The logic of Buddhist philosophy (2014)

Seems to me that the catuskoti was already a concept in western philosophy, only we didn't give the group a name because we prioritised true and false above the other two possibilities: contradiction and indeterminacy.

Also seems to me that ineffability falls under indeterminacy. The author seems to try to distinguish between the two by saying there are things we might be able to know, and things we will never be able to know. Being a layman and not studied in philosophy and logic, it seems to me that indeterminacy is enough to encapsulate ineffability. This is illustrated by the numerous examples the author gives on attempts to explain the ineffable: this immediately makes it indeterminate, going by the author's use of logic. The author then goes on to talk about ordinal numbers, and presents what is purported to be an ineffable phrase:

the least ordinal that cannot be referred to

There are more ordinals than ordinary language can refer to, and one of these must be the least. But, by using that phrase we are referring to it. This is an obvious contradiction, but we know there must be one such ordinal. The author uses this to say that since we cannot talk about it, but it exists, it is ineffable. I say that this is unnecessary, it is enough to say the ordinal is indeterminate precisely because we cannot refer to it (determine it).

That it took us until the 20th century to imagine these ideas in mathematics and logic doesn't speak to any shortcomings of western logic with regards to contradiction and indeterminacy, in my opinion. It merely reflects the priorities of eastern and western thought. This is illustrated by the efforts of Bertrand Russell with his Principia. Through the centuries, western thinkers had made advances by considering what is true and what is false, and taking contradictions as dead ends that do not produce interesting areas of study. Russell tried to take this as far as he could with Principia, and in doing so inadvertently revealed the limitations of how far we can advance, limitations that were detailed by Kurt Godel and his incompleteness theorems. I say that, since we have advanced so far as to know the limits, now we are having more to say about contradiction and indeterminacy, and we are now saying it in a more precise way than Buddhist philosophers imagined in their day.

Explanation from Henk Barendregt (logician and Vipassana teacher) http://www.cs.ru.nl/~henk/BP/bp1.html

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1.7 Explaining apparent contradictions

Now we will explain how contradictions, which happen to occur in some buddhist texts, are possible. Suppose some part of reality U is described using some language L. Some of the regularities observed in L are in fact physical laws, but may be confused with logical laws. If we extend the reality U to U+, but keep as the describing language L, then statements may result that contradict statements made about U. Although the contradictions are only apparent, because the statements are about different `worlds', it may seem that logical laws are violated.

An example will be helpful. Consider a tribe living on an isolated island. Vision of the tribesman is such that they can only see the colors black and white. In their description of the world they say: ``Something is either black or white." Although we know that this is for them in fact an empirical law, the people of the island are tempted to consider this as a logical law. Sometimes they use the words `white' and `non-black' interchangeably. On some day someone has a mystical experience. In our language we can say that that person has seen the color green. In the language of the tribe she says: ``I have seen something very impressive. It was neither black nor white." For most of the people of her tribe she was saying: ``It was neither black, nor non-black." Therefore on the island one may think she is speaking nonsense. However, we know that she is not.

There are, however, stronger contradictions. In his book Exploring Mysticism already mentioned, F. Staal discusses the following so called `tetra lemma' occurring in buddhist texts.

  	It is not A;
  	it is not non-A;
  	it is both A and non-A;
  	and it is neither A nor non-A.

Even this contradiction may be explained. Simply consider again the tribe seeing only black and white. But now our mystic sees the color gray. Indeed gray is not white, not black. And it can be said that gray is both white and black. But also that it is neither white nor black.

I hope that the examples show that contradictions occurring in texts of mystics are not a sign that something essential is wrong. Nevertheless it is preferable that descriptions of altered states of consciousness are free from contradictions in the sense of logic. I will try to fulfill this requirement in sections 2 and 3.

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Personal note: this "Buddhist logic" is useful in the context of phenomenology and how to communicate certain fundamental changes in viewpoint that come from meditation. It's not new better way to think.