the usual form of normal proofs in FOL. Thereafter, we extend the basic HL by extending the heterogeneous rule in the style of general elimination rules to include a wider range of heterogeneous systems. (shrink)

インド、中国そして日本。古代から近代へと、東洋思想の核心を求めて。この世界は、実体的存在などなく、あらゆるものが互いに関係し合って存在している。ではそこで自己とはいかなる存在で、どのようにあるべきなの か。唯識の事的世界観から華厳の事事無礙法界へ、さらに空海の人人無礙の曼荼羅、そして西田の「個物の哲学」へ。東洋の大地にそびえたつ哲学の連峰を縦横に踏破し、その叡智の真髄を未来に向けて照らし出す壮大な書 。.

The aim of this article is to explore how a self-referential social system, although it is not a human being, can be said to “observe.” For this purpose, the article reformulates Niklas Luhmann’s theory of social systems as sociological phenomenology, or the de-consciousness philosophized phenomenology, because a social system has the same structure of intentionality as consciousness: Just as consciousness is always consciousness of something, communication is always communication of something. In correlation to this communicative intentionality, communicated environments come and (...) go as social phenomena. A social system is not a thing, but an autonomously observing subject. Hence, this systems theory takes on the role of a second-order observer: It observes how social systems as first-order observers observe self-referentially because phenomena given to the natural attitude of the first-order observer constitute multiple social realities in daily life. Therefore, the theory of self-referential social systems is not objectivism, but a variation of mundane subjectivist phenomenology. (shrink)

The aim of this article is to explore how a self-referential social system, although it is not a human being, can be said to “observe.” For this purpose, the article reformulates Niklas Luhmann’s theory of social systems as sociological phenomenology, or the de-consciousness philosophized phenomenology, because a social system has the same structure of intentionality as consciousness: Just as consciousness is always consciousness of something, communication is always communication of something. In correlation to this communicative intentionality, communicated environments come and (...) go as social phenomena. A social system is not a thing, but an autonomously observing subject. Hence, this systems theory takes on the role of a second-order observer: It observes how social systems as first-order observers observe self-referentially because phenomena given to the natural attitude of the first-order observer constitute multiple social realities in daily life. Therefore, the theory of self-referential social systems is not objectivism, but a variation of mundane subjectivist phenomenology. (shrink)

We introduce subsystems WLJ and SI of the intuitionistic propositional logic LJ, by weakening the intuitionistic implication. These systems are justifiable by purely constructive semantics. Then the intuitionistic implication with full strength is definable in the second order versions of these systems. We give a relationship between SI and a weak modal system WM. In Appendix the Kripke-type model theory for WM is given.

A Correction to this paper has been published: 10.1007/s11186-021-09436-2.

When Thomas Luckmann, a pioneer of the “linguistic turn” in sociology, regarded Émile Durkheim as a source for the sociology of language, he had lifeworldly community–building in mind. However, the French sociologist himself understood language in the context ofcivil society–building. To Durkheim, language was a “social thing in the highest degree” that enabled general ideas and intermediated them to people. Abstract human ideals like the civil religion since the French Revolution could be shared through (a common) language. Thus, Durkheim took (...) the exclusive use of French in the Third Republic’s laic public education for granted, ignoring the patois in the country: This “child of the Enlightenment” considered French to be a universal language ofGesellschaftand, beyond ethno-communal elements, to work as a basis for the organic solidarity of French national civil society where the social division of labor was progressing. Durkheim’s theory was predicated on civil-linguistic, not ethnolinguistic, nationalism. (shrink)

Sister chromatid separation in anaphase is an important event in the cell's transmission of genetic information to a descendent. It has been investigated from different aspects: cell cycle regulation, spindle and chromosome dynamics within the three‐dimensional cell architecture, transmission fidelity control and cellular signaling. Integrated studies directed toward unified understanding are possible using multidisciplinary methods with model organisms. Ubiquitin‐dependent proteolysis, protein dephosphorylation, an unknown function by the TPR repeat proteins, chromosome transport by microtubule‐based motors and DNA topological change by DNA (...) topoisomerase II are all necessary for progression from metaphase to anaphase. Chromosome condensation, mitotic kinetochore function and spindle formation require a large number of proteins, which are prerequisites for successful sister chromatid separation. Factors that help to retain sister chromatid connection after replication and prevent premature separation remain to be determined. Although sister chromatid separation occurs in anaphase, gene functions in other cell cycle stages also ensure the progression of correct chromatid separation. (shrink)

Girard introduced phase semantics as a complete set-theoretic semantics of linear logic, and Okada modified phase-semantic completeness proofs to obtain normal-form theorems. On the basis of these works, Okada and Takemura reformulated Girard’s phase semantics so that it became phase semantics for proof-terms, i.e., lambda-terms. They formulated phase semantics for proof-terms of Laird’s dual affine/intuitionistic lambda-calculus and proved the normal-form theorem for Laird’s calculus via a completeness theorem. Their semantics was obtained by an application of computability predicates. In this (...) paper, we first formulate phase semantics for proof-terms of second-order intuitionistic propositional logic by modifying Tait-Girard’s saturated sets method. Next, we prove the completeness theorem with respect to this semantics, which implies a strong normalization theorem. (shrink)

The paper traces the development and the role of syntactic reduction in Edmund Husserl’s early writings on mathematics and logic, especially on arithmetic. The notion has its origin in Hermann Hankel’s principle of permanence that Husserl set out to clarify. In Husserl’s early texts the emphasis of the reductions was meant to guarantee the consistency of the extended algorithm. Around the turn of the century Husserl uses the same idea in his conception of definiteness of what he calls “mathematical manifolds.” (...) The paper argues that the notion anticipates the notion of reduction in term rewrite theory in computer science. The role of the reduction for Husserl is, however, primarily epistemological: its purpose is to impart clarity to formal mathematics. (shrink)

The thesis according to which the meaning of a mathematical sentence is given by its proof was held by both Wittgenstein and the intuitionists, following Heyting and Dummett. In this paper, we clarify the meaning of this thesis for Wittgenstein, showing how his position differs from that of the intuitionists. We show how the thesis originates in his thoughts, from the middle period, about proofs by induction, and we sketch his answers to a number of objections, including the idea that, (...) given the particular meaning he gives to this thesis, he cannot account for mathematical conjectures. We conclude by showing how his views find a favourable echo today in the paradigm of “proposition-as-type” and extensions of the Curry-Howard isomorphism from which this paradigm originates. (shrink)

This article aims at clarifying the philosophical (=phenomenological) implication of Talcott Parsons’s analytical realism. Generally, his theory is understood as being confrontational to phenomenology; however, in his first book, The Structure of Social Action, Parsons positively referred to Husserl’s Logical Investigations. They shared a sense of crisis: Husserl thought that there was no certain basis in modern science, and Parsons had the feeling that there was no common theory to establish sociology as a science. Thus, both of them criticized the (...) factual sciences of positivism (positivistic empiricism) and showed a strong orientation to the general theory. For this, they depended on conceptual realism (Platonic realism). According to Husserl, scientific knowledge will be arbitrary if the Ideal is not there as the norm of fact. He believed that in truth all people always see Ideas. Similarly, Parsons thought that in truth all people always act toward the Ideal, because the Ideal element is necessarily found through the logical framework of sociology, i.e., the action frame of reference. Hence, he maintained that the Ideal element that gives a normative orientation to actions is real, though analytical, insofar as the social order is established. (shrink)