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In this article http://aeon.co/magazine/world-views/logic-of-buddhist-philosophy/

Philosopher/Logician Graham Priest talks about some of the differences that Western logic has with Buddhist logic.

Quickly said: Western/Aristotelian logic doesn't tolerate contradictions (principle of non-contradiction) and everything has to be either true or false (principle of the excluded middle), but Buddhist logic follows a system called the catuskoti which implies that statements can be true, false, true and false, or neither true nor false. Tibetan philosopher Gorampa even included the 'ineffable'.

My question is this: In buddhist logic, where does "hey man, that's illogical!" fit in? I mean, it pretty much seems everything can be valid in Buddhist logic, and there's just no place for the illogical, which pretty much points to the inefficacy of that system.

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    I'm not sure I understand what exactly you are asking. Are you asking how Buddhism looks at contradictions? You say there is no place for the illogical in Buddhist logic, but to me it looks like it is the other way around. There is no place for the illogical in Western/Greek classical logic since they reject the idea that something can be true and not true at the same time. – THelper Jul 23 '14 at 8:16
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    To me the question seems: In western logic there is a clear line between logical and Illogical statements and clear rules how a logical argument should be formulated. Is there the same in Buddhist logic? Can statements be bad or illogicaly fomulated? – DirkM Jul 23 '14 at 11:47
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    "Western" philosopher, Ludwig Wittgenstein, also included the ineffable. – tkp Jul 23 '14 at 13:47
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    BUDDHIST ILLOGIC: A Critical Analysis of Nagarjuna’s Arguments by Avi Sion, Ph.D. thelogician.net/3b_buddhist_illogic/3b_bl_frame.htm – catpnosis Jul 26 '14 at 11:56
  • I never understood the use of the phrase "Buddhist Logic". Isn't the point of logic to give us a system wherein we can derive new information from previous data? No such thing is possible with "Buddhist Logic" because it negates all. This rejection could be valuable from the standpoint of practicing, but calling it any kind of logic (given accepted connotations of logic) is going too far, and it seems like an attempt to turn Buddhism into something like Western philosophy. – R. Barzell Sep 17 '15 at 17:42
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Originally the Catuṣkoṭi or Tetralemma was just an indication of all possible combinations of two predicates, and obviously, if these two predicates don't contradict, there is no problem.

Now, the Buddha himself does make seemingly contradictory statements, like when he refuses to answer the questions of Vacchagotta in SN 44.10, who asks first whether there is a self, then whether there is no self. Questioned by Ananda as to why he did not answer, the Buddha effectively claims, that both answers would have been wrong.

In this case, since there is only one predicate (and its contradiction), there do arise logical problems. The only attempt, to solve these kinds of problems I am aware of is in the article

Klaus Butzenberger: Einige Aspekte zur catuskoti unter besonderer Berücksichtigung Nagarjunas, in: Synthesis Philosophica 1990, 567–580.

If you know German, then go read it. If not, let me summarize that it attempts to solve these problems in three ways: by classical logic, non-classical logic and thirdly by admitting its insolubility, but Butzenberger admits, that each of these attempts at solution does remain unconvincing to fruitless.

This might - now here comes my 50 cents - be due to the case, that the Tetralemma is used by a great number of authors in Indian logic and they do not handle it the same way. In the case of the Buddha's refusal to answer, it might be conjectured, that the Buddha is talking in two different levels of truth: a conventional truth and an absolute truth. So in order to remain truthful on the absolute level, we may have to accept contradictions on the conventional level, if - what the Buddha sometimes blames questioners for - the question is posed in a wrong way.

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    Good answer. I'll just add that even in "western" logic, we have to deal with the problem of incompleteness of some formal systems. Specifically, tracing a line from Hilbert through Frege, and Russell, we end up at Goedel who showed that contradiction was inherent in certain situations. However, Goedel's proofs didn't mean there was no longer a place for "hey man, that's illogical!". They just meant you have to broaden your scope of view. In the western logic case, that sometimes involves adding axioms; in the Buddhist case it sometimes involves refusing to answer the question :-) – tkp Jul 23 '14 at 13:42
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    Goedel wanted to solve one of hilbert's problems which was that of the completeness of arithmetic. He showed that you can't have completeness and consistency at the same time. Now, in mathematics we sacrifice completeness in order to keep consitency because if there's a contradiction in a formal system anything can be proven and that renders the system as a failure. This principle is called the principle of explosion or "ex falso quodlibet". – DLV Jul 23 '14 at 20:29
  • This seems to be analogous to "The present King of France is bald" problem. See en.wikipedia.org/wiki/Definite_description – Thiago Dec 16 '14 at 20:29
  • For a current discussion in a philosophy newsgroup I'd like to read that Butzenberger-article; unfortunately the "Synthesis Philosophica"-website has archives only back to some 2005... Is there any way to get access to that article? – Gottfried Helms Nov 24 '16 at 12:50
  • Try any university library where the university has a department of indology. – zwiebel Jan 31 '17 at 18:31
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I would like to comment on a few points:

