maldv/crabcanon · Datasets at Hugging Face

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All the limitative Theorems of metamathematics and the theory of computation
suggest that once the ability to represent your own structure has reached a certain critical
point, that is the kiss of death: it guarantees that you can never represent yourself totally.
Godel’s Incompleteness Theorem, Church's Undecidability Theorem, Turing's Halting
Theorem, Tarski's Truth Theorem-all have the flavor of some ancient fairy tale which
warns you that "To seek self-knowledge is to embark on a journey which ... will always
be incomplete, cannot be charted on any map, will never halt, cannot be described."

But do the limitative Theorems have any bearing on people? Here is one way of arguing
the case. Either I am consistent or I am inconsistent. (The latter is much more likely, but
for completeness' sake, I consider both possibilities.) If I am consistent, then there are
two cases. (1) The "low-fidelity" case: my self-understanding is below a certain critical
point. In this case, I am incomplete by hypothesis. (2) The "high-fidelity" case: My self¬
understanding has reached the critical point where a metaphorical analogue of the
limitative Theorems does apply, so my self-understanding
undermines itself in a Godelian way, and I am incomplete for that reason. Cases (1) and
(2) are predicated on my being 100 per cent consistent-a very unlikely state of affairs.
More likely is that I am inconsistent-but that's worse, for then inside me there are
contradictions, and how can I ever understand that?

Consistent or inconsistent, no one is exempt from the mystery of the self.
Probably we are all inconsistent. The world is just too complicated for a person to be able
to afford the luxury of reconciling all of his beliefs with each other. Tension and
confusion are important in a world where many decisions must be made quickly, Miguel
de Unamuno once said, "If a person never contradicts himself, it must be that he says
nothing." I would say that we all are in the same boat as the Zen master who, after
contradicting himself several times in a row, said to the confused Doko, "I cannot
understand myself."

Godel’s Theorem and Personal Nonexistence

Perhaps the greatest contradiction in our lives, the hardest to handle, is the knowledge
"There was a time when I was not alive, and there will come a time when I am not alive."
On one level, when you "step out of yourself" and see yourself as "just another human
being", it makes complete sense. But on another level, perhaps a deeper level, personal
nonexistence makes no sense at all. All that we know is embedded inside our minds, and
for all that to be absent from the universe is not comprehensible. This is a basic
undeniable problem of life; perhaps it is the best metaphorical analogue of Godel’s
Theorem. When you try to imagine your own nonexistence, you have to try to jump out
of yourself, by mapping yourself onto someone else. You fool yourself into believing that
you can import an outsider's view of yourself into you, much as TNT "believes" it
mirrors its own metatheory inside itself. But TNT only contains its own metatheory up to
a certain extent-not fully. And as for you, though you may imagine that you have jumped
out of yourself, you never can actually do so-no more than Escher's dragon can jump out
of its native two-dimensional plane into three dimensions. In any case, this contradiction
is so great that most of our lives we just sweep the whole mess under the rug, because
trying to deal with it just leads nowhere.

Zen minds, on the other hand, revel in this irreconcilability. Over and over again,
they face the conflict between the Eastern belief: "The world and I are one, so the notion
of my ceasing to exist is a contradiction in terms" (my verbalization is undoubtedly too
Westernized-apologies to Zenists), and the Western belief: "I am just part of the world,
and I will die, but the world will go on without me."

