Wednesday, September 13, 2006

True Contradictions

The philosopher Graham Priest has written a book called Beyond the Limits of Thought. He argues that all large-scale philosophical systems will have contradictions at their limits and these should not be regarded, as philosophers do, as the problems we have to solve but as truths about what happens to reason when it pushes the bounds of thinking. These contradictions as true contradictions. All our world views will have them. Priest also says that the central “law” of philosophy, The Law of Non-Contradiction, has never been proved and the arguments for it are quite weak. He and others have developed “paraconsistent” logics, meaning logics that leave room for some inconsistency. He gives the example of certain Eastern logics which provide of contradiction. The online Stanford Encyclopedia of Philosophy has an article by him on "Dialetheism", which is the view that there are true contradictions.

I found his work quite liberating because I always viewed contradiction as the enemy. In contrast with this, and, in another way, in keeping with it, I always loved the Tao te Ching which has many contradictory passages which convey great insight and wisdom.


John said...

Kurt Godel has proven that contradictions are necessary in mathematical theories, or at least in number theory. The book "Godel, Escher, Bach" by Hofstadter discusses this idea.

John said...

Contra.diction: words (diction) that are opposed (contra). Why worry that some words cannot get along with each other? Does that mean that we have to choose sides? They are just words, not reality. Is reality consistent? Not in general. This is the beauty of science: to reveal the hidden consistencies in nature.

Jeff Meyerhoff said...

Yes, Godel's a good example. There's also a mathematician named Gregory Chaitin who's done something similar.

Your second post is more problematic. It's not just words that can't get along. Words are the carriers of our beliefs, morals, principles, sense of reality and if they conflict it is disturbing.

Although the non-linguistic experiencing of reality in some Eastern mystical practices leads to an ineffable experience in which emptiness is form, form is emptiness or nirvana is samsara, i.e. the unconditioned world is the conditioned world. People have profound experiences of these contradictions being true.

In pure intellectual reflection an ideal is to not choose sides but examine neutrally, but, I don't know that we ever attain that. Maybe we can be more or less neutral in inherently non-neutral contexts.

Words are reality too. What is the wordless reality you speak of? The physical world? Priest deals with this in a book called "Doubt Truth to Be a Liar". I'm forgetting the examples of contradictory reality though. Oh, here it is. He describes some perceptual contradictions like in Escher's drawings, but seems to believe that the perceptual world is consistent.

You say reality is not consistent in general, but then say that science reveals hidden realities. What are you thinking of?

John said...

Reality is not consistent, in general. I'm thinging that scientific laws are rare and not common. The consistencies they reveal are the exception, not the rule. Most hypothesis that are proposed are contradicted sooner or later. Such proposals fail the criterion for a general scientific theory that holds true in all cases and places.

Just to clarify, I would say that science, at best reveals hidden consistencies in reality, not hidden realities.

Further, I think that the reason mathematics is so prevalent as the language of science is due to the limitations of other languages with respect to describing consistencies found in nature.

John said...

Please pardon my spelling errors above. I meant to say "thinking" not "thinging" and "hypotheses", not "hypothesis." I'm hoping at least that the content is more defensible than the diction.

Jeff Meyerhoff said...

We might be discussing different things. Priest was referring to perceptual inconsistencies. Like if we routinely saw and didn't see, at the same time, a tree or if things fell up and down at the same time.

You're describing lawful physical patterns and the consistency between our attempts to describe the world and what we find in the world. I'm not sure I'd say that world is contradictory just because our hypotheses so often result in anomalies.

So I'd say that science can reveal hidden lawlike patterns. And mathematics certainly is good at describing regularities and so allowing prediction.