In lieu of an abstract, here is a brief excerpt of the content:Ōmori Shōzō and Kotodama Theory: How Can We Overcome the Need for Bodily Encounters?Maki SatoIntroductionŌmori Shōzō is known for his theory of tachi-araware monism. Tachiaraware monism is his attempted counter-argument to the Cartesian dualism of the object–subject divide, or in his words, a divide between physical (butsuri, mono, science, object) and non-physical consciousness (ishiki, koto, perception, incident), perception (chikaku, 知覚) and conception (shikō, 思考). His concept of Kasane-egaki is (...) also often cited as a core concept of his theory of time.1 The main aim of this paper is to first overview the works of Ōmori since there is only a limited amount of his translated work so far.2 Consecutively, the paper focuses on Ōmori’s theory of kotodama and its related arguments with an intention to expand his concept of Kowaburi into the ethics of online encounters during the pandemic.The world in 2020 was suddenly forced to face the pandemic caused by COVID-19. What COVID-19 alerted us to is tremendous, and there are countless problems that the invisible virus has revealed. Among those are the hidden problems of contemporary society, not limited to the discrimination among races, gender, and jobs (white-collars versus essential workers), the problem of zoonosis, and the related environmental problems (climate change and intrusion into wild nature) caused by over-exploitation of nature. In developed countries, most students and those serving as intellectual workers face their daily lives being overly occupied with online lectures and meetings. COVID-19 worked to normalize remote work, which further normalized and forced our everyday life to shift to cyberspace. [End Page 101]In introducing and overviewing Ōmori’s philosophy, this paper attempts to see the current situation through Ōmori’s philosophy to draw out some ethical implications related to non-physical online encounters and how we can perceive human interactions and relationships under such conditions. Under the constraints caused by COVID-19, humans’ limitless desires to interact with others are expanding more so to the sphere of cyberspace, leading to technological development, such as VR. In short, first, the paper overviews Ōmori’s philosophy. Second, through the overview of Ōmori’s philosophy, the paper seeks adaptable philosophy of his that may work as soft binding grounding ethics for cyberspace encounters where substantial bodily encounters are void. In doing so, the paper intends to draw out weak binding ethics implied in Ōmori’s philosophy that may work to empathetically engage with others in cyberspace where embodied encounters with others are dissolved.Ōmori Shōzō and His Philosophy: A Short Introduction and OverviewIn his short essay introducing the Japanese philosophy of the 1970s, Yasuo Kobayashi coined the term “Komaba quartet” by selecting four active eminent philosophers based on the Komaba campus at the University of Tokyo.3 Among them is Ōmori Shōzō (1921–97), aligning with Hiromatsu Wataru (1933–94), Sakabe Megumi (1936–2009), and Inoue Tadashi (1926–2014). Ōmori is the oldest of the Komaba quartet and received higher education before World War II. He served at the Naval Technology Institute Mitaka Laboratory during the war with his physics degree from the Tokyo Imperial University.4 After the war, he studied philosophy at the University of Tokyo with an interest in phenomenology, leading him to study at Harvard and Stanford in the United States.During his professorship at the University of Tokyo, he inspired countless students who are now leading the philosophy academy in Japan, such as Noe Keiichi (1949–) and Noya Shigeki (1954–). In the round-table discussion titled “Explanatory Round-Table on the Charm of Ōmori’s Philosophy,” four of his former students—Iida Takashi and Tanji Nobuharu, in addition to Noe and Noya—worked on selecting his works. It is impressive to read that all four [End Page 102] of them recall how exciting and inspiring it was to take his classes.5 Iida recalls that Ōmori’s classes were exceptional since philosophy courses were all about reading, with might and main, the texts written in a language other than Japanese at the University of Tokyo. However, Ōmori, with his postwar American education, welcomed discussion with the students and was keen on questioning... (shrink)

Why would a philosopher choose to convey his ideas in the form of Manga? This discussion between Masahiro Morioka, author of Manga Introduction to Philosophy, and the translator of its French edition, Pierre Bonneels, shows how philosopher and artist Morioka became acquainted, through images, with fundamental abstract notions. After a short historical analysis of the aesthetic advantages of Manga, consideration is given to this unique way of provoking thought. On this basis, theoretical aspects of “time” and the “I” proposed by (...) Ōmori Shōzō are compared with Morioka’s Manga presentation. Although the questions raised are universal, the authors note that the use of Japanese metaphors enables these two thinkers to draw on a concrete understanding of notions like temporality and identity. (shrink)

