Aristotle, Nagarjuna and the Law of Non-Contradiction in Buddhist Philosophy

By Peter G. Jones

(This is a guest essay submitted to the Metaphysical Speculations Discussion Forum, reviewed, commented on and approved for publication by forum members. The opinions expressed in the essay are those of its author.)

Nagarjuna and Agatsaya. Source: Wikimedia Commons.

Life, they urge, would be intolerable if men were to be guided in all they did by reason and reason only. Reason betrays men into the drawing of hard and fast lines, and to the defining by language—language being like the sun, which rears and then scorches. Extremes are alone logical, but they are always absurd; the mean is illogical, but an illogical mean is better than the sheer absurdity of an extreme.
Samuel Butler, Erewhon

This quotation from Butler’s topsy-turvy land of Erewhon describes the view of the professors of the Colleges of Unreason. His satire of academia is an odd mix of good sense and madness but by the way it questions so many of our intellectual habits and assumptions it provides much food for thought. The professors of Unreason argue that reason forces us to draw lines and make divisions and that it enslaves us to language. This is usually considered a conclusion of rational thought and not at all an unreasonable idea. ‘Unreason’ enters with the idea that the ‘illogical’ mean is better than the absurdity of the extreme views into which language forces us.

The professors of Unreason teach their students that in order to endorse a middle way or ‘doctrine of the mean’ as the solution for metaphysical dilemmas we must embrace unreason and illogic. This seems a reasonable idea to them for it is, after all, their reason that allows them to see the absurdity of the extremes in the first place. In this case their endorsement of ‘illogic’ is an outcome of sound reasoning. Yet it is questionable whether we should ever abandon the ‘laws of thought’ in this way even where logic can find no other way forward. Butler’s professors would answer that we should, but real professors generally say we should not on the grounds that metaphysical questions must be decidable even if nobody can actually decide one. What is not questionable, for it would be a matter of logic and definition, is whether endorsing the middle way would in fact require that we modify or abandon Aristotle’s logic and embrace Unreason and Illogic. Butler’s students are taught that the mean is ‘illogical,’ that this solution breaks or modifies the rules by which we prove it is the best solution, and so are most students everywhere. Yet it is not possible to prove it, and the consequence of assuming it is an incomprehensible metaphysics.

A great many philosophers share the view of logic held by the professors of Unreason and perhaps almost all those who would call themselves ‘Western’ thinkers. It is endorsed in a recent article for Aeon on Buddhist philosophy by Graham Priest under the title ‘Beyond True and False,’ in which he proposes that while the extremes are logically absurd the mean would require a major modification to classical logic. He discusses various complex ideas that would make Buddhist philosophy very difficult to understand. The implication is that one would have to be extremely clever to understand Buddhist philosophy and perhaps even a mental contortionist able to believe two opposite things at once.

It must be conceded that many people who read Nagarjuna, the Buddhist philosopher who most clearly describes the logical scheme of Buddhism and more generally ‘nondualism,’ conclude that he did not fully understand the nature of Reality. Some even read him as proving that a full understanding would be impossible. It must also be conceded that this view may only arise when we are failing to understand him. Nobody can tell us who is right about this and we must make up our own mind. Priest’s view is that Nagarjuna "thought that certain things might be simultaneously true and false." This implies that nobody would be capable of understanding Buddhist philosophy for it seems unlikely that anyone could perform this intellectual feat. In fact his philosophy is much simpler than it may appear. Indeed, its simplicity is what makes it so difficult to understand.

Nagarjuna is completely intolerant of contradictions and demonstrates this in his Fundamental Verses on the Middle Way. In this text he proves that all extreme metaphysical positions are logically absurd. This is just as professors everywhere conclude. He does not prove that his own view is logically absurd. He clearly intends to prove that the mean is the only logically defensible view. In metaphysics the phrase ‘Middle Way’ indicates neutrality in respect of all extreme views and so it is an explicit denial of the reality of the divisions and distinctions on which metaphysical contradictions depend. There would be no such thing as a metaphysical dilemma. His proof is a classic demonstration of logic-chopping that follows Aristotle’s rules to the letter and entirely depends on them for its success. He shows that there is no such thing as a true contradiction and that no contradictions would arise for a true description of the Universe.

