# Re: Fuzzy Logic (Was Tarsky)

Daniel Fabulich (daniel.fabulich@yale.edu)
Sun, 24 May 1998 19:22:48 -0400 (EDT)

On Sun, 24 May 1998, Christian Whitaker wrote:

> 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
> hell.

Er, no. I do not assert that this thinking is flawed because you're going
to hell. That argument itself is inherently problematic. Instead, I want
to fall back on my previous argument (I think this was before you walked
in) that IF an objective reality exists, then acting as if it doesn't or
presuming false things to be true to any degree will ultimately be bad for
us; that is, that adhering to falsehood is directly opposed to our own
self interests.

I don't think I need to provide a lot of examples to demonstrate this; I'm
sure you can come up with a wide variety on your own. Falsehood is
inextricably coupled with human suffering and death in a non-trivial way.

I'm not opposed to fuzzy logic as a tool to help us to better approximate
the truth; ultimately it may be the only tool available to prove certain
facts which escape axiomatic logic. However, I am opposed to assertions
that the truth ITSELF is fuzzy; even in quantum mechanics, arguably the
weirdest branch of physics we've ever discovered, things are weird in a
very specific way. An electron, despite its particulate nature, will
diffract in a VERY specific way described by our equations. The fact that
the cat in the box is, to some extent, dead and not dead simultaneously
does NOT mean that all things are and are not true; the diffraction of
light on a screen is not ambiguous in any way. The behavior of photons
may be weird, and may be truly random, but there are certain behaviors
which you will never see and which quantum mechanics predicts can never
happen.

> 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.

Listen to what you're saying! "True conclusions from true premises..."
Not conclusions which are true to some degree from true premises, but TRUE
conclusions. Again, I'll buy your logic as an approximation of the real
truth, but not your fuzzy truth.

> You have caught me. I am a mystic. In fact, I am a Jungian
> psychologist.;)

Hah! Gotcha. I have a nose for these things. :)

> There are three definitions of mysticism in my dictionary <American
> Heritage> :
> 1. Immediate consciousness of the transcendent or ultimate reality or
> God.
> 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.

Depends on which idea you're referring to. That the brain is a quantum
computer? This is not unbelievable, a priori, but once you get down to
the evidence, we will ultimately find out if the brain is a quantum
computer. Science, even QM, always wants to boil down to truth
or falsehood.

> 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
> dichotomies.

Your physics themselves are a bit fuzzy here. In a quantum computer, not
ALL dichotomies are eliminated, but rather what makes the quantum computer
useful is that all possible conclusions interact with one another in such
a way as to produce the correct solution to the assigned problem, and
never the wrong one. And when I say correct, I mean REALLY correct, TRULY
correct; the equations, again, provide no ambiguity on this point.
Certain principles which we use in modern chemistry are derived from the
fact that quantum mechanics states that some things always (or never)
happen; the Pauli exclusion principle leaps to mind.

So again, even in quantum mechanics, we ultimately find ourselves looking
at certain things which are definitely true and others which are
definitely false. Quantum provides no support for the conclusions which
you have drawn; not that it matters, because truth and falsehood are

> 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.

Yet we find the most adherent followers of objectivism are atheists, not
mysticists, with an eye on the truth, not on the abolition of truth. And
though I doubt such things would interest you, since you reject the axiom
of non-contradiction, those philosophers which you refer to throughout the
ages were mysticists, yes, it's true, but that's about the extent to which
they agreed on anything.