On Saturday, August 17, 2002, at 08:06 PM, George Levy wrote: > The arbitrariness of "my," "your" or anybody's own mind point to the > need for the relativistic approach which I have been advocating. The > frame of reference here is the logical system residing in the > observer's mind. It may not be the type of formal system which has > been discussed in the list. There may be a need to develop some kind of > "fuzzy" logical system for human mental processes corresponding to the > formal systems already in existence. As far as I know Fuzzy Logic has > not been developped to the same extent as the branches of logic that > have been discussed in the list.

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Well, count me as skeptical that the hype about "fuzzy set theory" and "fuzzy logic" has ever, or will ever, live up to some of the claims made by Bart Kosko, Lofti Zadeh, and others. Most of what passes for fuzzy logic just looks like ordinary Bayesian probability. Here's a comment from Saunders Mac Lane in his book "Mathematics: Form and Function," 1986: "Not all outside influences are really fruitful. For example, one engineer came up with the notion of a _fuzzy_ set--a set X where a statement x elementof X of membership may be neither true nor false but lies somewhere in between, say between 0 and 1. It was hoped that this ingenious notion would lead to all sorts of fruitful applications, to fuzzy automata, fuzzy decision theory and elsewhere. However, as yet most of the intended applications turn out to be just extensive exercises, not actually applicable; there has been a spate of such exercises." (. pp 439-40). While maybe Mac Lane is a little too snippily dismissive, here we are more than 15 years later and what do we have? Fuzzy rice cookers which look like nothing more than rice cookers with various algorithms Newton could have calculated, fuzzy-logic elevators which are simply implementing similar acceleration algorithms, and not much else. Certainly fuzzy logic has not been significantly in the foundations of mathematics. Logicians have not been using fuzzy sets and fuzzy logic in any significant way, judging by the books and articles I've seen. I agree that formal logic is not easily applied to minds. Logicians would agree. A mind is weighing large numbers of inputs, far beyond what would normally fill an entire page of First Order Logic equations....survival has made the ability to reason with uncertainty (a better core concept that calling it "fuzzy logic," in my opinion) a survival trait. Those minds which can find solutions in the midst of noise and uncertainty tend to reproduce more than those minds which are paralyzed or too slow in reaching survival-enhancing conclusions. What we have talked about here in this sub-thread on _modal logic and possible worlds_ is an idealization of logic, just a snapshot or facet of things, in much the same way a "line" or a "plane" is a facet of the world around us (and understandable at some level by birds and reptiles even). --Tim May (.sig for Everything list background) Corralitos, CA. Born in 1951. Retired from Intel in 1986. Current main interest: category and topos theory, math, quantum reality, cosmology. Background: physics, Intel, crypto, Cypherpunks