There are hundres of places in the suttas where the Buddha said that something was wrong or didn't make any sense, it is not that "anything goes", not at all, sometimes he did that using examples, a nice one was when the Buddha came across a trible, in this trible when someone dies, they used to turn the person facing the skies and call his name, screaming, they believed this way the person would see Heaven and go up there, the Buddha said: "Suppose I throw a stone in a river and scream "come to the surface!" will it come? In the same way the person you go up and down according to kamma, not because someone is calling him"

Buddhism may not be so imperative or black and white as other religions, take the precepts for example, Buddha said we should refrain from doing A, because the consequence B will lead you to suffering, in other religions you will probably read: you shall not do that, end of story. I'm noy saying buddhism is better or worse, just different.

Finally, Nagarjuna was a great buddhist, but his texts have different weight in different traditions, meaning we all deeply respect him and Milarepa for example, but the level of devotion changes.

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    We have to bear in mind that "Buddhist logic" is rather a branch of "Indian logic" than of "Buddhism", which is in the nature of the subject-matter of it. Logic is a rather universal phenomenon. – zwiebel Jul 23 '14 at 16:37
  • Buddhist logic is Aristotle's logic, as Nagarjuna shows. It is just a particularly thorough application of it. Nagarjuna's logical argument should have the same weight in any tradition or even on another planet. .It is either valid or not, and where it is valid and sound we cannot ignore it without abandoning our reason. . – PeterJ Mar 31 at 10:53
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Graham Priest promotes a wildly incorrect view of Buddhist logic and teachings. He believes that Buddhist doctrine contains contradictions, which is utter nonsense. His problem is that he does not properly understand Aristotle's logic so cannot understand Nagarjuna. Not being a Buddhist, Priest has no grasp of the Two Truths doctrine and seems to believe it leads to contradictions, which is such a complete misunderstanding it seems almost wilful.

Let's examine the question here.

..."Western/Aristotelian logic doesn't tolerate contradictions (principle of non-contradiction)..."

True.

..."and everything has to be either true or false (principle of the excluded middle),

This is wrong. The principle of bivalence is what you're thinking of and this is not necessary for dialectical logic. This logic works with statements that are true or false (in the form A/not-A) but it does not say that all statements must be true or false. The LEM is applicable where a pair of statements meet Aristotle's specification, (which is that one is true and one false), but statements do not have meet this specification. Where they do not the law does not apply. This is the point that Priest misunderstands, and it is why Buddhist doctrine contains no contradictions.

..." but Buddhist logic follows a system called the catuskoti which implies that statements can be true, false, true and false, or neither true nor false."

This is an utterly ridiculous idea. I can't imagine how anyone could arrive at it. Buddhist logic is no different from Aristotle's, it's just that it is applied to pairs of statements on two axes (this or that, neither or both). Priest muddles the issues and creates complications where none are necessary. He does Buddhism a massive disservice, as is shown by the low view you have formed of Buddhist logic after reading him. He seems to believe that Buddhists are idiots.

I would suggest that Priest is ignored. Nagarjuna offers us a rigorous application of Aristotelian logic and if it were not rigorous the whole argument in Fundamental Wisdom would fall apart.

For a longer response I have an essay on Bernardo Kastrup's blog entitled, 'Aristotle, Nagarjuna and the Law of Non-Contradiction in Buddhist Philosophy'. https://www.bernardokastrup.com/2017/05/aristotle-nagarjuna-and-law-of-non.html

This puts paid to Priest's anti-Buddhist ideas. He should take the trouble to study Buddhism.

There are NO dialectical or 'true' contradictions in Buddhist doctrine and this is exactly what Nagarjuna proves.

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