Ce texte présente une partie de la pensée trouvée au sein de l’oeuvre de jeunesse du philosophe japonais Ōmori Shōzō qui appartient à l’école de Tokyo. L’objet de l’analyse proposée est celui de la logique. Le défi est de décrire que la nécessité des énoncés logiques exacts repose sur l’expérience. Ainsi cet examen découvre et expose le logicisme hyper empirique auquel Ōmori nous invite. Nous parlerons du sens possible de la logique « non scientifique » pour insister ensuite sur le (...) sens scientifique de cette dernière. Finalement, nous discuterons de la provenance de la nécessité que comportent en elles les phrases logiques. Nous présenterons ainsi deux origines distinctes de la nécessité. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Guest Editor’s IntroductionNakajima Takahiro 「東京学派」とは聞きなれない名称であろう。日本研究において「京都学派」は大変よく知られている。たとえ「京都学派」が、「無の論理は論理ではない」と述べた上で、戸坂潤が発明した批判的な概念であったとしても 、現在ではそれは西田幾多郎や田辺元を中心とした一大哲学運動として世界的に認知されている。ところが、西田にしても田辺にしてももともとは東京帝国大学で学んだ学生であった。また、戦前においては、井上哲次郎か ら桑木厳翼へと続く東京帝国大学哲学科の流れは、当時の社会状況と相互に影響しあって、一定の意義を示していたのである。また、大森荘蔵、廣松渉、坂部恵といった戦後の東京大学の哲学者たちは、「京都学派」の問題 系を乗り越えることを重視していた。 この特別号では、発見的概念として「東京学派」を用いて、戦前・戦後におけるその意義と広がりを探究することにした。それは東京大学もしくは東京帝国大学に限定されたものではなく、それ以外の東京圏の大学との相互 交流も含まれるものである。「京都学派」に対しては、政治との距離をどう測るかがしばしば議論されてきたが、「東京学派」は政治により密着したものである。日本の近代の哲学の有している政治性そして倫理性を考える のであれば、やはり「東京学派」の議論は避けて通る ことのできないものである。 無論、「学派」というほどのまとまりを「東京学派」が有しているわけではないことも確かである。西田幾多郎が「京都学派」で果たした中心性は、「東京学派」にはない。そこで、トマス・カスリスが示唆するように、「 学派」の代わりに「サークル」や「スタイル」という言葉を使った方がより正確かもしれない。それでも、あえて「東京学派」と呼ぶのは、「京都学派」に比べて関心を持たれることの少ない、しかし当時は圧倒的な影響力 を有し、戦後決定的に忘却されていった東京の哲学者たちに光をあて、近代日本の哲学の総体を明らかにしたいからである。「東京学派」の研究は緒についたばかりである。今後、国際的な研究の高まりを期待しながら擱筆 する。The “Tokyo School” may be an unfamiliar term to readers. The Kyoto School is very well known in Japanese studies. Even if the Kyoto School is a critical concept invented by Tosaka Jun, who stated [End Page 2] that “the logic of nothingness is not logic,” it is now recognized worldwide as a major philosophical movement led by Nishida Kitarō and Tanabe (...) Hajime. However, both Nishida and Tanabe were originally students at Tokyo Imperial University. In addition, before the war, the output of the Department of Philosophy at Tokyo Imperial University, from Inoue Tetsujirō to Kuwaki Gen’yoku, had a certain significance because it interacted with the social conditions of the time. In addition, postwar philosophers at the University of Tokyo, such as Ōmori Shōzō, Hiromatsu Wataru, and Sakabe Megumi emphasized overcoming the problematics of the Kyoto School.In this special issue, we use the Tokyo School as a heuristic concept to explore its significance and spread in the prewar and postwar periods. It is not limited to the University of Tokyo or Tokyo Imperial University but includes interactions with other universities in the Tokyo area. While the Kyoto School has often been discussed in terms of how to measure its distance from politics, the Tokyo School is more closely connected to politics. If we consider the political and ethical dimensions of modern Japanese philosophy, we cannot avoid discussing the Tokyo School.Of course, it is true that the Tokyo School is not as coherent as a “school.” The central role that Nishida fulfilled in the Kyoto School is perhaps lacking in the Tokyo School. Therefore, as Thomas P. Kasulis suggests, it might be more accurate to use the term “circle” or “style” instead of “school.” Nevertheless, I dare to call it the Tokyo School because I would like to shed light on the Tokyo philosophers who were less popular than those of the Kyoto School but whose influence was overwhelming at the time and who were definitively forgotten after the war, so as to clarify the totality of philosophy in modern Japan.Research on the Tokyo School has only just begun. I am writing this introductory note in anticipation of further international research on the Tokyo School. [End Page 3]Copyright © 2023 State University of New York Press... