In this paper, we argue that a distinction ought to be drawn between two ways in which a given world might be logically impossible. First, a world w might be impossible because the laws that hold at w are different from those that hold at some other world (say the actual world). Second, a world w might be impossible because the laws of logic that hold in some world (say the actual world) are violated at w. We develop a novel (...) way of modelling logical possibility that makes room for both kinds of logical impossibility. Doing so has interesting implications for the relationship between logical possibility and other kinds of possibility (for example, metaphysical possibility) and implications for the necessity or contingency of the laws of logic. (shrink)

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...) this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics. (shrink)

There was a time when 'logic' just meant classical logic. The climate is slowly changing and non-classical logic cannot be dismissed off-hand. However, a metatheory used to study the properties of non-classical logic is often classical. In this paper, we will argue that this practice of relying on classical metatheories is problematic. In particular, we will show that it is a bad practice because the metatheory that is used to study a non-classical logic often rules out the very logic it (...) is designed to study. (shrink)

What does it mean for the laws of logic to fail? My task in this paper is to answer this question. I use the resources that Routley/Sylvan developed with his collaborators for the semantics of relevant logics to explain a world where the laws of logic fail. I claim that the non-normal worlds that Routley/Sylvan introduced are exactly such worlds. To disambiguate different kinds of impossible worlds, I call such worlds logically impossible worlds. At a logically impossible world, the laws (...) of logic fail. In this paper, I provide a definition of logically impossible worlds. I then show that there is nothing strange about admitting such worlds. (shrink)

It has been an open question whether or not we can define a belief revision operation that is distinct from simple belief expansion using paraconsistent logic. In this paper, we investigate the possibility of meeting the challenge of defining a belief revision operation using the resources made available by the study of dynamic epistemic logic in the presence of paraconsistent logic. We will show that it is possible to define dynamic operations of belief revision in a paraconsistent setting.

Logic in Buddhist Philosophy concerns the systematic study of anumāna (often translated as inference) as developed by Dignāga (480-540 c.e.) and Dharmakīti (600-660 c.e.). Buddhist logicians think of inference as an instrument of knowledge (pramāṇa) and, thus, logic is considered to constitute part of epistemology in the Buddhist tradition. According to the prevalent 20th and early 21st century ‘Western’ conception of logic, however, logical study is the formal study of arguments. If we understand the nature of logic to be formal, (...) it is difficult to see what bearing logic has on knowledge. In this paper, by weaving together the main threads of thought that are salient in Dignāga’s and Dharmakīti’s texts, I shall re-conceive the nature of logic in the context of epistemology and demarcate the logical part of epistemology which can be recognised as logic. I shall demonstrate that we can recognise the logical significance of inference as understood by Buddhist logicians despite the fact that its logical significance lies within the context of knowledge. (shrink)

Priest holds anti-exceptionalism about logic. That is, he holds that logic, as a theory, does not have any exceptional status in relation to the theories of empirical sciences. Crucial to Priest’s anti-exceptionalism is the existence of ‘data’ that can force the revision of logical theory. He claims that classical logic is inadequate to the available data and, thus, needs to be revised. But what kind of data can overturn classical logic? Priest claims that the data is our intuitions about the (...) validity of inferences. In order to make sense of this claim, I will appeal to the Madhyamaka Buddhist philosopher Candrakīrti. I will then pose a problem for Priest’s anti-exceptionalism. Finally, I will suggest a way out of the problem for Priest. Whether or not he accepts my solution, I will let him decide. (shrink)

The problem of how to accommodate inconsistencies has attracted quite a number of researchers, in particular, in the area of database theory. The problem is also of concern in the study of belief change. For inconsistent beliefs are ubiquitous. However, comparatively little work has been devoted to discussing the problem in the literature of belief change. In this paper, I examine how adequate the AGM theory is as a logical framework for belief change involving inconsistencies. The technique is to apply (...) to Grove’s sphere system, a semantical representation of the AGM theory, logics that do not infer everything from contradictory premises, viz., paraconsistent logics. I use three paraconsistent logics and discuss three sphere systems that are based on them. I then examine the completeness of the postulates of the AGM theory with respect to the systems. At the end, I discuss some philosophical implications of the examination. (shrink)

