FTA: Buddhist thought, and Asian thought in general, has often been written off by Western philosophers. How can contradictions be true? What’s all this talk of ineffability? This is all nonsense. The constructions I have described show how to make precise mathematical sense of the Buddhist views. This does not, of course, show that they are true. That’s a different matter. But it does show that these ideas can be made as logically rigorous and coherent as ideas can be. As the Buddha may or may not have said (or both, or neither): ‘There are only two mistakes one can make along the road to truth: not going all the way, and not starting.’
Calling the Mulamadhyamakakarika cryptic is an understatement, IMO, but I don't agree with the author's interpretation of the verse cited at the beginning of the article:
"The nature of things is to have no nature; it is their non-nature that is their nature. For they have only one nature: no-nature."
The author interprets this in the context of formal logic and the law of the excluded middle, but I think it's clear enough from Nagarjuna's argument that this isn't his subject. In fact he relies on more or less standard modes of logical argumentation in the text, even if it's obscured by technical language and the poetic form.
I don't think Nagarjuna is concerned with logic or epistemology as much as he is concerned with ontology. The first part of the text is all about the "essence" of things (or their nature, as rendered above: you can relate this to Greek concepts of ousia, to some extent). The point is not to challenge the law of non-contradiction, but to challenge the idea that "things" have some essential nature, that there is something like an "essence" of tree-ness that lies within all trees, and so on. The lack of essence is the foundation of the doctrine of Sunyata, and it gives rise to his later work on interdependent origination (pratityasamutpada).
In Garfield's translation and commentary ([amazon.com], he puts it like this:
"For Nagarjuna and his followers this point is connected deeply and directly with the emptiness of phenomena. That is, for instance, when a Madhyamika philosopher says of a table that it is empty, that assertion by itself is incomplete. It invites the question, Empty of what? And the answer is, Empty of inherent existence, or self-nature, or in more Western terms, essence (svabhava). To say that it lacks essence, the Madhyamika philosopher will explain, is to say, as the Tibetans put it, that it does not exist "from its own side" -- that its existence as the object that it is -- as a table -- depends not on it, nor on any purely nonrelational characteristics, but depends on us as well." (p. 89, cf. the discussion of svabhava here: [plato.stanford.edu]
So, calling the nature of a thing "non-nature" is -- despite the poetic language -- not intended to suggest both a state of truth and falsehood of a proposition at the same time, it's just a rejection of essentialistic ontology.
Actually ineffability is also a Christian thing (see early mystics and monastics). It's called apophatic theology, and it holds that God has no attributes, no features, and cannot be known by the mind. It is similar to the idea of Brahman in the Hinduism that influenced Buddha. Paradoxes in Eastern though refer to a nonlinear way of knowing, one that is achieved through meditation and right action. It doesn't have to be "math" to be valuable. That desire for logical coherence is a Western disease (scientism).
As someone who studied logic it is a very interesting read but it didn't really convince me that it makes sense or is useful. The problem I have with it is that it takes natural languages and tries to somehow fit it into a logical structure, which is always possible even with things that make no sense. The way I find more useful is to first look what the language could be used for and then construct it logically - like we did with formal logic and math - and skip the step where we look at natural languages, because paradoxes necessarily follow from them because of the way they are constructed. Do we want to say something about the world? Then we need the principle of the excluded middle (PEM). Do we want to analyze paradoxes? Then we can construct systems which might help us without PEM.
But we always have to keep in mind, when we reason and try to find out if something makes sense at all we presuppose PEM. The author of this article makes sentences that are either true or false. He doesn't describe this "Buddhist logic" with Buddhist logic, but with classical logic in mind. In fact no logical system makes sense without it. So the meta language is always classical. That seals the deal for me.
That is a very interesting essay for me, and I am bookmarking it for future reference. The ideas merit further study.
I had to look up the word “ineffable”, but it is a familiar concept. Many questions or statements are simply meaningless from a higher perspective. Questions about immortality are ineffable because time is an artificial human construct.
“Is there an Ultimate Reality beyond the senses”? The question is grounded in our sensory world and has meaning only from that limited perspective. If I answer “yes”, all I am saying is that I don’t have the whole picture—that my perspective is symbolic only. Ultimate Reality is ineffable and can not be described, but I can make statements about my limited reality, or it seems that way to me. If I have been in a house with no windows all my life, it would seem logical to say, “These walls are the limit to my world. I know nothing of what is beyond, but I know there is a beyond. The beyond I define as that which is not contained by these walls”.
IMO the ego is a put-up job and we actually don’t exist in the way we think. Therefore any statement or question about ourselves has meaning only within our limited, symbolic reality.
Time has flown—gotta go.