Recapture, Transparency, Negation and a Logic for the Catuṣkoṭi

Abstract

The recent literature on Nagarjuna's catuskoti centres around Jay Garfield's (2009) and Graham Priest's (2010) interpretation. It is an open discussion to what extent their interpretation is an adequate model of the logic for the catuskoti, and the Mula-madhyamaka-karika. Priest and Garfield try to make sense of the contradictions within the catuskoti by appeal to a series of lattices - orderings of truth-values, supposed to model the path to enlightenment. They use Anderson & Belnaps's (1975) framework of First Degree Entailment. Cotnoir (2015) has argued that the lattices of Priest and Garfield cannot ground the logic of the catuskoti. The concern is simple: on the one hand, FDE brings with it the failure of classical principles such as modus ponens. On the other hand, we frequently encounter Nagarjuna using classical principles in other arguments in the MMK. There is a problem of validity. If FDE is Nagarjuna's logic of choice, he is facing what is commonly called the classical recapture problem: how to make sense of cases where classical principles like modus pones are valid? One cannot just add principles like modus pones as assumptions, because in the background paraconsistent logic this does not rule out their negations. In this essay, I shall explore and critically evaluate Cotnoir's proposal. In detail, I shall reveal that his framework suffers collapse of the kotis. Taking Cotnoir's concerns seriously, I shall suggest a formulation of the catuskoti in classical Boolean Algebra, extended by the notion of an external negation as an illocutionary act. I will focus on purely formal considerations, leaving doctrinal matters to the scholarly discourse - as far as this is possible.