Today, I want to share some of my thoughts about Buddhism. This piece may be a bit difficult for those unfamiliar with propositional logic. However, I have ensured that this exposition is accessible to everyone, not just the logicians.

Buddhism, and Eastern philosophy by large, is often dismissed as mysticism. Overloaded with aphorisms, seemingly non-sensical claims, and stories which go nowhere, there tends to be a knee-jerk reaction from Western philosophers. They sense a lack of logical rigour in Buddhism. However, this would be a grievous miscalculation.

I would like to share with you one such example of seeming incoherence and offer a way out from this philosophical cold-take, that Buddhism is a form of mysticism.

I will introduce the logical argument found in Buddhism known as tetralemma and the philosopher Nagarjuna who employed it. To do so, I will explain who Nagarjuna is and describe the tetralemma. Then I will demonstrate how this proposition is applied in basic terms of logic. Then finally, I will show how it was utilized by Nagarjuna and provide insight into its application to Buddhist philosophy.

Who & What

Nagarjuna is considered one of the most influential philosophers in Buddhist history.  He is believed to have lived between 150–250 BCE. His seminal works include philosophical treatises on epistemology, ontology, and metaphysics and touch on topics such as emptiness, causation, knowledge, language, and personal identity. The most influential of his written work is The Foundations of the Middle Way (Mūlamadhyamakakārikā) (MMK), a collection of stanzas exploring the philosophical concept of The Middle Way. The Middle Way finds its Western equivalent somewhere near Aristotelian virtue ethics, where one attempt to find a ‘happy medium’ between extreme dispositions. The Middle Path is a seminal element of Buddhist Philosophy. (Westerhoff, 2018)

The tetralemma is catuṣkoṭi, which in Sanskrit roughly translates to “four alternatives.” A tetralemma is a logical argument that provides four possible conclusions for any given proposition. It is important to note that Nagarjuna was not the first to employ the catuṣkoṭi. Its usage can be traced back to the Vedas in ancient India and to the early skepticism of Pyrrhonism in ancient Greece. The tetralemma is akin to a dilemma or a trilemma. The prefix tetra, tri or di refers to the number of possible choices within a scenario. In a typical dilemma, one must choose between two unfavourable options, whereas the trilemma that number is three. The four propositions of a tetralemma share a similar quality of  “unfavourable” not because they are bad in themselves but because Nagarjuna employs a tetralemma in hopes that one concludes that all options provide a false interpretation.  (Westerhoff, 2018) This will be explored further in section 3, but first, we will investigate the logical structure of the tetralemma.

The Logical Structure

Tertalemma’s logical structure is composed of four alternatives, an affirmation, a negation, a refutation, and a refutation of the refutation.  It is said there are two rules considered when employing this ancient form of logic. That is, (1) one of the options must be true, and (2) at any given point, only one can be true. That is to say, they are exclusive. The four propositions, P,  are displayed as such:

1. P
2. ~P (Not P)
3. P ^ ~P  (P and Not P)
4. ~(P ^ ~P) (Neither P nor Not P)

Unless one is familiar with propositional logic, the statements above might not make much sense. However, when we replace the generic proposition, P, with something specific and convert it back into ordinary language, the catuṣkoṭi becomes clearer. We shall use the example by Nagarjuna when describing the definitive nature of Buddhist philosophy in the MMK. (Adamson. 4:00)

1. It is such as it is. (affirmation)
2. It is not such as it is. (negation)
3. It is both such as it is and not such as it is. (refutation)
4. It is neither such as it is nor not such as it is. (refutation of the refutation)

Seems contradictory… what does it mean?

In the Western tradition of Aristotelian logic, we find that statement 3 directly violates the law of noncontradiction. Something can not be both positive and negative at the same time. However, it would not be sufficient to stop there, for Nagarjuna explicitly endorses the law of noncontradiction, stating,

“No one can perform an action that is both existent and non-existent for they are contradictory. Where can existence and nonexistence co-exist?” (Adamson. 8:00)

The challenge then becomes what sorts of applications the tetralemma have, considering it seemingly endorses a mystical, non-binary, or flat-out incomprehensible logical structure. 

It has been suggested that tetralemmic logic was employed by Nagarjuna to give us further insight into the properties, or qualities, of an object as opposed to the truth value of the object itself. As such, we can use the colour blue, as a property, in the tetralemma to show how statement 3 is not as nonsensical as initially thought. Number 3, then becomes:  Everything is both blue and not blue. This could be a comprehensible option, as it could mean that everything that exists either contains the property of blue or it does not. (Adamson. 5:30) 

Nagarjuna makes a further step, adding to the confusion of those attempting to understand this logic through the Western tradition. He refutes all four propositions as equally false. Thus the tetralemma consists of not only the original four propositions but four additional propositions, which negate the original four. Thus the new argument is represented by an octave and expressed in terms of geometry.

1.  P                     
2. ~P (Not P)   
3. P ^ ~P  (P and Not P)
4. ~(P ^ ~P) (Neither P nor Not P)

1. ~P (Not P)
2.   P 
3.  ~(P ^ ~P) (Not P nor Not P)
4.  ~(~(P ^ ~P)) (Not neither P nor Not P)

By exploring properties, Nagarjuna’s tetralemmic thinking can be employed in concepts such as the Middle Way or the notorious concept of emptiness. The Middle Way encourages the rejection of strong dispositions and dogmas. We can see how the refutation of specific qualities or properties is useful in aligning oneself toward rejecting definitive universal claims. As such, quality is never definitively on or off, yes or no, P or Not P. Emptiness can also be thought of as the rejection of the essential qualities of objects as well. The self, for example, is permanent, non-permanent, permanent as well as non-permanent, and neither permanent nor not permanent. Further, the self is all of those things in its negation! In this way, the self is empty, not in the idea of a void, but of the meanings we consider inherent. Its meaning, as understood as an essential quality of the object of self, is rejected by the refutation of all four propositions of the tetralemma. Through this negation of property, it creates the space needed in the development of emptiness, as Buddhism proposes. (Lusthaus, 2010)

Conclusion

Even from a cursory survey of Nagarjuna’s tetralemma, the topic is deeply provocative. It has led some to assume that Eastern and Western philosophy can be understood along their logical propositions, which is understandable when confronted with seemingly contradictory statements such as P ^ ~P. However, once applied to the tenants of Buddhism, we begin to see how it compliments the belief system. Buddhism posits a limitation to the knowledge and insights provided by rationality alone, and Nagarjuna was very aware of these limitations. This is not to say that Buddhist philosophy is mysticism alone. Applying the tetralemma not only helps one challenge the logical rigour of an argument but also offers a method for dispelling irrational beliefs and dogmas towards specific ideas. We can recognize this philosophy as a form of epistemic humility, putting Nagarjuna much closer to the western philosophies of Plato and Immanuel Kant—who all hold that we were epistemically limited in our cognition about the world around us. 

 

Cited Work:

• Adamson, Peter. “46. No Four Ways About It: Nāgārjuna’s Tetralemma.” No Four Ways About It: Nāgārjuna’s Tetralemma | History of Philosophy without Any Gaps, historyofphilosophy.net/nagarjuna-tetralemma. Accessed April 7, 2020.
• Lusthaus, Dan. “Nāgārjuna.” Http://Www.acmuller.net/, 27 Apr. 2010, www.acmuller.net/yogacara/thinkers/nagarjuna-bio.html.
• Westerhoff, Jan Christoph. “Nāgārjuna.” Stanford Encyclopedia of Philosophy, Stanford University, 8 June 2018, plato.stanford.edu/entries/nagarjuna/. Accessed Apri 5, 2020.