Re: modal logic and possible worlds

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
> 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.

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