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)

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.

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)

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 In addition, the collection also features a well-known but previously unpublished manuscript of Dunn, an interview with Belnap, and a new essay (...)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)

ベストセラー『7日間で突然頭がよくなる本』の著者による、はじめてのニッポン論。古代の神話や仏教、儒学、武士道から国学、さらには福澤諭吉らによる啓蒙書さえも「日本哲学である」と定義する。1500年にもお よぶ日本思想の遺伝子的深層を新視点から読み解く最新の入門書。.

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)

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 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)

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)

ドゥルーズの「リゾーム」、フーコーの「脱中心化」、バタイユの「蕩尽」、デリダの「ディコンストラクション」。80年代のニューアカデミズム、ポストモダンとは何だったのか?世界を席捲した現代思想のキイ・ワー ドが、20年の歳月をへて、今よみがえる。新たに第5部を書き加えて、21世紀の思想状況に斬り込む「増補決定版」が、ここに登場!現代思想はいま、どの地点にまでたどりついたのか。.

The United Nations Scientific, Education and Cultural Organisation (UNESCO) Universal Declaration on Bioethics and Human Rights (UDBHR) expresses in its title and substance a controversial linkage of two normative systems: international human rights law and bioethics. The UDBHR has the status of what is known as a ‘non-binding’ declaration under public international law. The UDBHR’s normative foundation within bioethics (and association, for example, with virtue-based or principlist bioethical theories) is more problematic. Nonetheless, the UDBHR contains socially important principles of technology (...) transfer and transnational benefit (articles 14, 15 and 21). This paper is one of the first to explore how the disciplines of bioethics and international human rights law may interact in the UDBHR to advance the policy relevance and health impact of technology transfer and transnational benefit principles. It investigates their normative ancestry in the UDBHR, as well as relevant conceptual differences between bioethics and public international law in this respect and how these may be relevant to their conceptual evolution and application. (shrink)

Thomas Alured Faunce, College of Law, Fellows Road, Acton, Canberra ACT 0200, Australian National University, Fax: 61 2 61253971, Email: Thomas.Faunce{at}anu.edu.au ' + u + '@' + d + ' '//-->This paper sets out to analyse three different academic proposals for addressing the needs of the poor in relation to new, rather than ‘essential’ medicines. It focuses particularly on research and development prize funds, a health impact fund system and a multilateral treaty on health technology cost-effectiveness evaluation and competitive tender. (...) It compares the extent to which each responds to the ‘market fundamentalist’ philosophy and begins to analyse their respective strengths and weaknesses. CiteULike Connotea Del.icio.us What's this? (shrink)

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)

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)

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)

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)

Connectives such as Tonk have posed a significant challenge to the inferentialist. It has been recently argued that the classical semanticist faces an analogous problem due to the definability of “nasty connectives” under non-standard interpretations of the classical propositional vocabulary. In this paper, we defend the classical semanticist from this alleged problem.

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.

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)

This article compares the theory of knowledge of Fichte with that of the Japanese Philosopher Kitaro Nishida and brings out an essential correspondence between them. Both philosophers are not satisfied with the usual epistemology which is based on the contraposition of subject and object, and consider it necessary to go beyond the scheme of the contraposition because it covers the truth of knowledge. They both diagnose that the scheme of contraposition stems from the objectification by the I, and suggest that (...) the objectifying I should be nullified. According to the view that the I can be nullified only by the I itself, they take the selfnullification of the I as their theme. They think that the I does not vanish by selfnullification, but rather touches its own life which by its nature cannot be objectified. The Absolute of Fichte as well as the absolute Nothing of Nishida are characterizable as an unobjectifiable life which can be reached only by the selfnullification of the I.Dieser Aufsatz vergleicht die Wissenslehre Fichtes mit der des japanischen Philosophen Kitaro Nishida und hebt eine wesentliche Gemeinsamkeit zwischen beiden hervor. Die beiden Philosophen sind mit gängiger Erkenntnistheorie, die auf der substantiellen Gegenüberstellung von Subjekt und Objekt gründet, nicht zufrieden und halten es für nötig, über dieses Schema der Gegenüberstellung hinauszugehen, weil es die Wahrheit des Wissens verhüllt. Sie stellen gemeinsam fest, dass das Schema aus der Objektivierung durch das Ich stammt, und denken, dass das objektivierende Ich vernichtet werden soll. Aufgrund der Ansicht, dass das Ich nur durch das Ich selbst vernichtet werden kann, machen sie die Selbstvernichtung des Ich zum Thema. Durch die Selbstvernichtung des Ich verschwindet das Ich nach ihnen jedoch nicht, sondern vielmehr berührt es dadurch sein eigenes Leben, das seiner Natur nach nicht objektiviert werden kann. Sowohl „das Absolute“ bei Fichte als auch „das absolute Nichts“ bei Nishida sind als ein unobjektivierbares, nur durch die Selbstvernichtung des Ich erreichbares Leben zu charakterisieren. (shrink)