Nargarjuna
The Catuṣkoṭi was employed particularly by Nagarjuna who developed it and engaged it as a 'learning, investigative, meditative' portal to realize the 'openness' (Sanskrit: Śūnyatā), of Shakyamuni's Second Turning of the Dharmacakra, as categorized by the Sandhinirmocana Sutra.
Robinson (1957: p. 294), building on the foundations of Liebenthal (1948) to whom he gives credit, states:
What Nagarjuna wishes to prove is the irrationality of Existence, or the falsehood of reasoning which is built upon the logical principle that A equals A.... Because two answers, assertion and denial, are always possible to a given question, his arguments contain two refutations, one denying the presence, one the absence of the probandum. This double refutation is called the Middle Path.
Read more about this topic: Catuskoti