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 In addition, the collection also features a well-known but previously unpublished manuscript of Dunn, an interview with Belnap, and a new essay (...)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

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.

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)

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 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)

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.

Continuous deep sedation (CDS) has the effect of making the patient unconscious until death, and that it has this effect is clearly an undesirable aspect of CDS. However, some authors have recently maintained that many physicians do not intend this effect when practicing CDS. According to these authors, CDS is differentiated into two types; in what is called “gradual” CDS (or CDS as a result of proportionate palliative sedation), physicians start with low doses of sedatives and increase them only gradually, (...) whereas in “rapid” CDS (or palliative sedation to unconsciousness), physicians rapidly administer a heavy dose that clearly induces unconsciousness from the beginning. The claim is that the physicians intend permanent unconsciousness only if they rapidly administer a heavy dose, but they do not intend it when the unconsciousness is the result of a gradual increase of sedatives. This paper attempts to refute these claims based on a close examination of the protocol of gradual CDS. If my argument is valid, the doctrine of double effect would not be useful in justifying most, if not all, cases of CDS. (shrink)

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)

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.

Three multifunctional protein kinases, cyclic AMP‐dependent protein kinase, protein kinase C, and calmodulin‐dependent protein kinase II, are involved in signal transduction in response to their respective second messengers, cyclic AMP, diacylglycerol, and Ca2+. This review will summarize the key findings on calmodulin‐dependent protein kinase II.

Fichte as well as Jacobi posit that the Absolute cannot be grasped from the standpoint of knowledge. Therefore we must go beyond this point, in order to achieve the Absolute. Both agree that knowledge is negated in the face of the Absolute. What, however, Fichte understands by the negation of knowledge differs from Jacobi’s understanding. The negation of knowledge refers to, in Fichte’s case, the self-negation of knowledge. Whereas in Jacobi’s case it refers to the renunciation of knowledge. In this (...) essay the author attempts to bring out the salient characteristics of the negation of knowledge in Fichte on the basis of Jacobi to Fichte, Vocation of Man and Science of Knowledge 1801/02. Knowledge cannot grasp the Absolute. Knowledge knows, however, that it cannot grasp the Absolute (i.e. the Absolute, which it cannot grasp, exists). According to Fichte the Absolute appears in this way through knowledge. Knowledge is not merely negated in the face of the Absolute, but rather lets the Absolute, through its self-negation, appear. This knowledge is so in its self-negation in contact with the Absolute. In Fichte the Absolute is not something not-appearing. The misunderstanding, that the Absolute is something not-appearing, comes from objective cognition. The Absolute appears, as an appearance appears as an appearance (i.e. without confusing it with the Absolute). Sowohl Fichte als auch Jacobi meinen, dass das Absolute auf dem Standpunkt des Wissens nicht erfasst werden kann, und dass man daher über den Standpunkt des Wissens hinausgehen muss, um das Absolute zu erreichen. Die beiden sind in dem Punkt einig, dass das Wissen angesichts des Absoluten negiert wird. Was aber Fichte dabei unter der Negation des Wissens versteht, unterscheidet sich davon, was Jacobi darunter versteht. Die Negation des Wissens meint bei Fichte Selbstnegation des Wissens, während sie bei Jacobi Abschaffung desselben meint. Im vorliegenden Aufsatz versucht der Verfasser, das Charakteristische der Negation des Wissens bei Fichte anhand von Jacobi an Fichte, Bestimmung des Menschen und Wissenschaftslehre 1801/02 herauszuarbeiten. Das Wissen kann kein Absolutes erfassen. Das Wissen weiß aber, dass es kein Absolutes erfassen kann, d. h. dass es ein Absolutes gibt, das es nicht erfassen kann. Nach Fichte erscheint das Absolute auf diese Weise im Wissen. Das Wissen wird dabei angesichts des Absoluten nicht bloß negiert sondern lässt vielmehr durch seine Selbstnegation das Absolute erscheinen. So steht das Wissen durch seine Selbstnegation mit dem Absoluten in Berührung. Das Absolute ist bei Fichte nicht etwas Nicht-erscheinendes. Das Missverständnis, dass das Absolute ein Nicht-erscheinendes wäre, stammt daraus, es gegenständlich zu erfassen. Das Absolute erscheint, indem die Erscheinung als Erscheinung (d. h. ohne Verwechselung mit dem Absoluten) erscheint. (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)

Nicholas of Cusa (1401-1464) was one of the most original thinkers of the Renaissance. This collection examines, from several viewpoints, his speculative thought and reviews his ideas on dialogue with non- Christians in the light of his theories. The articles originated in papers presented at several conferences sponsored by the American Cusanus Society, 1981-1988. Annotation copyrighted by Book News, Inc., Portland, OR.

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)

History of Buddhist philosophy, with special reference to canonical and early philosophical literature, presenting Sarvāstivāda and Theravāda school.

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。.

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

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.

日本の原風景とその影響。現代社会における教育やこころのゆがみを正し、あるべき日本の姿を明らかにした、珠玉の十二編。.

This article offers the results of emergy analysis used to evaluate four different soybean production systems in Brazil that were divided into two main categories: biological models (organic and ecological farms) and industrial models (green-revolution chemical farms and herbicide with no-tillage farms). The biological models show better environmental, economical, and social performance indicators; however, at the national level, discussion of transgenic soybean seed release considers only industrial models without any mention of biological models. Classic emergy analysis shows biological options are (...) the better alternatives but does not explain why decisions taken by farmers and government in Brazil were in opposition to these options. New research is proposed to identify and quantify the external forces that strongly interfere in the definition of public policy for soybean production. New parameters are proposed to enrich emergy methodology: Renewability of each input was considered in emergy calculations and negative externalities were included as additional services. (shrink)