That is to say, Nagarjuna painstakingly proves that there are no contradictions in Buddhist philosophy. And yet, highlighted at the top of Priest’s article is the statement "Buddhist philosophy is full of contradictions." It is not clear who makes this statement and it may be an editorial addition but that it can be made so boldly suggests that it expresses a common view. So what is going on here? Is the Buddhist universe paradoxical or is it a model of logical soundness?

Let us examine two oft-quoted statements that encapsulate Buddhist philosophy and follow their logical implications. The first is the statement of Heraclitus "We are and are-not." For Buddhist philosophy this would not be exactly a true statement (as Nagarjuna proves), but it would be rigorous in that it would point accurately towards the truth and not mislead. Does it embody a contradiction?

Aristotle’s law of non-contradiction (LNC) states that for any A it is impossible for both A and ~A to be true. That is to say, if the assertion ‘x is square’ is true, then the assertion ‘x is-not square’ cannot also be true. The law of the excluded middle (LEM) states that for any A it is necessary for one of A and ~A to be true. Either x is square or it is not and there is no third alternative. Where there is a third alternative then what we are calling A and ~A are not legitimate dialectical propositions. Given these rules, should we agree with the professors of Unreason that this statement of Heraclitus is an example of ‘illogic’? Must we reject it for embodying a contradiction and breaking Aristotle’s rules?

The second statement is Lao Tsu’s famous aphorism, "True words seem paradoxical." Is this statement true? If so, it should seem paradoxical. Nagarjuna proves that it is true. The whole of ‘nondualism,’ ‘Mysticism’ or the ‘Perennial’ philosophy proposes that it is true. This is the explanation for the use of a language of seeming paradox and contradiction in the Perennial philosophy. This language is required precisely in order to avoid the paradoxes and contradictions that we are led into by our everyday language and that may become conceptual errors where we allow ordinary language to restrict our reason, the very problem identified by the professors of Unreason.

The idea that the view of Heraclitus, Lao Tsu and Nagarjuna requires that we abandon or modify the LNC or LEM depends on one crucial assumption, which is that for complementary and contradictory pairs of extreme metaphysical positions one member is true and the other false.

Would either of these statements imply a rejection of Aristotle’s LNC or LEM? Despite appearances they would not. Lao Tsu tells us that true words seem paradoxical not that they actually are, and Aristotle was a rigorous thinker who would not have written a set of rules for rational thinking that did not cover all situations, even that described by Heraclitus and Lao Tsu.

The idea that the view of Heraclitus, Lao Tsu and Nagarjuna requires that we abandon or modify the LNC or LEM depends on one crucial assumption, which is that for complementary and contradictory pairs of extreme metaphysical positions one member is true and the other false. How many of us do not make this assumption? We ask ‘Does the world begin with Something or Nothing?’ or ‘Do we have Freewill?’ and expect a straight answer, and when we do not get one the same assumption prevents us from understanding why not. When we make this assumption we must insist that Heraclitus make up his mind for now he cannot endorse compatibilism without appearing to break the rules. He must say either we exist or we do not. But Heraclitus knows that such words would not be true. By his juxtaposition of opposites he tells us that for his view it would not be metaphysically rigorous to state either that we exist or we do not. When we use language we are forced into stating two half-truths just as Nagarjuna proves and explains with his ‘Doctrine of Two Truths,’ and this would be why a statement that is rigorously (thus metaphysically) true must be complex and is bound to seem paradoxical.

The reason why such statements are not actually paradoxical would be that Aristotle carefully defines what he means by a contradiction. He saw that it was vital to closely define the pair of opposites ‘A/not-A’ in order that his rules for the dialectic would not be misapplied and produce incorrect results. For any system of computation the rule is ‘garbage in, garbage out.’ His Rule of Contradictory Pairs (RCP) is clear and simple:

Of every contradictory pair, one member is true and the other false.

