Tetralemma

In the tetralemma (catuskoti) of Buddhist philosopher Nagarjuna (which has some similarities to the Aristotelian "Laws of Thought"), with reference to any two logical propositions X and Y, there are four possibilities:


 * $$X \land Y$$ (both)
 * $$\neg X \land \neg Y$$ (neither)
 * $$X \land \neg Y$$ (X but not Y)
 * $$\neg X \land Y$$ (Y but not X)

It was expressed differently by Nagarjuna, who was the founder of the Madhyamaka school of Mahayana Buddhism. Nagarjuna took the case where Y = X and applied to questions such as those regarding the existence of the self, and the true nature of reality. He used the tetralemma to illustrate the seemingly contradictory nature of reality, where "conventional" reality suggests that entities are separate and have essence, and the "ultimate" reality of Mahayana Buddhism, that of shunyata, that all is lacking of self essence.

The self exists (conventionally true)
 * X

The self does not exist (ultimately true)
 * not X

The self exists and does not exist (both conventionally true and ultimately true)
 * Both X and not X

The self is neither real nor not real (neither ultimately real nor nonexistent)
 * Neither X nor not X