4 minute read
CATUSKOTI - An Indian Logic System
from June 2021
By Ramya Mudumba
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A: Yes, it does have a beginning. B: No, it doesn’t have a beginning.
A Buddhist: “No, the world does not have a beginning; it does not fail to have a beginning; it does not have and not have a beginning; nor does it neither have nor not have a beginning. ”
This makes no sense intuitively! How can there be a possibility that something is both true and false at the same time? How can it be neither true nor false? Or worse, how can it be neither of the above two?
Classical logic as we know it does not allow for such possibilities. It adheres to the law of non-contradiction, which simply states that ‘X exists’ and ‘X does not exist’ cannot simultaneously be true. Further, it constrains either one of them to be true. In fact this was taken as ultimate with such gusto that an important Aristotelian, Avicenna declared: “Anyone who denies the law of noncontradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned.”
Indian logic, on the other hand, is a store of uncommon, mind-boggling logic systems, of which some not only overthrow the law of non-contradiction but pushes the reader to wonder how contradictions can co-exist.
The mainstream western logic allows for two-valued truths (true or false) whereas Indian logic systems like Catuskoti or Sapthabhanga allow for more, even upto seven truth values. In the example that we started with, the four possibilities of Catuskoti are put forward. In negation, the possibilities are 1. ‘The world has a beginning’ 2. ‘The world doesn’t have a beginning’ 3. ‘Both’ and 4. ‘Neither’.
In a famous dialogue between a student and Buddha himself, whether an enlightened being (Tathagata) exists after death, we see a similar construct of the four-cornered logic. The student asks Buddha if he holds the view that a Tathagata exists after death, Buddha says, “I do not”. He asks whether a Tathagata does not exist after death to which Buddha again replies, “I do not hold such a view”.
Surely, one must think the possibilities end here. Either Tathagata exists or does not exist after death. An Aristotelean might give up on Buddha and take a break. But the dialogue here goes on. He asks if a Tathagata both exists and does not exist after death, to which Buddha replies “No”. He then asks Buddha if a Tathagata neither ‘exists’ nor ‘does not exist’ after death (simply put neither ‘A’ nor ‘not-A’), and Buddha says no again.
Though Buddha, and subsequently Nagarjuna in his ‘Madhyamakarika’ reject all the four possibilities to describe the ineffable, ultimate reality( hinting at a fifth possibility), it is nevertheless exhilarating to know that such a logic system comes from India.
Contrary to intuition, Catuskoti, which allows for ‘both’ and ‘neither’ values is not just some esoteric system but is recognized as perfectly coherent in mathematics Catuskoti is dated back even before Buddha to Rig Veda itself which flirts with such possibilities:
The astonishing aspect to note here is that rejecting something (X doesn’t exist) doesn’t necessarily have to mean accepting it (X exists). For example, consider these statements: ‘The King of France is bald’ and ‘The King of France is not bald’ (1). If the presupposition that France has a king is not true, then both the statements are negated. Neither is he bald nor is he not bald.
Let us consider a situation where two contradicting statements can be both true. In west, there is a famous paradox called the liar's paradox. Consider a person A who always lies. He then declares:
If he always lies, then even this statement should be false that 'everything he says is a lie'. This would mean that in fact everything he says is not a lie. This contradicts what we started with. So, it follows that the statement is true and not true. It remains a paradox within the confines of classical logic. From Catuskoti’s perspective though, this possibility happily fits in!
Is this all supposed to be mystic? I suppose not. Such many-valued logic systems are a indispensable part of modern logic and are perceived as better alternatives to talk about various concepts. Nagarjuna, in his Madhayamakarika, uses it as a clever tool to reject that things in the world have absolute nature of existence, of being red or sweet etc. He shows how contradictions can co-exist where the nature of things is that they have no inherent nature (and hence everything is interdependent).
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