Notes : An Apprenticeship on Signs & Matters

The Catuskoti, also known as the Tetralemma, is a philosophical concept originating from the early Indian thought and first becomes codified in the tipikata in suttas such as the Aggivacchasutta, Anurādhasutta and for different means by the ascetic Sañjaya Belaṭṭhiputta in the Sāmaññaphala Sutta (c.f 3.6). It represents a way of understanding and discussing reality that is markedly different from the binary logic commonly found in Western philosophy. The term itself is derived from two Sanskrit words: “catuḥ,” meaning “four,” and “koti,” which can mean “cases,” “alternatives,” or “possibilities.” Thus, Catuskoti translates to “the four possibilities.”

Etymology

• Catuḥ (चतुः): This part of the term means “four” in Sanskrit, indicating the number of propositions offered by the Catuskoti.
• Koti (कोटि): This term can be translated as “case,” “category,” or “possibility,” suggesting the nature of the alternatives the Catuskoti presents.

Origin and Historical Use

The Catuskoti was used as a method to approach and understand complex philosophical and metaphysical debates, where simple binary distinctions (true or false) were found to be inadequate. From the early buddhist text standpoint you have its use to demonstrate the limitations of language and conceptual thinking, particularly around metaphysical questions and the opposing use, the Sanjaya “eel-wriggling” (amarāvikkhepa), neither…nor, construction to systematically evade taking any position:

Several centuries later you have one of the most famous proponents of the Catuskoti in Buddhism: Nagarjuna, the founder of the Madhyamaka school of Mahayana Buddhism, who employed it to discuss the nature of emptiness and/or to demonstrate dependent origination. He most famously employs the catuskoti in the Mūlamadhyamakakārikā to analyze fundamental concepts and show that they lack svabhāva (inherent existence). He typically examines four possibilities for how something might exist or arise:

In Jainism, the logic of Anekantavada (the doctrine of multiple aspects) employs a similar structure to the Catuskoti, emphasizing the complexity and multifaceted nature of truth. Jains integrate catuskoti-style reasoning into their broader syādvāda (seven-fold predication) system. Rather than rejecting positions, they see multiple viewpoints as simultaneously valid in different contexts. The Jain approach is affirmative rather than negative – they use this type of logic to build a positive theory of reality’s many-sided nature (anekāntavāda). Each perspective is seen as partially true rather than ultimately false.

The fundamental difference between the Jain and Buddhist iterations lies in their aims: Buddhist usage tends toward demonstrating the inadequacy of conceptual thinking and language, while Jain usage aims to build up metaphysical claims to capture what they see as the complex, multi-faceted nature of reality through acknowledging multiple valid perspectives.

Comparison and Difference with Other Forms of Logic

The most striking difference between the Catuskoti and Western forms of logic is the inclusion of two additional possibilities beyond the simple binary of true and false. Western logic traditionally relies on the principle of bivalence, which asserts that every proposition is either true or false. In contrast, the Catuskoti introduces a fourfold logical structure that allows for more nuanced discussions about reality, including statements that are both true and false, as well as neither true nor false.

Examples Using Formal Logic Notation

In formal logic notation, the four possibilities offered by the Catuskoti can be expressed as follows, where “P” is a proposition:

1. P (It is the case that P)
2. ¬P (It is not the case that P)
3. P ∧ ¬P (It is both the case that P and not the case that P)
4. ¬(P ∨ ¬P) (It is neither the case that P nor not the case that P)

For example, consider the proposition P: “The current king of France is bald.” In classical Western logic, this proposition is either true or false. However, under the Catuskoti framework, we can explore it more nuancedly, especially considering that there is no current king of France:

1. P: The current king of France is bald. (Asserting a fact about a non-existent entity)
2. ¬P: The current king of France is not bald. (Denying a fact about a non-existent entity)
3. P ∧ ¬P: The current king of France is both bald and not bald. (Acknowledging a paradoxical nature of discussing non-existent entities)
4. ¬(P ∨ ¬P): It is neither correct to say the current king of France is bald nor not bald. (Reflecting the inapplicability of such assertions about non-existent entities)

One might say then that the Catuskoti opens up a space for more complex and nuanced discussions about reality, truth, and existence, accommodating the limitations and paradoxes that arise in conventional logic systems. But I think there is a pre-logical activity with the historical Buddha that should be made distinct. The Catuskoti is employed as a way of demonstrating something that is only of relevance upon the posing of a question. The Buddha’s prior activity relates to a discernment of skillful (i.e. what leads to liberation) vs unskillful (what leads to confusion or greater attachments) questions. It’s what in 20th century terms one might call a soteriological Problematics (which perhaps I will write about another day). But the basic idea is that from the perspective of the Buddha’s soteriological objectives, the field comes to a point of being cleared of questions or concerns of logical consistency. What quicker way, than through a Catuskoti to note the non-soteriological metaphysical questioning and re-elevate a discussion to the level of the Problem? Logic is not set to the side, only the unskillful use.