Max Cresswell and Hilary Putnam seem to hold the view, often shared by classical logicians, that paraconsistent logic has not been made sense of, despite its well-developed mathematics. In this paper, I examine the nature of logic in order to understand what it means to make sense of logic. I then show that, just as one can make sense of non-normal modal logics (as Cresswell demonstrates), we can make `sense' of paraconsistent logic. Finally, I turn the tables on classical logicians (...) and ask what sense can be made of explosive reasoning. While I acknowledge a bias on this issue, it is not clear that even classical logicians can answer this question. (shrink)

Buddhist philosophers have developed a rich tradition of logic. Buddhist material on logic that forms the Buddhist tradition of logic, however, is hardly discussed or even known. This article presents some of that material in a manner that is accessible to contemporary logicians and philosophers of logic and sets agendas for global philosophy of logic.

Dharmakīrti argues that there is no pramāṇa (valid means of cognition or source of knowledge) for a thesis that is a self-contradiction (svavacanavirodha). That is, self-contradictions such as ‘everything said is false’ and ‘my mother is barren’ cannot be known to be true or false. The contemporary scholar Tillemans challenges Dharmakīrti by arguing that we can know that self-contradictions are false by means of a formal logical inference. The aims of the paper are to answer Tillemans’ challenge from what we (...) take to be Dharmakīrti’s or Dharmakīrtian (someone who is like Dharmakīrti) perspective and to demonstrate the unique features of Dharmakīrti’s view of inference. By so doing, we show that the epistemology in relation to the formal conception of logic that underlies Tillemans’ challenge is problematic from Dharmakīrti’s or Dharmakīrtian perspective. The paper, thus, presents Dharmakīrti’s view of inference and logical reasoning as well as a Dharmakīrtian challenge to the formal conception of logic that is the dominant contemporary conception. (shrink)

A logic is said to be paraconsistent if it does not allow everything to follow from contradictory premises. There are several approaches to paraconsistency. This paper is concerned with several philosophical positions on paraconsistency. In particular, it concerns three ‘schools’ of paraconsistency: Australian, Belgian and Brazilian. The Belgian and Brazilian schools have raised some objections to the dialetheism of the Australian school. I argue that the Australian school of paraconsistency need not be closed down on the basis of the Belgian (...) and Brazilian schools’ objections. In the appendix of the paper, I also argue that the Brazilian school’s view of logic is not coherent. (shrink)

In his book review of Graham Priest's The Fifth Corner of Four, Mark Siderits, while criticising Priest's philology, suggests that Priest's work is 'of considerable interest' for two reasons. First, 'when two independent traditions use similar methods to work on similar issues, it is always possible that one may have hit on approaches that the other missed'. Second, 'the decentering that can be induced by looking at another tradition may trigger fresh insights, even if those insights are not ones that (...) were actually developed by the tradition marked 'other''. The main task of this paper is to unpack Siderits' thought. By analysing some of Priest's work, I will suggest a decentering that must have taken place in China when Buddhism was 'exported to China in Buddhist shipping containers'. For anyone familiar with the forms of Buddhist philosophy developed in India, various forms of Chinese Buddhism can often look strange. Some ideas that were debated and defended by Indian Buddhists do not appear anywhere in Chinese Buddhism and some assumptions have been quietly added to Buddhism by Chinese Buddhists. By showing that Priest's work brings out the 'innovation' that Chinese Buddhists gave to Buddhism, I will suggest that it is this decentering that Siderits suggests Priest makes use of. (shrink)