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Guest Editor’s Concluding RemarksMaki SATO 本特別号は戦前・戦後の東京、特に東京帝国大学、東京大学を活躍の場に据えた哲学者たちの智の営みに光をあて特集した初の試みである。「東京学派」との掛け声に対して、いったいどれくらいの論文が集まるのだろうか 、蓋を開けてみるまでは全く分からなかった。特別号編者の一人としては、東京という場で行われた様々な哲学者たちによる知的営みのうち、いつの時代の、どの哲学者が研究対 象となっているのかを知ることは大変興味深かった。巻頭論文としては、『日本哲学小史(Engaging Japanese Philosophy: A Short History)』を上梓されたオハイオ州立大学名誉教授のトマス・カスリス先生に、2019年1月下旬に東京大学東洋文化研究所にて行われた国際ワークショップ「日本哲学と東京大学の哲学」、また同年11月下旬 に東京大学本郷キャンパスにおいて開催された集中講義でお話しいただいた内容に基づき、基調論文を執筆いただいた。快くお引き受け下さったことに、ここに心から感謝の意 を示したい。 今回、収録した論文が取り上げていたのは、井上哲次郎(1856~1944)、清沢満之(1863~1903)、桑木厳翼(1874~1946)、大森荘蔵(1921~1997)である。西周(1829~1897 )がphilosophyを「希哲学」と翻訳してから、新たな学問として日本に哲学が根付き、西洋哲学の解釈から日本独自の哲学へと花開き始めた頃の哲学者が主に取り上げられている。東京の哲学者たちの知的営みの 多くは「京都学派」と比較すると忘却され、埋もれてしまった概念が他にも多々あるだろう。しかしながら、東京という場所において、彼ら哲学者たちが掴もうとしていた新たな概念は、常に確実に日本の中枢、政治や経済 のダイナミックな動向への応答としてあったものである。今後、日本哲学を通して私たち人類の行く先を見据える上でも、東京という場所において活躍した過去の哲学者たちが、言葉や概念で掴もうとしていたものを、本特 集号が、再度、取り上げて見直す一機会にな れば幸いである。 [End Page 125]This special issue is the first attempt to highlight the intellectual activities of philosophers who were active in prewar and post-war Tokyo, particularly at the Tokyo Imperial University and the University of Tokyo. I had no idea how many papers we would receive under the special issue “Tokyo School” until we closed (...) our call for papers. As one of the editors of the special issue, it was exciting to know, among the intellectual activities conducted by various philosophers based in Tokyo, which philosophers were the subjects of contemporary research from which period. It is fascinating to see and to read how the philosophical thinking of the past may resonate and still keep on inspiring us to face humanity’s issues of the twenty-first century.For the opening article, we invited Professor Emeritus Thomas P. Kasulis of Ohio State University, who published Engaging Japanese Philosophy: A Short History back in 2018, to write a keynote paper. He kindly sent us an article based on his presentations at the international workshop “Japanese Philosophy and the Philosophy of the University of Tokyo” held in late January 2019 at the University of Tokyo’s Institute for Advanced Studies on Asia and during an intensive lecture held in late November 2019 at the Hongo Campus. I would like to express our sincere gratitude to him for contributing to this special issue.The papers included in this volume cover Inoue Tetsujiro (1856–1944), Kiyosawa Manshi (1863–1903), Kuwaki Genyoku (1874–1946), and Omori Shozo (1921–97). The focus of this volume is on philosophers from the period when philosophy took root in Japan as a new discipline after Nishi Amane (1829–97) translated the word “philosophy” as tetsugaku. The late nineteenth to the early twentieth century was a transition period when philosophical thoughts began to blossom from an interpretation of Western philosophy into a unique style of Japanese philosophy, which I see as an attempt at amalgamation to close the gap between West and East.Compared to the well-studied Kyoto School centered around Nishida, from the Tokyo School there are probably many other concepts that have been forgotten and buried. The new concepts that philosophers of Tokyo were trying to grasp were always a response to the significant trends of the time, including responses to the dynamism of Japan’s political and economic situation, Tokyo being the capital of Japan. We hope that this special issue will provide [End Page 126] an opportunity to take a fresh look at and discover what the philosophers active in Tokyo were trying to grasp through words and concepts that still engage well with universal questions that remain relevant to the humanity of the current time. [End Page 127]Copyright © 2023 State University of New York Press... (shrink)

