The Indian philosopher Acarya Nagarjuna (c. 150-250 CE) was the founder of the Madhyamaka (Middle Path) school of Mahayana Buddhism and arguably the most influential Buddhist thinker after Buddha himself. Indeed, in the Tibetan and East Asian traditions, Nagarjuna is often referred to as the "second Buddha." This book presents a survey of the whole of Nagarjuna's philosophy based on his key philosophical writings. His primary contribution to Buddhist thought lies in the further development of the concept of sunyata or (...) "emptiness." For Nagarjuna, all phenomena are without any svabhava, literally "own-nature" or "self-nature," and thus without any underlying substance. Particular emphasis is put on discussing Nagarjuna's thinking as philosophy. The present discussion shows how his thoughts on metaphysics, epistemology, the self, language, and truth present a unified theory of reality with considerable systematic appeal. The book offers a systematic account of Nagarjuna's philosophical position. It reads Nagarjuna in his own philosophical context, but also shows that the issues of Indian and Tibetan Buddhist philosophy have at least family resemblances to issues in European philosophy. (shrink)

Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set (...) theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science. (shrink)

A pivotal focus of exegesis of Nāgārjuna's Mūlamadhyamakakārïkā (MMK) for the past half century has been the attempt to decipher the text's philosophy of language, and determine how this best aids us in characterizing Madhyamaka thought as a whole. In this vein, MMK 24:18 has been judged of particular weight insofar as it purportedly insists that the concepts pratītyasamutpāda (conditioned co-arising) and śūnyatā (emptiness), both indispensable to Buddhist praxis, are themselves only "nominal" or "conventional," that is, they are merely labels (...) that do not referentially signify anything that can be taken to be an ontologically ultimate reality. In various guises, as a result of this explication, Nāgārjuna's thought has been seen to embrace an overarching linguistic nominalism or conventionalism in which words, whether they are used for the purposes of theory or practice, though they serve as commonly accepted currency in the transactions of worldly business (vyavahāra), are in the end only ideas (prajñapti) or metaphysical fabrications (prapanca). This interpretation is largely due to tenaciously inaccurate translations and expositions of MMK 24:18 and their dependence on Candrakīrti's peculiar analysis of this verse in his Prasannapadā. This essay will attempt to correct both the diction of the major translations of MMK 24:18 and the fictions of nominalism and conventionalism that the consequent interpretations of this stanza have perpetuated. The argument that will be developed in the course of this essay is that Candrakīrti's reading of this verse proffers a strong form of linguistic nominalism that Nāgārjuna himself does not embrace. It will be shown, based on everything else found in the MMK, that Nāgārjuna, rather than advocating the mere nominal or conventional status of terms such as pratītyasamutpāda and sunyata, demands they be accepted as both pedagogically useful and even referentially accurate descriptions of the world as it is. (shrink)