The doctrine of the two truths - a conventional truth and an ultimate truth - is central to Buddhist metaphysics and epistemology. The two truths (or two realities), the distinction between them, and the relation between them is understood variously in different Buddhist schools; it is of special importance to the Madhyamaka school. One theory is articulated with particular force by Nagarjuna (2nd ct CE) who famously claims that the two truths are identical to one another and yet distinct. One (...) of the most influential interpretations of Nagarjuna's difficult doctrine derives from the commentary of Candrakirti (6th ct CE). In view of its special soteriological role, much attention has been devoted to explaining the nature of the ultimate truth; less, however, has been paid to understanding the nature of conventional truth, which is often described as "deceptive," "illusion," or "truth for fools." But because of the close relation between the two truths in Madhyamaka, conventional truth also demands analysis. Moonshadows, the product of years of collaboration by ten cowherds engaged in Philosophy and Buddhist Studies, provides this analysis. The book asks, "what is true about conventional truth?" and "what are the implications of an understanding of conventional truth for our lives?" Moonshadows begins with a philosophical exploration of classical Indian and Tibetan texts articulating Candrakati's view, and uses this textual exploration as a basis for a more systematic philosophical consideration of the issues raised by his account. (shrink)

This paper shows that a collection of modal relevant logics are conservatively extended by the addition of Boolean negation.

Buddhist philosophers have investigated the techniques and methodologies of debate and argumentation which are important aspects of Buddhist intellectual life. This was particularly the case in India, where Buddhism and Buddhist philosophy originated. But these investigations have also engaged philosophers in China, Japan, Korea and Tibet, and many other parts of the world that have been influenced by Buddhism and Buddhist philosophy. Several elements of the Buddhist tradition of philosophy are thought to be part of this investigation. -/- There are (...) interesting reasoning patterns discernible in the writings of Buddhist philosophers. For instance, the Mādhyamika philosopher Nāgārjuna presents arguments for the emptiness of all things in terms of catuṣkoṭi (four ‘corners’: roughly speaking, truth, false, both, neither). There are also the Indian vāda (debate) literature and Tibetan bsdus grwa (collected topics) that list techniques of debates. -/- The main interest here is the tradition of Buddhist philosophy, sometimes referred to as Pramāṇavāda, whose central figures are Dignāga (approx. 480–540 CE) and Dharmakīrti (6th– 7th CE). This philosophy is understood to be the Buddhist school of logic-epistemology. ‘Pramāṇavāda’ is not a doxographical term traditionally used to refer to a recognised school of Buddhist philosophy. It is a conventional term that is sometimes used in modern literature. Nevertheless, in what follows, we think of it as a tradition within Buddhist philosophy and ‘Buddhist logic’ refers to what is developed in this tradition. -/- Buddhist logicians have systematically analysed the kind of reasoning involved in acquiring knowledge. They hold that there are valid ways to reason that are productive of knowledge. In what follows, some of the main elements of their analyses will be described. Note, however, that, while exegetical studies of Buddhist texts are important, we must step back from them and consider what is involved in taking a Buddhist approach to logic in light of modern formal logic. This analysis will be done against the backdrop of the contemporary literature on logic and related subjects in contemporary philosophy to make sense of the logical studies by Buddhist logicians. (shrink)

How can Buddhists prove that non-existent things do not exist? With great difficulty. For the Buddhist, this is not a laughing matter as they are largely global error theorists and, thus, many things are non-existent. The difficulty gets compounded as the Buddhist and their opponent, the non-Buddhist of various kinds, both agree that one cannot prove a thesis whose subject is non-existent. In this paper, I will first present a difficulty that Buddhist philosophers have faced in proving that what they (...) take to be non-existent does not exist. I will then survey two main solutions that they have provided. Those 'solutions' may not solve the problem or solve the problem but creates other problems. I will not survey the Buddhist treatment of the problem of proving about non-existence in order to present a new solution that we have yet to see. Instead, I will articulate a problem about non-existence that is unique to Buddhist philosophers. I will do so in order to present an interesting puzzle about non-existence that has largely escaped attention in the 'Western' literature. (shrink)

A logic is said to be paraconsistent if it doesn’t license you to infer everything from a contradiction. To be precise, let |= be a relation of logical consequence. We call |= explosive if it validates the inference rule: {A,¬A} |= B for every A and B. Classical logic and most other standard logics, including intuitionist logic, are explosive. Instead of licensing you to infer everything from a contradiction, paraconsistent logic allows you to sensibly deal with the contradiction.