Aristotle’s system is tautological in the sense that the LNC and the LEM would apply to pairs of statements only where we already know that they apply. If we do not know that they apply then we may be making a mistake by applying them and our reasoning will be unsafe. Members of a true dichotomy are jointly exhaustive and mutually exclusive, but not all seemingly contradictory pairs will meet this criterion. If we know that a switch has only two positions and that no other position is possible then the statements ‘the switch is on’ and ‘the switch is off’ would form a contradictory pair such that one is true and other false. We can then use the dialectic method to decide which position it is most likely to be in given what else we know about it. For instance, if the room is dark we might use this fact to reduce to absurdity the idea that the switch is on. However, if we are not certain that no other position is possible then the LNC and LEM cannot decide this for us. We would have to go and look. Aristotle ensured that there was no possibility of the world breaking his laws by formulating them so that wherever they might be broken they would not apply. His definition for contradictory pairs protects his system from any tricks that Reality might pull on him. Perhaps more importantly, it requires us to closely examine our assumptions before building them into our questions and our reasoning and by so doing rendering both more a hindrance than a help. The system is sophisticated and reliable but only when used with rigour. This would be the danger of category-errors in philosophy, where they can run so deep that even one can undermine the integrity of the entire system.

Heraclitus ... was not suggesting that the atomic statements ‘We exist’ and ‘We exist-not’ form a contradictory pair but precisely the opposite, that they would not form a contradictory pair for there is another alternative. ... Heraclitus and Nagarjuna tell us, Existence and non-Existence are seen not to form a contradiction but two ways of describing a situation that defies description in language because of the very nature of language.

In the literature of the Perennial philosophy, which would include Nagarjuna’s writings, it is very difficult to find pairs of statements that would meet Aristotle’s definition. This would be the reason why its language seems paradoxical, for it is difficult to avoid such statements. There would be no true contradictions and this requires that we deny them in our statements about the world. Heraclitus shows us how to do it. He was not suggesting that the atomic statements ‘We exist’ and ‘We exist-not’ form a contradictory pair but precisely the opposite, that they would not form a contradictory pair for there is another alternative. If his statement seems formally contradictory to us then this must be because we are assuming it would be true to say either ‘we exist’ or ‘we do not exist.’ Lao Tsu tells us that this language is nonsense. It embodies assumptions that have nothing to do with logic but depend on a misunderstanding of Existence and Personhood. The professors of Unreason would mark us down for allowing language to limit what our reason will allow. Once comprehended, Heraclitus and Nagarjuna tell us, Existence and non-Existence are seen not to form a contradiction but two ways of describing a situation that defies description in language because of the very nature of language. It would not be that there is no truth of the matter, as if Buddhist philosophy is not informed by truth or grounded in it. Heraclitus’ statement could hardly be more simple and clear or more packed with meaning, while on metaphysics Nagarjuna says all that he needs to say. From a logical perspective the latter’s famous proof states no more than that all positive or extreme metaphysical positions are logically absurd, an analytical result that it is difficult not to reach upon which even the professors of Unreason agree. We need not study Nagarjuna’s proof to verify that this is a perennial result of metaphysical analysis. The problem is only understanding his explanation of this result.

It is well-known that Heraclitus, Nagarjuna, Lao Tsu and the Buddha never endorse a metaphysical view that would qualify as a member of a contradictory-pair. Nagarjuna is famous for his argument that we should never do this.  How can contradictions arise? Heraclitus implies by his juxtaposition of extreme views that on their own each half of his complex statement would be unrigorous, inadequate, more false than true, and a contradiction cannot arise for two falsities. His statement is certainly not easy to understand but on what grounds can we argue that it breaks the laws of logic? If there is a third alternative then there is no contradiction. The contradiction would be in the eye of the beholder for such words only seem paradoxical.

