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Buddhist logic and Nagarjuna

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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.

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.

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?

"Western" philosopher, Ludwig Wittgenstein, also included the ineffable. –

BUDDHIST ILLOGIC: A Critical Analysis of Nagarjuna’s Arguments by Avi Sion, Ph.D.

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.

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 :-)

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".

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.

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