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From: Tim May <tcmay.domain.name.hidden>

Date: Sat, 17 Aug 2002 20:52:55 -0700

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
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*> 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
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*> "fuzzy" logical system for human mental processes corresponding to the
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*> 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.
*

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

Received on Sat Aug 17 2002 - 21:03:04 PDT

Date: Sat, 17 Aug 2002 20:52:55 -0700

On Saturday, August 17, 2002, at 08:06 PM, George Levy wrote:

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

Received on Sat Aug 17 2002 - 21:03:04 PDT

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