The logical analysis of Nāgārjuna’s catuṣkoṭi has remained a heated topic for logicians in Western academia for nearly a century. At the heart of the catuṣkoṭi, the four corners’ formalization typically appears as: A, Not A, Both, and Neither. The pulse of the controversy is the repetition of negations in the catuṣkoṭi. Westerhoff argues that Nāgārjuna in the Mūlamadhyamakakārikā uses two different negations: paryudāsa and prasajya-pratiṣedha. This paper builds off Westerhoff’s account and presents some subtleties of Nāgārjuna’s use of these (...) negations regarding their scope. This is achieved through an analysis of the Sanskrit and Tibetan Madhyamaka commentarial tradition and through a grammatical analysis of Nāgārjuna’s use of na and a- within a diverse variety of the catuṣkoṭi within the Mūlamadhyamakakārikā. (shrink)

The theory of negation developed in the grammatical-philosophical system of later Vyākaraṇa remains almost entirely unstudied, despite its close links with the (widely studied) approaches to negation found in other philosophical schools such as Nyāya and Mīmāṃsā, and despite its consequent importance for a comprehensive understanding of the theory of negation in ancient India. In this paper we present an edition, translation and commentary of the relevant sections of Nāgeśa’s _Paramalaghumañjūṣā_, a concise presentation by the final authority of the Pāṇinian (...) tradition, together with an explanatory introduction outlining the grammarians’ theory of negation and its relations particularly with the Nyāya theory of negation. (shrink)

In Indian philosophy, Bhāṭṭa Mīmāṃsakas and Advaita Vedāntins recognize abhāva or anupalabdhi (non-apprehension) as an independent source of knowledge; but no other school of Indian philosophy agrees with them on this issue, and for that reason, arguments have been given by the latter schools for rejecting anupalabdhi as an independent means of knowledge. In this paper, I am going to evaluate only those arguments which have been given by the Vaiśeṣika thinkers, who admit only two pramāṇa-s, viz. pratyakṣa and anumāna, (...) and reject anupalabdhi as an independent pramāṇa. There have been many scholarly studies dealing with the arguments against the reduction of non-apprehension to some other source of knowledge that have been offered by the Bhāṭṭa Mīmāṃsā and Advaita Vedānta, but there is hardly any full-length work that deals with the Vaiśeṣika’s reduction of non-apprehension to some other source of knowledge. In the present paper, an attempt has been made at providing a clear and specific account of the same. (shrink)

This paper introduces a special issue on logic and philosophy of religion in this journal. After discussing the role played by logic in the philosophy of religion along with classical developments, we present the basic motivation for this special issue accompanied by an exposition of its content.

A defining characteristic of modern science is its ability to make immensely successful predictions of natural phenomena without invoking a putative god or a supernatural being. Here, we argue that this intellectual discipline would not acquire such an ability without the mathematical zero. We insist that zero and its basic operations were likely conceived in India based on a philosophy of nothing, and classify nothing into four categories—balance, absence, emptiness and nonexistence. We argue that zero is a tangible representation of (...) nonexistence and constitutes all nonzero numbers, which together represent existence. It appears that zero’s journey out of India somewhat separated its mathematical and philosophical aspects, with the former being more valued by some cultures and the latter by others. The European culture, in which modern science grew, largely ignores a philosophy of nothing due to a deep-rooted Greek philosophical base, although this science relies on the notion of nonexistence through zero. Consequently, zero is a mere number of convenience without its foundational philosophy in science, and techniques to circumvent zero are developed. We insist that, while such techniques contribute to the progress of science and mathematics within the current framework, a tendency to avoid zero and its philosophy leads to approximations and may hinder a deeper understanding. Finally, we argue that nonexistence may notionally constitute existence, and hence may be the fundamental. This implies that, if a supernatural being exists, it is not the fundamental. The independence of modern science from a supernatural being is consistent with this. (shrink)

This paper introduces the special issue on Logic and Religion of the journal Logica Universalis (Springer). The issue contains the following articles: Logic and Religion, by Jean-Yves Beziau and Ricardo Silvestre; Thinking Negation in Early Hinduism and Classical Indian Philosophy, by Purushottama Bilimoria; Karma Theory, Determinism, Fatalism and Freedom of Will, by Ricardo Sousa Silvestre; From Logic in Islam to Islamic Logic, by Musa Akrami; Leibniz’s Ontological Proof of the Existence of God and the Problem of Impossible Objects, by Wolfgang (...) Lenzen; A Logical Analysis of the Anselm’s Unum Argumentum (from Proslogion), by Jean-Pierre Desclés; Monotonic and Non-monotonic Embeddings of Anselm’s Proof, by Jacob Archambault; Computer-Assisted Analysis of the Anderson–Hájek Ontological Controversy, by C. Benzmüller, L. Weber and B. Woltzenlogel Paleo. (shrink)