1. The tetralemma.
Western philosophical and scientific thought is based on Aristotelian logic, whose founding principles are the three “Laws of Thought”. These can be briefly stated as “A is A” (Identity), “Nothing is both A and non-A” (Non-contradiction) and “Nothing is neither A nor non-A” (Exclusion of the Middle). These are not claimed as mere hypotheses, note well, but as incontrovertible premises of all rational human thought.
Religions like Judaism, Christianity and Islam, even while adhering to these laws in much of their discourse and paying lip-service to them, in their bids to interpret their own sacred texts and to make their doctrines seem reasonable to their converts, have often ignored these same laws. This is especially true of mystical trends within these religions, but many examples could be given from mainstream writings. The same can be said of some aspects of Buddhist philosophy.
The tetralemma is a derivative of the laws of thought, with reference to any two terms or propositions, labeled A and B, and their opposites non-A and non-B. Four combinations of these four terms are conceivable, namely “A and B” (both), “non-A and non-B” (neither), “A and non-B” and “non-A and B” (one or the other only). According to Aristotelian logic, these four statements are incompatible with each other (only one of them can be true, because if two or more were affirmed then “A and non-A” or “B and non-B” or both would be true, and the latter implications are self-contradictory) and exhaustive (at least one of them must be true, since if they were all denied then “not A and not non-A” or “not B and not non-B” or both would be true, and the latter implications go against the excluded middle).
Now, what Nagarjuna does is insert the term A in place of B (i.e. he takes the case of B = A), and effectively claim that the above four logical possibilities of combination apply in that special case – so that “A and A (=B)”, “non-A and non-A (=non-B)”, “A and non-A (=non-B)”, “non-A and A (=B)” seem logically acceptable. He then goes on to argue that there are four existential possibilities: affirmation of A (A + A = A), denial of A (non-A + non-A = non-A), both affirmation and denial of A (A and non-A) and neither affirmation nor denial of A (not A and not non-A). He is thus apparently using the principles and terminology of common logic to arrive at a very opposite result. This gives him and readers the impression that it is quite reasonable to both affirm and deny or to neither affirm nor deny.
But in Aristotelian logic, the latter two alternatives are at the outset excluded – “both A and non-A” by the Law of Non-contradiction and “neither A nor non-A” by the Law of the Excluded-Middle – and the only logical possibilities left are “A” or “non-A”. The anti-Aristotelian position may be viewed, in a positive light, as an anti-Nominalist position, reminding us that things are never quite what they seem or that things cannot be precisely classified or labeled. But ultimately, they intend the death of Logic; for without the laws of thought, how are we to distinguish between true and false judgments?
The law of identity “A is A” is a conviction that things have some identity (whatever it specifically be) rather than another, or than no identity at all. It is an affirmation that knowledge is ultimately possible, and a rejection of sheer relativism or obscurantism. Nagarjuna’s goal is to deny identity.
It should be noted here that Aristotle is very precise in his formulation of the law of contradiction, stating in his Metaphysics “The same attribute cannot at the same time belong and not belong to the same subject in the same respect” (italics mine). Thus, an alternative statement of the laws of thought would be the ‘trilemma’ (let us so call it) “either wholly A, or wholly non-A, or both partly A and partly non-A”, which excludes the fourth alternative “both wholly A and wholly non-A”. The Buddhist attack on the laws of thought draws some of its credibility from the fact that people subconsciously refer to this ‘trilemma’, thinking superficially that indeed opposite things may occur in the same place at different times or at the same time in different places or in various respects, without thereby giving rise to logical difficulty incapable of resolution. But it should be clear that the Buddhist position is much more radical than that, accepting thoroughgoing antinomy.
Similarly with regard to the law of the excluded middle, which affirms the situation “neither A nor non-A” to be impossible in fact. People are misled by the possibility of uncertainty in knowledge, as to whether A or non-A is the case in fact, into believing that this law of thought is open to debate. But it must be understood that the thrust of this logical rule is inductive, rather than deductive; i.e. it is a statement that at the end of the knowledge acquisition process, either “A” or “non-A” will result, and no third alternative can be expected. It does not exclude that in the interim, a situation of uncertainty may occur. Nagarjuna’s position exploits this confusion in people’s minds.