The paper is concerned with the development of the paradoxical theme of Daoism. Based on Chad Hansen's interpretation of Daoism and Chinese philosophy in general, it traces the history of Daoism by following their treatment of the limit of language. The Daoists seem to have noticed that there is a limit to what language can do and that the limit of language is paradoxical. The 'theoretical' treatment of the paradox of the limit of language matures as Daoism develops. Yet the (...) Daoists seem to have noticed that the limit of language and its paradoxical nature cannot be overcome. At the end, we are left with the paradoxes of the Daoists. In this paper, we jump into the abyss of the Daoists' paradoxes from which there is no escape. But the Daoists' paradoxes are fun! (shrink)

In one of his key texts, the Mūlamadhyamakakārikā, Nāgārjuna famously sets out to refute the ontology of essence.1 He presents numerous arguments to show that things don’t exist essentially—that is, that things are empty of essence or inherent existence. The doctrine of emptiness has been variously understood by traditional and contemporary commentators. Most radical is the recent interpretation presented by Garfield and Priest. They have rationally reconstructed Nāgārjuna’s doctrine of emptiness as an endorsement of the contradictory nature of reality. According (...) to them, Nāgārjuna can be seen to be arguing that the way in which things exist in reality and what we can truly say about them must be... (shrink)

Kenzo saw a slight movement of his opponent. “Now is the time to strike!” he thought. He started moving. But before he had time to raise his shinai (sword) he was struck on the men (head) by his opponent. “Ippon!” the judge called.

Some philosophers of mind, cognitive scientists, phenomenologists as well as Buddhist philosophers have claimed that an awareness of an object is not just an experience of that object but also involves self-awareness. It is sometimes argued that being aware of an object without being aware of oneself is pathological. As anyone who has been involved in martial arts, as well as any sports requiring quick responses such as cricket and tennis, can testify, however, awareness of the self at the time (...) of acting becomes problematic: you would not be able to respond to the slight movement of your opponent if you were aware of yourself responding to it. This suggests that it must be possible for us to be aware without being aware of ourselves. The aim of this paper is to clarify the notion of self-awareness and its relation to the self by investigating the phenomenology of the martial artist who is ‘in the act’. I shall argue that we can make sense of self-awareness without invoking awareness of oneself. (shrink)

In one of his influential works ‘One the Very Idea of a Conceptual Scheme’, Donald Davidson argues against conceptual relativism. According to Davidson, ‘we could not be in a position to judge that others had concepts or beliefs radically different from our own’. Davidson’s thesis seems to have a consequence for comparative philosophy, particularly in a comparative study between Chinese and Western traditions of philosophy which are often considered to differ conceptually. If Davidson is correct, it is not clear whether (...) or not we can have insight into how and why concepts differ between these traditions. -/- In this paper, I philosophically reflect on Davidson’s argument against conceptual relativism. Though this paper retains the backbone of his argument, I reject Davidson’s thesis that different ways of conceptualisation cannot be compared. I do this through a discussion of the comparative studies conducted by David Hall and Roger Ames. In conclusion, I self-reflectively examine the nature of the demarcation between different traditions of philosophy and show how the activities of comparative philosophy can proceed. (shrink)

The paper is concerned with John Searle’s famous Chinese room argument. Despite being objected to by some, Searle’s Chinese room argument appears very appealing. This is because Searle’s argument is based on an intuition about the mind that ‘we’ all seem to share. Ironically, however, Chinese philosophers don’t seem to share this same intuition. The paper begins by first analysing Searle’s Chinee room argument. It then introduces what can be seen as the (implicit) Chinese view of the mind. Lastly, it (...) demonstrates a conceptual difference between Chinese and Western philosophy with respect to the notion of mind. Thus, it is shown that one must carefully attend to the presuppositions underlying Chinese philosophising in interpreting Chinese philosophers. (shrink)

Nearly a decade has past since Grove gave a semantics for the AGM postulates. The semantics, called sphere semantics, provided a new perspective of the area of study, and has been widely used in the context of theory or belief change. However, the soundness proof that Grove gives in his paper contains an error. In this note, we will point this out and give two ways of repairing it.

