Chris Rahlwes

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.

In reading Nāgārjuna’s Mūlamadhyamakakārikā, one is struck by Nāgārjuna’s separation of conventional truth and ultimate truth. At the most basic level, these two truths deal with emptiness and the appearance of fundamental existence, but the meaning of “conventional” lends itself to two key senses: concealing and socially agreed-upon norms and practices. The tension between these two senses and how they relate to truth leads Nāgārjuna’s Tibetan commentators in different directions in their exegesis on conventional truth. Based on the debate between Tsongkhapa and Gorampa, I propose a Madhyamaka account of truth as trust. In so doing, I provide a novel account of truth, in which propositions and phenomena are truth-bearers, and one’s ability to trust in them establishes their truth-value.

The Jaina _saptabhaṅgī_ (seven angles of analysis or types of sentences) has drawn the attention of non-classical logicians due to its unique use of negation, contradiction, and _avaktavya_ (‘unutterable’). In its most basic structure, the _saptabhaṅgī_ appears as: (i) in a certain sense, _P_; (ii) in a certain sense, not _P_; (iii) in a certain sense, _P_ and not _P_; (iv) in a certain sense, inexpressibility of _P_; (v) in a certain sense, _P_ and inexpressibility of _P_; (vi) in a certain sense, not _P_ and inexpressibility of _P_; (vii) in a certain sense, _P_, not _P_, and inexpressibility of _P_. This appearance has led many (e.g., Ganeri and Priest) to claim that the _saptabhaṅgī_ supports non-classical systems of logic, but such a reading is contested by Balcerowicz. Focusing on Vādidevasūri’s (12th c. CE) and Yaśovijaya’s (17th c. CE) accounts of the _saptabhaṅgī_, this paper puts forward a formalization of the _saptabhaṅgī_ that brings together the non-classical views and Balcerowicz’s view through relating the _saptabhaṅgī_ to the Buddhist unanswerable questions.