By calling the mean ‘illogical’ the professors of Unreason fail to take into account Aristotle’s simple definition for contradictory pairs. The mean is not ‘illogical’ or even unreasonable when it is the only alternative to the absurdity of the extremes. It is only when we misapply Aristotle’s rules that the mean need seem paradoxical. Buddhism is the claim that there is no such thing as a true contradiction. The Universe would be a Unity such that all contradictions would be illusory conceptual things. Aristotle gave us a well-designed precision instrument and if we follow his instructions for using it we will find it difficult to discover violations of his LNC or LEM in Buddhism’s Middle Way philosophy.

Buddhist philosophy uses Aristotle’s rules correctly, as Nagarjuna demonstrates by using it to refute all false views. By contrast, professors generally ignore Aristotle’s definition for contradictory pairs. Metaphysics then becomes an inconclusive muddle of flawed thinking. The only known solution for metaphysics will have been ruled out for being logically incoherent. If we are serious about the LNC then when our reason concludes that Something and Nothing, Mind and Matter, Freewill and Determinism or some other pair of extreme views are absurd then we have no option but to seek a resolution in some sort of compatabilism. Logic forces us all to follow Nagarjuna and Aristotle puts up no objection. This approach disposes of all metaphysical dilemmas and antinomies. However, if we believe that this approach would break the laws of ordinary logic then we will believe that Buddhist doctrine is ‘illogical,’ unreasonable or at best incomprehensible and may reject it. Even if we withhold judgement on its truth we are likely to believe that we would be incapable of understanding it. Thus the view that Aristotle and Nagarjuna are at odds may be profoundly damaging to Buddhism and something of a PR disaster. It seems disrespectful to both and history shows that it renders metaphysics intractable.

At this time the professors of the Colleges of Unreason are in full agreement with those in our universities. The mean is illogical and Buddhism must be considered logically tortuous and perhaps even incomprehensible. This is not a charitable interpretation of Nagarjuna and even if it were it would not be plausible. It makes his doctrine seem logically devious, as if he pulled some sort of trick on us by exploiting a loophole in the rules. In fact his entire logical argument depends on the Aristotelian idea that logical contradictions are a proof of falsity. Where a theory gives rise to contradictions he assumes we will all agree that it should be considered false and will reject it accordingly. If we do not then his proof of Buddhism is rendered useless.

When we are asked whether two plus two equals three or five we do not consider this to be a case of A/not-A because we know that there is an alternative. If we do the same for metaphysical antinomies then no logical problems arise and for exactly the same reason.

The Middle Way doctrine appears to be paradoxical only when we assume that the ‘mean’ represents a violation of reason and dialectical logic, an assumption that is not supported by Aristotle. There is a conceptual challenge here but no logical problem. Whether there is a third alternative for a pair of statements may sometimes be a matter of logic or definition, but where they are statements about the world it would be an empirical matter. Only where we know there is no third alternative would the LNC and LEM apply. If we ignore this proviso and use the system without rigour then Buddhist philosophy will seem to be full of contradictions and the whole of the Perennial philosophy along with it, while metaphysics will become incomprehensible.

When we are asked whether two plus two equals three or five we do not consider this to be a case of A/not-A because we know that there is an alternative. If we do the same for metaphysical antinomies then no logical problems arise and for exactly the same reason.  This creates difficulties for our intellect but not for logic. We cannot assume two statements meet Aristotle’s definition for a contradictory pairs but must know that they do, otherwise in our reasoning we will ask improper questions and reach unreliable results. Nagarjuna’s logical demolition of all metaphysical positions except his own proves that there is a third alternative for all metaphysical extremes and it would follow that no modification of Aristotle’s rules would be required for his view. As Kant notes, and as we all discover, selective conclusions about the world as a whole are undecidable. Both extremes are absurd. The reason would be, as Nagarjuna proves, that there are no true contradictions. The extremes would be conceptual mistakes. Metaphysical dilemmas would be misunderstandings.

In his Metaphysics the ninth-century Persian thinker Avicenna writes, “Anyone who denies the law of non-contradiction 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.”