In 1A:7 of the Mengzi, Mengzi tries to convince King Xuan of Qi that he is a “true” king. As a reading of Mengzi’s reasoning involved in his attempt at persuasion, David Nivison advances an inferential view, according to which Mengzi’s persuasion involves inferences. In this paper, I consider the assumptions underlying the objections raised against Nivison’s inferential view. I argue that these objections assume a contemporary Western view about the nature of logic and inferences. I propose an alternative characterisation (...) of the relevant sense of inference that, I believe, is more sensitive to the classical Chinese philosophical context and argue that certain insights can be derived from reading Mengzi in light of this alternative characterization of inferences. (shrink)

This paper is concerned with a natural deduction system for First Degree Entailment (FDE). First, we exhibit a brief history of FDE and of combined systems whose underlying idea is used in developing the natural deduction system. Then, after presenting the language and a semantics of FDE, we develop a natural deduction system for FDE. We then prove soundness and completeness of the system with respect to the semantics. The system neatly represents the four-valued semantics for FDE.

Possible worlds have revolutionised philosophy and some related fields. But, in recent years, tools based on possible worlds have been found to be limited in many respects. Impossible worlds have been introduced to overcome these limitations. This Element aims to raise and answer the neglected question of what is characteristically impossible about impossible worlds. The Element sheds new light on the nature of impossible worlds. It also aims to analyse the main features and utility of impossible worlds and examine how (...) impossible worlds can capture distinctions which are unavailable if we limit ourselves to possible world-based tools. (shrink)

In "The Way of the Dialetheist: Contradictions in Buddhism," Yasuo Deguchi, Jay L. Garfield, and Graham Priest argue that some (though not all) of the contradictions that appear in Buddhist texts should be accepted. An examination of their argument depends on what sort(s) of negation is (are) used in the texts. In order to see apparently contradictory statements as affirmations of true contradictions, we must assume that 'not' (or its variance) is used as a contradiction-forming operator. In this article, the (...) conception of negation(s) that is (are) salient in the writings of Dōgen is examined, and it is argued that he would not agree that his sentences are to be considered, and accepted, as contradictory. (shrink)

Logic in Buddhist philosophy concerns the systematic study of anumāna (often translated as inference) as developed by Dignāga and Dharmakīrti. The focus of this chapter is on the tradition of Buddhist philosophy called pramānavada, which is concerned mainly with epistemology and logic. The chapter contains a discussion of the philosophy of logic that is attributable to Buddhist logicians. It examines what “inference” or “logic” might mean for Buddhist logicians and then sketches the Buddhist conception of the nature of logic by (...) uncovering some of the presuppositions that underlie the thoughts expressed in Buddhist logic texts. Epistemology in the Buddhist philosophical tradition is generally concerned with instruments or sources of knowledge. (shrink)

The Moon Points Back comprises essays by both established scholars in Buddhist and Western philosophy and young scholars contributing to cross-cultural philosophy. It continues the program of Pointing at the Moon, integrating the approaches and insights of contemporary logic and analytic philosophy along with those of Buddhist Studies in order to engage with Buddhist ideas in a contemporary voice.The essays in the volume focus on the Buddhist notion of emptiness, exploring its relationship to core philosophical issues concerning the self, the (...) nature of reality, logic, and epistemology. The volume closes with reflections on methodological issues raised by bringing together traditional Buddhist philosophy and contemporary analytic philosophy.The Moon Points Back demonstrates convincingly that integration of Buddhist philosophy with contemporary analytic philosophy and logic allows for novel understandings of and insights into Buddhist philosophical thought. It also shows how Buddhist philosophers can contribute to debates in contemporary Western philosophy and how contemporary philosophers and logicians can engage with Buddhist material. (shrink)

Book Review of Impossible Worlds, by Francesco Berto and Mark Jago. Oxford: Oxford University Press, 2019.