Science and Dualism

Science is often criticized as being too "Western" or "dualistic"-that is, being permeated
by the dichotomy between subject and object, or observer
and observed. While it is true that up until this century, science was exclusively
concerned with things which can be readily distinguished from their human observers-
such as oxygen and carbon, light and heat, stars and planets, accelerations and orbits, and
so on-this phase of science was a necessary prelude to the more modern phase, in which
life itself has come under investigation. Step by step, inexorably, "Western" science has
moved towards investigation of the human mind-which is to say, of the observer.
Artificial Intelligence research is the furthest step so far along that route. Before AI came
along, there were two major previews of the strange consequences of the mixing of
subject and object in science. One was the revolution of quantum mechanics, with its
epistemological problems involving the interference of the observer with the observed.
The other was the mixing of subject and object in metamathematics, beginning with
Godel's Theorem and moving through all the other limitative'Theorems we have
discussed. Perhaps the next step after Al will be the self-application of science: science
studying itself as an object. This is a different manner of mixing subject and object-
perhaps an even more tangled one than that of humans studying their own minds.

By the way, in passing, it is interesting to note that all results essentially
dependent on the fusion of subject and object have been limitative results. In addition to
the limitative Theorems, there is Heisenberg's uncertainty principle, which says that
measuring one quantity renders impossible the simultaneous measurement of a related
quantity. I don't know why all these results are limitative. Make of it what you will.

Symbol vs. Object in Modern Music and Art

Closely linked with the subject-object dichotomy is the symbol-object dichotomy, which
was explored in depth by Ludwig Wittgenstein in the early part of this century. Later the
words "use" and "mention" were adopted to make the same distinction. Quine and others
have written at length about the connection between signs and what they stand for. But
not only philosophers have devoted much thought to this deep and abstract matter. In our
century both music and art have gone through crises which reflect a profound concern
with this problem. Whereas music and painting, for instance, have traditionally expressed
ideas or emotions through a vocabulary of "symbols" (i.e. visual images, chords,
rhythms, or whatever), now there is a tendency to explore the capacity of music and art to
not express anything just to be. This means to exist as pure globs of paint, or pure sounds,
but in either case drained of all symbolic value.

In music, in particular, John Cage has been very influential in bringing a Zen-like
approach to sound. Many of his pieces convey a disdain for "use" of sounds-that is, using
sounds to convey emotional states-and an exultation in "mentioning" sounds-that is,
concocting arbitrary juxtapositions of sounds without regard to any previously formulated

out?

All the limitative Theorems of metamathematics and the theory of computation

suggest that once the ability to represent your own structure has reached a certain critical

point, that is the kiss of death: it guarantees that you can never represent yourself totally.

Godel’s Incompleteness Theorem, Church's Undecidability Theorem, Turing's Halting

Theorem, Tarski's Truth Theorem-all have the flavor of some ancient fairy tale which

warns you that "To seek self-knowledge is to embark on a journey which ... will always

be incomplete, cannot be charted on any map, will never halt, cannot be described."

But do the limitative Theorems have any bearing on people? Here is one way of arguing

the case. Either I am consistent or I am inconsistent. (The latter is much more likely, but

for completeness' sake, I consider both possibilities.) If I am consistent, then there are

two cases. (1) The "low-fidelity" case: my self-understanding is below a certain critical

point. In this case, I am incomplete by hypothesis. (2) The "high-fidelity" case: My self¬

understanding has reached the critical point where a metaphorical analogue of the

limitative Theorems does apply, so my self-understanding

undermines itself in a Godelian way, and I am incomplete for that reason. Cases (1) and

(2) are predicated on my being 100 per cent consistent-a very unlikely state of affairs.

More likely is that I am inconsistent-but that's worse, for then inside me there are

contradictions, and how can I ever understand that?

Consistent or inconsistent, no one is exempt from the mystery of the self.

Probably we are all inconsistent. The world is just too complicated for a person to be able

to afford the luxury of reconciling all of his beliefs with each other. Tension and

confusion are important in a world where many decisions must be made quickly, Miguel

de Unamuno once said, "If a person never contradicts himself, it must be that he says

nothing." I would say that we all are in the same boat as the Zen master who, after

contradicting himself several times in a row, said to the confused Doko, "I cannot

understand myself."

Godel’s Theorem and Personal Nonexistence

Perhaps the greatest contradiction in our lives, the hardest to handle, is the knowledge

"There was a time when I was not alive, and there will come a time when I am not alive."

