This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society (co-sponsored by the Centre for Logic, Epistemology and the History of Science, State University of Campinas, Sao Paulo) in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading (...) Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and updated by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)
The Fang Bian Xin Lun is a text on Buddhistlogic which is thought to be the earliest one still to be extant. It appears in Chinese only (T1632). The great Italian indologist Giuseppe Tucci, believing that the text was originally a Sanskrit text, translated it into Sanskrit and gave it the title Upāyahṛdaya. The paper provides the historical background of the development of logic in Classical India up to the time of this text, summarizes its content (...) and translates its first section. (shrink)
The problem of empty terms is one of the focal issues in analytic philosophy. Russell’s theory of descriptions, a proposal attempting to solve this problem, attracted much attention and is considered a hallmark of the analytic tradition. Scholars of Indian and Buddhist philosophy, e.g., McDermott, Matilal, Shaw and Perszyk, have studied discussions of empty terms in Indian and Buddhist philosophy. But most of these studies rely heavily on the Nyāya or Navya-Nyāya sources, in which Buddhists are portrayed as (...) opponents to be defeated, and thus do not truly reflect Buddhist views on this issue. The present paper will explore how Dignāga, the founder of Buddhistlogic, deals with the issue of empty subject terms. His approach is subtle and complicated. On the one hand, he proposes a method of paraphrase that resembles Russell’s theory of descriptions. On the other, by relying on his philosophy of language—the apoha theory, he tends to fall into a panfictionalism. Through the efforts of his follower Dharmakīrti, the latter approach would become more acceptable among Indian and Tibetan Buddhists. Dignāga’s Chinese commentators, who were free from the influence of Dharmakīrti, dealt with the empty term issue in three ways: (1) by adhering to Dignāga’s method of paraphrase; (2) by allowing exceptions for non-implicative negation; and (3) by indicating the propositional attitude of a given proposition. Among these, the third proved most popular. (shrink)
A glimpse of the new application of Buddhistlogic in the seventeenth century leads us to reflect about our approach to logic in a given religious tradition: Should we isolate a logical system from the very context that has given rise to the genesis and development of such an intellectual apparatus? Methodologically, we do have the legitimate right to approach Buddhistlogic from a purely logical point of view. However, when we study the actual use (...) of Buddhistlogic in the seventeenth-century anti-Christian polemic, an analysis of its intentional application allows us to conclude that Buddhistlogic in the context of controversy is primarily apologetic. Therefore, with a methodological concern, I suggest that philosophers and logicians should reconsider the apologetic nature of logic in any given religious tradition. (shrink)
This volume collects essays by philosophers and scholars working at the interface of Western philosophy and Buddhist Studies. Many have distinguished scholarly records in Western philosophy, with expertise in analytic philosophy and logic, as well as deep interest in Buddhist philosophy. Others have distinguished scholarly records in Buddhist Studies with strong interests in analytic philosophy and logic. All are committed to the enterprise of cross-cultural philosophy and to bringing the insights and techniques of each tradition (...) to bear in order to illuminate problems and ideas of the other. These essays address a broad range of topics in the philosophy of mind, philosophy of language, logic, epistemology, and metaphysics, and demonstrate the fecundity of the interaction between the Buddhist and Western philosophical and logical traditions. (shrink)
Buddhist logicians have rejected the reality of universals on the one hand, and, on the other hand, given a substitute in the form of the doctrine of Apoha. The doctrine of apoha first appears in Dinnaga’s Pramanasamuccaya, according to which words and concepts are negative by their very nature. They proceed on thebasis of negation. They express their own meaning only by repudiating their opposite meaning. The Buddhist logicians talk of two types of knowledge, viz., pratyaksa, which is (...) non- relational and anumana, which is relational. They accept nirvikalpaka pratyaksa as a pure pratyaksa, and savikalpaka pratyaksa has been merged with anumana by them. According to them, cognition is either a direct awareness of an object, which is independent of any mentalconstructionor it is an awareness of an object which is a mentalconstruction. Further, according to the Buddhist logicians inferences are of two kinds, viz., svarthanumana and pararthanumana. But they do not accept pararthanumana as a source of knowledge. Now, since perception is devoid of kalpana, perceptual knowledge is essentially non-linguistic and does not involve any general concept or universal. Thus,Apoha has no role to play in perceptual knowledge. On the other hand, savikalpaka pratyaksa and anumana are based on kalpana, thus according to the Buddhist logicians knowledge of universal is essential for both, savikalpaka pratyaksa and anumana. (shrink)
A Buddhist-Christian Logic of the Heart explores the philosophies of Being and Nothingness as expounded in the Buddhist and Christian point of view with particular emphasis on the socioethical implication that all human beings, despite vast differences in history, language, and culture, share the cognitional, intentional makeup as emphasized by Nishida and Lonergan.
This work proposes a logical analysis for the kind of knowledge or insight provided by Buddhist enlightenment, which is often presented only in the form of contradictions and riddles. The comprehension of contradictions is perplexing to most western logic, and yet developed here is a theory demonstrating how a non truth-functional interpretation can be attached to certain naturalistic contradictions. In this way, the logical and psychological status of Enlightenment can be analysed in a manner consistent with the claims (...) of much Eastern thought. For example, it is argued that by breaking the logical principle of identity, it is possible to understand the contradiction "Everybody's friend is nobody's friend" in such a way as to learn something new about friendship, thereby causing us to modify our concept of friendship. In this way our grasp of contradictions can lead to conceptual change. -/- It is further noted that conflicts in all areas of life can be expressed by contradictions, so that our capacity in general to grasp naturalistic contradictions is also a basis for conflict-resolution -thus justifying the term 'Enlightenment'. This pragmatic comprehension of contradictions is thus shown to formalise, not only the Middle Way of Buddhism, but also Socratic dialectic. Finally, the analysis explains why gnomic utterances in every religion and Zen in particular, are sometimes expected to trigger spiritual enlightenment. (shrink)
The Conciliatory Character of Jaina Logic. In the previous pages there has been given an indication of the services rendered by the Jainas and N° Brihrna^1 H,e the Buddhists in the formation of the Mediaeval School of Indian Logic. Since the ...