Paradoxes and Their Resolutions

A Thematic Compilation by Avi Sion

14. Buddhist antinomic discourse


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[1].

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[2] 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[3]. 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).

The above-stated property of symbols, i.e. their applicability only conditionally within the constraints of consistency, 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.


2.    Neither real nor unreal

But Nagarjuna also conceives ultimate reality (“emptiness”[4]) as a “middle way” [5] – so that the world of experience is neither to be regarded as real, nor to be regarded as unreal (“there is nothing, neither mental nor non-mental, which is real” and it “cannot be conceived as unreal,” reports Cheng). In this context, Nagarjuna is clearly relying on one of the above-mentioned logically impossible disjuncts, namely “neither A nor non-A” (be it said in passing). I want to now show why Nagarjuna’s statement seems superficially reasonable and true.

As I have often clarified and explained[6], knowledge has to be regarded or approached phenomenologically (that is the only consistent epistemological thesis). We have to start by acknowledging and observing appearances, as such, without initial judgment as to their reality or illusion. At first sight all appearances seem real enough. But after a while, we have to recognize that some appearances conflict with other appearances, and judge such appearances (i.e. one or more of those in conflict) as illusory. Since there is nothing in our ‘world’ but appearances, all remaining appearances not judged as illusions (i.e. so long as they are not logically invalidated by conflicts with other appearances) maintain their initial status as realities.

That is, the distinction between appearances as realities or illusions emerges within the world of appearances itself, merely classifying some this way and the rest that way. We have no concept of reality or illusion other than with reference to appearance. To use the category of reality with reference to something beyond appearance is concept stealing, a misuse of the concept, an extrapolation which ignores the concept’s actual genesis in the context of appearance. To apply the concept of illusion to all appearances, on the basis that some appearances are illusions, is an unjustified generalization ignoring how this concept arises with reference to a specific event (namely, inconsistency between certain appearances and resulting diminishment of their innate credibilities). Moreover, to claim that no appearances are real or that all are illusions is self-defeating, since such claim itself logically falls under the category of appearance.

The illusory exists even though it is not reality – it exists as appearance. The real is also apparent – some of it, at least. Therefore, appearance per se is neither to be understood as reality (since some appearances are illusory), nor can it be equated to illusion (since not all appearances have been or can be found illusory). Appearance is thus the common ground of realities and illusions, their common characteristic, the dialectical synthesis of those theses and antitheses. It is a genus, they are mutually exclusive species of it. (The difference between appearance and existence is another issue, I have dealt with elsewhere – briefly put, existence is a genus of appearance and non-appearance, the latter concepts being relative to that of consciousness whereas the former is assumed independent.)

None of these insights allows the conclusion that appearances are “neither real nor unreal” (granting that ‘unreal’ is understood to mean ‘non-real’). All we can say is that some appearances are real and some unreal. Formally, the correct logical relation between the three concepts is as follows. Deductively, appearance is implied by reality and illusion, but does not imply them; for reality and illusion are contradictory, so that they cannot both be true and they cannot both be false. Moreover, inductively, appearance implies reality, until and unless it is judged to be illusion (by virtue of some inconsistency being discovered).

More precisely, all appearances are initially classed as real. Any appearance found self-contradictory is (deductively) illusory, and its contradictory is consequently self-evident and (deductively) real. All remaining appearances remain classed as real, so long as uncontested. Those that are contested have to be evaluated dynamically. When one appearance is belied by another, they are both put in doubt by the conflict between them, and so both become initially problematic. Thereafter, their relative credibilities have to be tentatively weighed in the overall context of available empirical and rational knowledge – and repeatedly reassessed thereafter, as that context develops and evolves. On this basis, one of these appearances may be judged more credible than the other, so that the former is labeled probable (close to real) and the latter relatively improbable (close to illusory). In the limit, they may be characterized as respectively effectively (inductively) real or illusory. Thus, reality and illusion are the extremes (respectively, 100% and 0%) in a broad range of probabilities with many intermediate degrees (including problemacy at the mid-point).

To be still more precise, pure percepts (i.e. concrete appearances, phenomena) are never illusory. The value-judgment of ‘illusory’ properly concerns concepts (i.e. abstract appearances, ‘universals’) only. When we say of a percept that it was illusory, we just mean that we misinterpreted it. That is, what we initially considered as a pure percept, had in fact an admixture of concept, which as it turned out was erroneous. For example, I see certain shapes and colors in the distance and think ‘here comes a girl on a bike’, but as I get closer I realize that all I saw was a pile of rubbish by the roadside. The pure percept is the shapes and colors I see; the false interpretation is ‘girl on bike’, the truer interpretation is ‘pile of rubbish’. The initial percept has not changed, but my greater proximity has added perceptual details to it. My first impression was correct, only my initial judgment was wrong. I revise the latter concept, not through some superior means to knowledge, but simply by means of further perception and conception.

Strictly speaking, then, perception is never at issue; it is our conceptions that we evaluate. It is in practice, admittedly, often very difficult to isolate a percept from its interpretation, i.e. from conceptual appendages to it. Our perception of things is, indeed, to a great extent ‘eidetic’. This fact need not, however, cause us to reject any perception (as many Western philosophers, as well as Buddhists, quickly do), or even all conception. The conceptual ‘impurities’ in percepts are not necessarily wrong. We know them to have been wrong, when we discover a specific cause for complaint – namely, a logical or experiential contradiction. So long as we find no such specific fault with them, they may be considered right. This just means that we have to apply the rules of adduction[7] to our immediate interpretations of individual percepts, just as we do to complex theories relative to masses of percepts. These rules are universal: no judgment is exempt from the requirement of careful scrutiny and reevaluation.