On one level, when you "step out of yourself" and see yourself as "just another human

being", it makes complete sense. But on another level, perhaps a deeper level, personal

nonexistence makes no sense at all. All that we know is embedded inside our minds, and

for all that to be absent from the universe is not comprehensible. This is a basic

undeniable problem of life; perhaps it is the best metaphorical analogue of Godel’s

Theorem. When you try to imagine your own nonexistence, you have to try to jump out

of yourself, by mapping yourself onto someone else. You fool yourself into believing that

you can import an outsider's view of yourself into you, much as TNT "believes" it

mirrors its own metatheory inside itself. But TNT only contains its own metatheory up to

a certain extent-not fully. And as for you, though you may imagine that you have jumped

out of yourself, you never can actually do so-no more than Escher's dragon can jump out

of its native two-dimensional plane into three dimensions. In any case, this contradiction

is so great that most of our lives we just sweep the whole mess under the rug, because

trying to deal with it just leads nowhere.

Zen minds, on the other hand, revel in this irreconcilability. Over and over again,

they face the conflict between the Eastern belief: "The world and I are one, so the notion

of my ceasing to exist is a contradiction in terms" (my verbalization is undoubtedly too

Westernized-apologies to Zenists), and the Western belief: "I am just part of the world,

and I will die, but the world will go on without me."

Science and Dualism

Science is often criticized as being too "Western" or "dualistic"-that is, being permeated

by the dichotomy between subject and object, or observer

and observed. While it is true that up until this century, science was exclusively

concerned with things which can be readily distinguished from their human observers-

such as oxygen and carbon, light and heat, stars and planets, accelerations and orbits, and

so on-this phase of science was a necessary prelude to the more modern phase, in which

life itself has come under investigation. Step by step, inexorably, "Western" science has

moved towards investigation of the human mind-which is to say, of the observer.

Artificial Intelligence research is the furthest step so far along that route. Before AI came

along, there were two major previews of the strange consequences of the mixing of

subject and object in science. One was the revolution of quantum mechanics, with its

epistemological problems involving the interference of the observer with the observed.

The other was the mixing of subject and object in metamathematics, beginning with

Godel's Theorem and moving through all the other limitative'Theorems we have

discussed. Perhaps the next step after Al will be the self-application of science: science

studying itself as an object. This is a different manner of mixing subject and object-

perhaps an even more tangled one than that of humans studying their own minds.

By the way, in passing, it is interesting to note that all results essentially

dependent on the fusion of subject and object have been limitative results. In addition to

the limitative Theorems, there is Heisenberg's uncertainty principle, which says that

measuring one quantity renders impossible the simultaneous measurement of a related

quantity. I don't know why all these results are limitative. Make of it what you will.

Symbol vs. Object in Modern Music and Art

Closely linked with the subject-object dichotomy is the symbol-object dichotomy, which

was explored in depth by Ludwig Wittgenstein in the early part of this century. Later the

words "use" and "mention" were adopted to make the same distinction. Quine and others

have written at length about the connection between signs and what they stand for. But

not only philosophers have devoted much thought to this deep and abstract matter. In our

century both music and art have gone through crises which reflect a profound concern

with this problem. Whereas music and painting, for instance, have traditionally expressed

ideas or emotions through a vocabulary of "symbols" (i.e. visual images, chords,

rhythms, or whatever), now there is a tendency to explore the capacity of music and art to

not express anything just to be. This means to exist as pure globs of paint, or pure sounds,

but in either case drained of all symbolic value.

In music, in particular, John Cage has been very influential in bringing a Zen-like

approach to sound. Many of his pieces convey a disdain for "use" of sounds-that is, using

sounds to convey emotional states-and an exultation in "mentioning" sounds-that is,

concocting arbitrary juxtapositions of sounds without regard to any previously formulated