In this anthology, works of ten Japanese thinkers, many of whom are no longer alive but who have been household names among the Japanese intellectual community, are selected and translated into English, accompanied by a brief introduction of each thinker. An additional three substantial essays by scholars of Japanese philosophy make this volume a compelling read for anyone interested in the Japanese philosophical endeavor since 1945. This anthology clearly goes beyond the familiar parameter of the Kyoto School of Philosophy.

L’acte de la philosophie japonaise est celui d’un évidement de soi: acte d’accueil des traditions philosophiques du monde, acte en résonance, créateur d’une terminologie, d’une logique, d’une conceptualité originales, s’alimentant aux sources d’une pensée mythique jamais tarie. Les textes présentés ici en feront sentir l’inclassable nouveauté: cette philosophie n’est ni purement shintoïste, bouddhique, chrétienne, néoconfucianiste ; elle n’est ni « orientale » ni « occidentale », mais proprement japonaise.

One of the problems we face in many-valued logic is the difficulty of capturing the intuitive meaning of the connectives introduced through truth tables. At the same time, however, some logics have nice ways to capture the intended meaning of connectives easily, such as four-valued logic studied by Belnap and Dunn. Inspired by Dunn’s discovery, we first describe a mechanical procedure, in expansions of Belnap-Dunn logic, to obtain truth conditions in terms of the behavior of the Truth and the False, (...) which gives us intuitive readings of connectives, out of truth tables. Then, we revisit the notion of functional completeness, which is one of the key notions in many-valued logic, in view of Dunn’s idea. More concretely, we introduce a generalized notion of functional completeness which naturally arises in the spirit of Dunn’s idea, and prove some fundamental results corresponding to the classical results proved by Post and Słupecki. (shrink)

Dialetheism is the metaphysical claim that there are true contradictions. And based on this view, Graham Priest and his collaborators have been suggesting solutions to a number of paradoxes. Those paradoxes include Russell’s paradox in naive set theory. For the purpose of dealing with this paradox, Priest is known to have argued against the presence of classical negation in the underlying logic of naive set theory. The aim of the present paper is to challenge this view by showing that there (...) is a way to handle classical negation. (shrink)

We show that there is a simple derivation of triviality with very few assumptions involving the formula that the negated conditional entails the antecedent of the conditional.

In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar many-valued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson and Beall, noticing that none of them discusses (...) our main question. This is why we finally turn to the analysis of the truth-conditions for conjunction and disjunction in infectious logics, employing the framework of plurivalent logics, as discussed by Priest. In doing so, we arrive at the interesting conclusion that —in the context of infectious logics— conjunction is conjunction, whereas disjunction is not disjunction. (shrink)

The present note offers a proof that systems developed by Majkić are actually extensions of intuitionistic logic, and therefore not paraconsistent.

In [1] Béziau developed the paraconsistent logic Z, which is definitionally equivalent to the modal logic S5, and gave an axiomatization of the logic Z: the system HZ. In the present paper, we prove that some axioms of HZ are not independent and then propose another axiomatization of Z. We also discuss a new perspective on the relation between S5 and classical propositional logic with the help of the new axiomatization of Z. Then we conclude the paper by making a (...) remark on the paraconsistency of HZ. (shrink)

We investigate the notion of classical negation from a non-classical perspective. In particular, one aim is to determine what classical negation amounts to in a paracomplete and paraconsistent four-valued setting. We first give a general semantic characterization of classical negation and then consider an axiomatic expansion BD+ of four-valued Belnap–Dunn logic by classical negation. We show the expansion complete and maximal. Finally, we compare BD+ to some related systems found in the literature, specifically a four-valued modal logic of Béziau and (...) the logic of classical implication and a paraconsistent de Morgan negation of Zaitsev. (shrink)

