Fuzzy Logic (Was Tarsky)

Christian Whitaker (christcream@hotmail.com)
Sun, 24 May 1998 14:38:05 PDT

>> I admire faith, and thus I choose not to argue against it. As
>> truth is the foundation of an information system, it cannot be
>> using the precepts of that system, any more than you can say that the
>> Pope is infallible because the infallible Pope said so. A foundation
>> cannot have foundations. I chose to allow for fuzzy truth because I
>> find it more relaxing philosophically and allows me to see more
>> possibilities. My support of fuzzy truth does not have any more
>> basis than your support of binary truth.

>Hardly. The truth of certain axioms is unquestionable; A=A leaps to
>You cannot logically support a position under which 0.99A=A, unless A
>0. In other words, if anything exists, then A = A; logic does not
>for contradictions.

I can't support 0.99A=A if I subscribed to bivalent logic and its forms
of expression, but since I don't, there isn't any problem. Fuzzy logic
expressions are less concise than bivalent, because it is more precise.
A=A and .99A=A are expressed in fuzzy logic as follows (although I will
be less than economical by not putting it all in symbolic notation)

1.00A=1.00A to a 1.00 degree
.99A=1.00A to a .99 degree

When expressed in proper notation the supposed contradictions
disappear. The main argument against fuzzy notation is that Aristotle
didn't use it, and therefore anybody who does is a Satanist and going to

>Frankly, I think you have simply misspoken with respect to your point
>about logic; in logic, things ARE either true or false. It's one of
>defining characteristics of logic.

It's one of the defining characteristics of bivalent logic, and it's
philosophical child, logical atomism. I do not believe that historical
precedence is sufficient reason to declare all other systems of logic to
be impossible or immoral. All that is necesary for a system of logic to
be valid is that true conclusions follow from true premises, which fuzzy
logic satisifies.

If you wish to adhere to fuzzy truth,
>then you had best dump all pretenses of logic altogether and claim some
>other higher ground; mysticism seems popular these days. However, one
>thing we logicians have shown, time and time again, is that the mystics
>cannot beat us on our own turf.

You have caught me. I am a mystic. In fact, I am a Jungian

There are three definitions of mysticism in my dictionary <American
Heritage> :
1. Immediate consciousness of the transcendent or ultimate reality or
2. A belief in the existence of essential realities beyond perceptual of
intellectual apprehension that are accessible to subjective experience.
3.Vague, groundless speculation

I suppose that you mean mysticism in the third sense, while I support
the second definition and have occasionally experienced the first. You
are correct that mystical beliefs are spreading quite rapidly in the
Western scientific world. This change in acceptance started with the
quantum physics revolution, but I think the current upswing can be
blamed on the spread of the Penrose/Hameroff quantum brain meme. Many
people still disagree with the theory that the human brain works via
quantum computation, but the point has been reached that most people
will admit that it is possible to both give credence to the idea and be
in one's right mind.
Mysticism becomes sensible under these conditions by replacing 'God
or ultimate reality' in the first definition with 'undifferentiated
quantum field'. Transcendental Consciousness is a state of
consciousness in which there are no qualities (dichotomies) whatsoever,
which is equivalent to the state of a quantum computer before you open
it up and look inside. Such a state cannot be experienced by
intellectual or perceptual faculties (which I think are just different
manifestations of the same thing) because by definition the intellect
(logic) seperates things into parts. This includes fuzzy logic, which
differs from Aristotelian logic only in that it allows for partial
It is worth remembering that the seperation between mysticism and
logic has only been a recent historical phenomenon. All early
scientific systems had decidedly mystical elements; from the Jewish
Kabalists (who invented alchemy which begat chemistry) to the cult of
the Pythagorans, to Plato and his forms. It is not suprising that
mysticism and logic are once again uniting. I think the division only
occured in the first place because the Catholic Church decided the
ambiguity of mysticism to be a threat to its authority and managed to
mostly stamp it out in the Western world. Now that the power of the
church is waning, mysticism is once again flourishing.

-Christian Whitaker

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