Now, judging by Cheng’s account and certain quotations of Nagarjuna therein, we could interpret the latter as having been trying to say just what I have said. For instance, Cheng writes[8]: “What Nagarjuna wanted to deny is that empirical phenomena… are absolutely real…. However, [this] does not mean that nothing exists. It does not nullify anything in the world” (my italics). I interpret this non-nullification as an acknowledgment of appearance as the minimum basis of knowledge. Nagarjuna may have had difficulties developing an appropriate terminology (distinguishing existence, appearance and reality, as I do above), influenced no doubt by his penchant for paradoxical statements seeming to express and confirm Buddhist mystical doctrine.

But if that is what he meant, then he has not succeeded to arrive at a “middle way” (a denial of the Law of the Excluded Middle), but only at a “common way” (a granted common ground). As far as I am concerned, that is not a meager achievement – the philosophical discovery of phenomenology! But for him that would be trivial, if not counterproductive – for what he seeks is to deny ordinary consciousness and its inhibiting rationales, and to thereby leap into a different, higher consciousness capable of reaching transcendental truth or ultimate reality.

It is interesting to note that the Madhyamika school’s effective denial of reality to all appearance was not accepted by a later school of Mahayana philosophy, the Yogachara (7th-8th cent. CE). Cheng describes the latter’s position as follows[9]: “Every object, both mental and non-mental, may be logically or dialectically proven illusory. But in order to be illusory, there must be a certain thought that suffers from illusion. The very fact of illusion itself proves the existence and reality of a certain consciousness or mind. To say that everything mental and non-mental is unreal is intellectually suicidal. The reality of something should at least be admitted in order to make sense of talking about illusion” (italics mine). That is the tenor of the phenomenological argument I present above, although my final conclusion is clearly not like Yogachara’s, that everything is consciousness or mind (a type of Idealism), but leaves open the possibility of judging and classifying appearances as matter or mind with reference to various considerations.

The Madhyamika rejection of ‘dualism’ goes so far as to imply that “emptiness” is not to be found in nirvana, the antithesis of samsara (according to the earlier Buddhist viewpoint), but in ‘neither samsara nor nirvana’. In truth, similar statements may be found in the Pali Canon, i.e. in the much earlier Theravada schools, so that it is not a distinctly Mahayana construct. The difference is one of emphasis, such statements, relatively rare in the earlier period, are the norm and frequently repeated in the later period. An example may be found in the Dhammapada, a sutra dating from the 3rd cent. BCE[10], i.e. four or five hundred years before Nagarjuna. Here, samsara is likened to a stream or this shore of it, and nirvana to the further shore; and we are told to get beyond the two.


When you have crossed the stream of Samsara, you will reach Nirvana… He has reached the other shore, then he attains the supreme vision and all his fetters are broken. He for whom there is neither this nor the further shore, nor both….


Such a formula is legitimate if taken as a warning that pursuing nirvana (enlightenment and liberation) is an obstacle to achieving it, just a subtle form of samsara (ignorance and attachment); there is no contradiction in saying that the thought of nirvana as a goal of action keeps us in samsara – this is an ordinary causal statement. The formula is also logically acceptable if taken as a reminder that no word or concept – not even ‘samsara’ or ‘nirvana’ – can capture or transmit the full meanings intended (i.e. ‘not’ here should more precisely be stated as ‘not quite’). There is also no contradiction in saying that one who has attained nirvana does not need to leave the world of those locked in samsara, but can continue to exist and act in it though distinctively in a way free of attachment.

But it would be a contradiction in terms to speak of ‘emptiness’ as ‘neither samsara nor nirvana’, given that nirvana as a concept is originally defined as non-samsara; the truth cannot be a third alternative. At best, one could say that emptiness is a higher level of nirvana (in an enlarged sense), which is not to be confused with the lower level intended by the original term nirvana, nor of course with samsara. In that case, nirvana (in a generic sense of the term, meaning literally non-samsara) includes both a higher species and a lower one; and the statement ‘neither samsara nor lower-nirvana’ is then compatible with the statement ‘higher nirvana’. There is a big difference between rough, poetic, dramatic language, and literal interpretation thereof.


From Buddhist Illogic 1 & 2.


[1]              See my Future Logic (Geneva: Author, 1996. Rev. ed.), ch. 2 and 20, and later essays on the subject (published on my website

[2]              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”.

[3]              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.

[4]              Beyond consciousness of “Shunyata” is a more vivid awareness called “Mahamudra”, according to Chögyam Trungpa, in Illusion’s Game (Shambhala: Boston, 1994). But such refinements need not concern us here.

[5]              See Cheng, pp. 38-39, on this topic. He there refers to MT XIII:9a and XVIII:7.

[6]              See my Future Logic, ch. 60-62, and later essays on the subject.

[7]              Adduction treats all conceptual knowledge as hypothetical, to be tested repeatedly – in competition with all conceivable alternative hypotheses – with reference to all available logic and experience.

[8]              P. 42.

[9]              P. 25.

[10]            London: Penguin, 1973. This is supposedly the date of composition, though the translator, Juan Mascaro, in his Introduction, states “compiled” at that time, thus seeming to imply an earlier composition. It is not clear in that commentary when the sutra is estimated to have been first written down. And if it was much later, say in the period of crystallization of Mahayana thought, say in 100 BCE to 100 CE, the latter may have influenced the monks who did the writing down. See ch. 26 (383-5) for the quotation.

Go Back


Blog Search

Blog Archive


There are currently no blog comments.