In this introduction to the special issue “40 years of FDE”, we offer an overview of the field and put the papers included in the special issue into perspective. More specifically, we first present various semantics and proof systems for FDE, and then survey some expansions of FDE by adding various operators starting with constants. We then turn to unary and binary connectives, which are classified in a systematic manner. First-order FDE is also briefly revisited, and we conclude by listing (...) some open problems for future research. (shrink)

In this introduction, we offer an overview of main systems developed in the growing literature on connexive logic, and also point to a few topics that seem to be collecting attention of many of those interested in connexive logic. We will also make clear the context to which the papers in this special issue belong and contribute.

There is a relatively recent trend in treating negation as a modal operator. One such reason is that doing so provides a uniform semantics for the negations of a wide variety of logics and arguably speaks to a longstanding challenge of Quine put to non-classical logics. One might be tempted to draw the conclusion that negation is a modal operator, a claim Francesco Berto, 761–793, 2015) defends at length in a recent paper. According to one such modal account, the negation (...) of a sentence is true at a world x just in case all the worlds at which the sentence is true are incompatible with x. Incompatibility is taken to be the key notion in the account, and what minimal properties a negation has comes down to which minimal conditions incompatibility satisfies. Our aims in this paper are twofold. First, we wish to point out problems for the modal account that make us question its tenability on a fundamental level. Second, in its place we propose an alternative, non-modal, account of negation as a contradictory-forming operator that we argue is superior to, and more natural than, the modal account. (shrink)

This edited volume collects essays on the four-valued logic known as Belnap-Dunn logic, or first-degree entailment logic. It also looks at various formal systems closely related to it. These include the strong Kleene logic and the Logic of Paradox. Inside, readers will find reprints of seminal papers written by the fathers of the field: Nuel Belnap and Michael Dunn. In addition, the collection also features a well-known but previously unpublished manuscript of Dunn, an interview with Belnap, and a new essay (...) by Dunn. Besides the original, monumental papers, the book also includes research by leading scholars. They consider the extraordinary importance of Belnap-Dunn logic from several perspectives. They look at how, philosophically, it has served as a basic system of inconsistency-tolerant reasoning, as the core of underlying logics for theories based on dialetheism, and, more recently, for theories based on Buddhist philosophy. Coverage also explores its contributions to computer science, such as knowledge representation and information processing. This mix of seminal papers and insightful analysis by top scholars offers readers a comprehensive outlook on Belnap-Dunn logic and its related expansions, which have been agenda setting for the debate on philosophical logic as well as philosophy of logic. The book will also enhance further discussion on the philosophical issues related to nonclassical logics in general. (shrink)

The present note revisits the joint work of Leonard Goddard and Richard Routley on significance logics with the aim of shedding new light on their understanding by studying them under the lens of recent semantic developments, such as the plurivalent semantics developed by Graham Priest. These semantics allow sentences to receive one, more than one, or no truth-value at all from a given carrier set. Since nonsignificant sentences are taken to be neither true nor false, i.e. truth-value gaps, in this (...) essay we show that with the aid of plurivalent semantics it is possible to straightforwardly instantiate Goddard and Routley’s understanding of how the connectives should work within significance logics. (shrink)

Sören Halldén’s logic of nonsense is one of the most well-known many-valued logics available in the literature. In this paper, we discuss Peter Woodruff’s as yet rather unexplored attempt to advance a version of such a logic built on the top of a constructive logical basis. We start by recalling the basics of Woodruff’s system and by bringing to light some of its notable features. We then go on to elaborate on some of the difficulties attached to it; on our (...) way to offer a possible solution to such difficulties, we discuss the relation between Woodruff’s system and two-dimensional semantics for many-valued logics, as developed by Hans Herzberger. (shrink)

A world is trivial if it makes every proposition true all at once. Such a world is impossible, an absurdity. Our world, we hope, is not an absurdity. It is important, nevertheless, for semantic and metaphysical theories that we be able to reason cogently about absurdities—if only to see that they are absurd. In this note we describe methods for ‘observing’ absurd objects like the trivial world without falling in to incoherence, using some basic techniques from modal logic. The goal (...) is to begin to locate the trivial world’s relative position in modal space; the outcome is that the less we assume about relative possibility, the more detail we can discern at the edge of reason. (shrink)

We observe that Jc Beall’s shrieking and shrugging strategy gives us an opportunity to reflect on the Australian plan for negation in FDE, a basic subclassical logic that is used in Beall’s argument for subclassical logics. An implication of our observation is applied to a recent defense of the Australian plan for negation by Francesco Berto and Greg Restall.