Nagarjuna interprets the limitation implied by the dilemma “A or non-A” as an arbitrary ‘dualism’ on the part of ordinary thinkers. It only goes to show that he misunderstands formalization (or he pretends to, in an attempt to confuse gullible readers). When logicians use a variable like “B” and allow that “non-A and B” and “A and non-B” are both in principle possible, they do not intend that as a generality applicable to all values of B (such as “A”), but only as a generic statement applicable to any consistent values of B. In the specific case where B = A, the said two combinations have to be eliminated because they are illegal (i.e. breach two of the laws of thought).
This property of symbols is evident throughout the science of formal logic, and it is here totally ignored by Nagarjuna. His motive of course was to verbalize and rationalize the Buddha’s doctrine that the ultimate truth is beyond nama and rupa, name and form (i.e. discrimination and discourse), knowable only by a transcendental consciousness (the Twofold Truth doctrine). More precisely, as Cheng emphasizes, Nagarjuna’s intent was to show that logic is inherently inconsistent and thus that reason is confused madness to be rejected. That is, he was (here and throughout) not ultimately trying to defend a tetralemma with B equal to A – or even to affirm that things are both A and non-A, or neither A nor non-A – but wished to get us to look altogether beyond the distinctions of conceptualization and the judgments of logic.
But as above shown he does not succeed in this quest. For his critique depends on a misrepresentation of logical science. He claims to show that logic is confused and self-contradictory, but in truth what he presents as the thesis of logical science is not what it claims for itself but precisely what it explicitly forbids. Furthermore, suppose logical theory did lead to contradictions as he claims, this fact would not lead us to its rejection were there not also a tacit appeal to our preference for the logical in practice. If logic were false, contradictions would be acceptable. Thus, funnily enough, Nagarjuna appeals to our logical habit in his very recommendation to us to ignore logic. In sum, though he gives the illusion that it is reasonable to abandon reason, it is easy to see that his conclusion is foregone and his means are faulty.
 See my Future Logic (Geneva: Author, 1996. Rev. ed.), ch. 2 and 20, and later essays on the subject.
 See Cheng, pp. 36-38, on this topic. He
there refers to MT opening statement, as well as XVII:12a and XXIII:1a. Etym. Gk. tetra = four, lemma = alternatives. Term
coined in contrast to the dilemma “A or non-A”.
He there refers to MT opening statement, as well as XVII:12a and XXIII:1a. Etym. Gk. tetra = four, lemma = alternatives. Term coined in contrast to the dilemma “A or non-A”.
 It is misleading to call this a ‘duality’ or ‘dichotomy’, as Buddhists are wont to do, because it suggests that a unitary thing was arbitrarily cut into two – and incidentally, that it might just as well have been cut into four. But, on a perceptual level, there is no choice involved, and no ‘cutting-up’ of anything. A phenomenon appearing is one single thing, call it ‘a’ (a proper name, or an indicative ‘this’), and not a disjunction. The issue of ‘dichotomy’ arises only on a conceptual level. Negation is a rational act, i.e. we can only speak of ‘non-a’, of what does not appear, by first bringing to mind something ‘a’, which previously appeared (in sensation or imagination). In initial conceptualization, two phenomena are compared and contrasted, to each other and to other things, in some respect(s); the issue is then, are they similar enough to each other and different enough from other things to be judged ‘same’ and labeled by a general term (say ‘A’), or should they be judged ‘different’ or is there an uncertainty. At the later stage of recognition, we have to decide whether a third phenomenon fits in the class formed for the previous two (i.e. falls under ‘A’) or does not fit in (i.e. falls under ‘non-A’) or remains in doubt. In the latter case, we wonder whether it is ‘A’ or ‘non-A’, and forewarn that it cannot be both or neither.