Buddhist philosophy would not disagree on the importance of the LNC. Nagarjuna and Lao Tsu claim that the metaphysical truth is not this or that in any case. If we assume this and that are the only available options then their claim will seem to break the laws of ordinary reason and logic. Should they be burned? Clearly not, for they argue that in metaphysics there is no case for which this and that exhaust the possibilities. Many philosophers and theologians endorse Compatibilism in respect of the Freewill-Determinism dualism for they see the possibility that this contradictory and complementary pair might be transcended for a reconciliation. Are they being unreasonable? Aristotle would say not. Compatibilism endorses neither extreme view and denies that they form a contradictory pair for the dialectic.

This statement on the LNC would seem muddled to Heraclitus because Avicenna forgets that it is not just the burning that matters but the identity of the victim. If ‘we are and are-not’ then it would never be rigorously true to say that we are being burned or not being burned. This is the subtlety of the Buddha’s teachings on suffering, that for an ultimate analysis there would be no such thing. Nagarjuna explains this. He shows that Avicenna is right to value the law of non-contradiction highly and he uses it to eliminate all extreme metaphysical positions. He denies the truth of either/or and both/neither for every pair of metaphysical opposites, showing that in no case and on neither axis would they meet Aristotle’s definition for a contradictory pair. The idea that he asks us to abandon the LNC or LEM is incredible. He asks us to enforce the rules with complete rigour and to make no exceptions. For metaphysical antinomies such as Mind-Matter or Something-Nothing there would be a third option and it would be that the words and concepts we are using inevitably misrepresent the true situation in just the way the professors of Unreason fear. If we hang on to these linguistic and conceptual distinctions then metaphysics cannot be solved. No fundamental theory would be possible. As Kant concludes, all concepts would have to be reduced for a complete theory. Both Matter and Mind must be reduced.

There are too many issues here to summarise. Although the discussion is an attempt to simplify it may yet give the impression that Buddhist philosophy is hopelessly complicated.  Yet the logical issue we are discussing is basic, a high-school level philosophical issue. For a contradictory pair of statements one of them must be true and the other false. If this holds for a pair of statements then we can use the dialectic method of refutation to decide which is true and which false. Where it does not hold then the dialectic is an inappropriate method for deciding and it will lead us to unreliable conclusions.

The difficulty of understanding Buddhist philosophy and the world it describes is intense precisely because there would be no true contradictions. This idea challenges our intellect, which depends on contradictions for its functioning. What Nagarjuna proves and Kant later concludes is that the only reasonable world-theory would be one for which our conceptual world-of-opposites is reduced to Unity, a phenomenon Nicolas de Cusa famously places "beyond the coincidence of contradictories." In this case it is not plausible that there are contradictions in Buddhist philosophy. If they seem to be all over the place it would be because true words seem paradoxical. They may seem less so if we take note of Aristotle’s rule for contradictory pairs and allow ourselves to abandon the absurd extremes for an exploration of the mean.  

(This discussion is heavily reliant on two texts and they are recommended to anyone wishing to pursue these matters: Whitaker C. W. A., Aristotle’s De Interpretatione: Contradiction and Dialectic, Oxford, 1996; and Gyamtso, Khenpo Tsütrim, The Sun of Wisdom: Teachings on the Noble Nagarjuna’s Fundamental Wisdom of the Middle Way, Shambala, 2003.)

Copyright © 2017 by Peter G. Jones. Published with permission.


  1. Your essay is very well argued, Peter. Your point that "our intellect depends on contradictions for its functioning" and "true words are paradoxical" is profound.

    It is interesting though, that it is words themselves (the words of Aristotle and Nagarguna, for instance) that have convinced you of the truth of nonduality. So it seems that sometimes, words can be enough. Oh dear, I hope I haven't created a metaphysical dilemma!

    1. Thanks Ben. I wouldn't say words convinced me, but logic did. My thesis is that if we follow the logic we arrive at the truth.


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