We outline the rather complicated history of attempts at axiomatizing Jaśkowski’s discussive logic $$\mathbf {D_2}$$ D2 and show that some clarity can be had by paying close attention to the language we work with. We then examine the problem of axiomatizing $$\mathbf {D_2}$$ D2 in languages involving discussive conjunctions. Specifically, we show that recent attempts by Ciuciura are mistaken. Finally, we present an axiomatization of $$\mathbf {D_2}$$ D2 in the language Jaśkowski suggested in his second paper on discussive logic, by (...) following a remark of da Costa and Dubikajtis. We also deal with an interesting variant of $$\mathbf {D_2}$$ D2, introduced by Ciuciura, in which negation is also taken to be discussive. (shrink)

Change of logic is typically taken as requiring that the meanings of the connectives change too. As a result, it has been argued that legitimate rivalry between logics is under threat. This is, in a nutshell, the meaning‐variance argument, traditionally attributed to Quine. In this paper, we present a semantic framework that allows us to resist the meaning‐variance claim for an important class of systems: classical logic, the logic of paradox and strong Kleene logic. The major feature of the semantics (...) is that the connectives have the same meanings in these systems, so that the meaning‐variance argument is straightforwardly blocked. We discuss the effects of this semantics for two uses of the argument of meaning variance, and also consider its impact on related issues. (shrink)

In a recent article, Mario Günther presented a conditional that is claimed to be connexive. The aim of this short discussion note is to show that Günther’s claim is not without problems.

In this paper, we introduce a new logic, which we call AM3. It is a connexive logic that has several interesting properties, among them being strongly connexive and validating the Converse Boethius Thesis. These two properties are rather characteristic of the difference between, on the one hand, Angell and McCall’s CC1 and, on the other, Wansing’s C. We will show that in other aspects, as well, AM3 combines what are, arguably, the strengths of both CC1 and C. It also allows (...) us an interesting look at how connexivity and the intuitionistic understanding of negation relate to each other. However, some problems remain, and we end by pointing to a large family of weaker logics that AM3 invites us to further explore. (shrink)

In this paper, we generalize the ordered-pair semantics advanced by Matthew Clemens for the Logic of Paradox to n-tuple semantics, for each fixed n. Moreover, we show that the resulting semantics can accommodate not only LP, but also classical logic as well as strong Kleene logic depending on the set of designated values that one chooses. Building on the technical observations, we offer intuitively plausible readings for the semantics, and we also discuss some weaknesses of the original intuitive reading advanced (...) by Clemens. (shrink)

In his “The simple argument for subclassical logic,” Jc Beall advances an argument that led him to take FDE as the one true logic (the latter point is explicitly made clear in his “FDE as the One True Logic”). The aim of this article is to point out that if we follow Beall’s line of reasoning for endorsing FDE, there are at least two additional reasons to consider that FDE is too strong for Beall’s purposes. In fact, we claim that (...) Beall should consider another weaker subclassical logic as the logic adequate for his project. To this end, we first briefly present Beall’s argument for FDE. Then, we discuss two specific topics that seem to motivate us to weaken FDE. We then introduce a subsystem that will enjoy all the benefits of Beall’s suggestion. (shrink)

Intuitionism can be seen as a verificationism restricted to mathematical discourse. An attempt to generalize intuitionism to empirical discourse presents various challenges. One of those concerns the logical and semantical behavior of what has been called ' empirical negation'. An extension of intuitionistic logic with empirical negation was given by Michael De and a labelled tableaux system was there shown sound and complete. However, a Hilbert-style axiom system that is sound and complete was missing. In this paper we provide the (...) missing axiom system which is shown sound and complete with respect to its intended semantics. Along the way we consider some further applications of empirical negation. (shrink)

