Sunday, September 30, 2012

The Eternal Problem of the Relationship between Logic and Convention

One of the great benefits of the blog is said to be that it allows and encourages scholars and theorists to speculate in "sophomoric" ways that would never be tolerated in a "serious" scholarly journal. I am going to test this proposition. I want to make some broad and sophomoric remarks and conjectures about the relationship between logic and convention. In the course of doing that, I will brazenly ignore numerous subtleties and refinements.

This is what I have to say: 

Ludwig Wittgenstein was initially preoccupied with (deductive) formal logic. He eventually came to think that such logic (by itself) could say nothing -- that such logic was necessarily caught in vacuous tautology. Wittgenstein then made his linguistic turn; he decided (roughly) that what really counts is how language is used. Many of us were captivated by this linguistic turn. But eventually some or many of us came to be uncomfortable with it -- because some of us we were uncomfortable with its seemingly relativistic implications. But then fuzzy logic and fuzzy set theory made their appearance. In recent years this theoretical direction, which perhaps emphasizes the centrality of conventional language and folk concepts, has also fallen into disfavor. (In the eyes of some theorists -- e.g., those strongly enamored of the standard probability calculus -- fuzzy logic never became even temporarily reputable.)

I wonder whether it is time to stop oscillating between extremes -- whether it is long past time to stop thinking that common language and concepts tell us nothing or that common language and concepts tell us everything. Is it perhaps the case that much of our knowledge of the world is encapsulated and embedded in (some of) the common language and concepts we inherit from (some of) our fellow human beings -- and that this is true even if such "folk language" and "folk concepts" will not (by themselves) unravel mysteries such as the Higgs Boson, the workings of AIDs, string theory, and other such matters? Is it not the case -- is it the case? -- that much of the knowledge that we use in our daily lives is "superficial" -- not based on our individual understanding of the causes of things or on our individual understanding of the underlying nature or structure of events -- but on words and concepts that we accept and use and believe (for the most part) somehow express or describe how the world works? If that is the case, is it possible to construct a formal language that describes the workings of ordinary (facial, "superficial") knowledge and concepts, a language that, despite its "superficiality," manages to capture the genuine knowledge that may, almost willy-nilly, be embedded in our conventional language and concepts?

I do not know if it is possible to do this. But I think the undeniable successes of fuzzy logic and fuzzy set theory (think: Japanese train schedules, automatically focusing Japanese cameras, the famous Dutch kiln, Google's search engine, etc., etc.) suggest that we need to investigate the power of ordinary language and thought and the sources of that power.
  • Without a theory such as fuzzy and rough logic and set theory it may not be possible -- I suspect it may be impossible in principle -- to explain how human beings manage to classify many matters and events in a useful and productive way, in a way that does not always end in disaster or catastrophe.
I am quite sure that I am not qualified to unravel this great riddle. But I very much hope that more serious thinkers in the West will occupy themselves more seriously (or more transparently) with the question the question of the relationship between logic (formal argument) and conventional language, concepts, and thinking.

It seems that many of us in the West are largely ignorant of the intense and broad interest in fuzzy logic in the "far East," in countries such as India, China, and Japan. I have the sense that a transformation in the understanding of logic and human thought is gradually taking place but that we in the West are largely (but not entirely) oblivious to this transformation, or theoretical revolution.
  • If fuzzy logic is an "error," I suspect it is an "error" of enormous theoretical importance. I suspect most of us do not yet understand fuzzy logic well enough to even begin to explain how and why current formulations and interpretations of fuzzy logic "go wrong." If fuzzy logic does go wrong, it may go wrong roughly in the way that classical Newtonian mechanics goes wrong in comparison with relativistic mechanics.

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