In one of their papers, Michael De and Hitoshi Omori observed that the notion of classical negation is not uniquely determined in the context of so-called Belnap-Dunn logic, and in fact there are 16 unary operations that qualify to be called classical negation. These varieties are due to different falsity conditions one may assume for classical negation. The aim of this paper is to observe that there is an interesting way to make sense of classical negation independent of falsity conditions. (...) We discuss two equivalent semantics, and offer a Hilbert-style system that is sound and complete with respect to the semantics. (shrink)

In [Waragai & Shidori, 2007], a system of paraconsistent logic called PCL1, which takes a similar approach to that of da Costa, is proposed. The present paper gives further results on this system and its related systems. Those results include the concrete condition to enrich the system PCL1 with the classical negation, a comparison of the concrete notion of “behaving classically” given by da Costa and by Waragai and Shidori, and a characterisation of the notion of “behaving classically” given by (...) Waragai and Shidori. (shrink)

Subintuitionistic (propositional) logics are those in a standard intuitionistic language that result by weakening the frame conditions of the Kripke semantics for intuitionistic logic. In this paper we consider two negation expansions of subintuitionistic logic, one by classical negation and the other by what has been dubbed “empirical” negation. We provide an axiomatization of each expansion and show them sound and strongly complete. We conclude with some final remarks, including avenues for future research.

This note offers a non-deterministic semantics for mbC1, introduced by Janusz Ciuciura, and establishes soundness and completeness results with respect to the Hilbert-style proof system. Moreover, based on the new semantics, we briefly discuss an unexplored variant of mbC1 which has a contra-classical flavor.

Metabolic dysfunction is a ubiquitous underlying feature of many neurological conditions including acute traumatic brain injuries and chronic neurodegenerative conditions. A central problem in neurological patients, in particular those with traumatic brain injuries, is an impairment in the utilization of glucose, which is the predominant metabolic substrate in a normally functioning brain. In such patients, alternative substrates including ketone bodies and lactate become important metabolic candidates for maintaining brain function. While the potential neuroprotective benefits of ketosis have been recognized for (...) up to almost a century, the majority of work has focused on the use of ketogenic diets to induce such a state, which is inappropriate in cases of acute disease due to the prolonged periods of time (i.e., weeks to months) required for the effects of a ketogenic diet to be seen. The following review seeks to explore the neuroprotective effects of exogenous ketone and lactate preparations, which have more recently become commercially available and are able to induce a deep ketogenic response in a fraction of the time. The rapid response of exogenous preparations makes their use as a therapeutic adjunct more feasible from a clinical perspective in both acute and chronic neurological conditions. Potentially, their ability to globally moderate long-term, occult brain dysfunction may also be relevant in reducing lifetime risks of certain neurodegenerative conditions. In particular, this review explores the association between traumatic brain injury and contusion-related dementia, assessing metabolic parallels and highlighting the potential role of exogenous ketone and lactate therapies. (shrink)

One of the oldest systems of paraconsistent logic is the set of so-called C-systems of Newton da Costa, and this has been generalized into a family of systems now known as logics of formal inconsistencies by Walter Carnielli, Marcelo Coniglio and João Marcos. The characteristic notion in these systems is the so-called consistency operator which, roughly speaking, indicates how gluts are behaving. One natural question then is to ask if we can let not only gluts but also gaps be around (...) and generalize the notion of consistency into classicality. This is already considered by Andréa Loparić and da Costa in the style of C-systems. The aim of this paper is to develop a family of systems that generalizes the system of Loparić and da Costa which may be called logics of formal classicality. (shrink)

In one of his papers, JC Beall advanced a new and interesting interpretation of Weak Kleene logic, in terms of on-topic/off-topic. In brief, Beall suggests to read the third value as off-topic, whereas the two classical values are read as true and on-topic and false and on-topic. Building on Beall’s new interpretation, the aim of this paper is threefold. First, we discuss two motivations to enrich Beall’s interpretation, and offer an alternative semantic framework that reflects our motivations. Second, by making (...) use of our new framework, we will offer a new interpretation of the logic of Catuskoti which combines Beall’s proposal of having FDE as the correct logic with the on-topic/off-topic divide. Finally, we will offer a general result that will allow us to make sense of a family of infectious logics in terms of Beall’s on-topic/off-topic reading. (shrink)