Dear Galen A. Johnson,
I was made an atheist from a childhood by standard Soviet education,
but I am not agree with V.I.Lenin's estimation of the George Berkeley
philosophy. Unfortunately, I am a simple professor in Mathematics, but a
Russian one. Therefore, I have naturally no financial possibility to
arrive at your Conference. But I would like to say something apropos of
George Berkeley and modern ill science (by virtue of the continued Third
Crisis in Foundations of Mathematics).
THE LORD CAN FORGIVE US MANY THINGS,
EXCEPT FOR INTELLECTUAL PRIDE.
Many years ago, in the very beginning of the XVIII C., the English
philosopher bishop G.Berkeley said that a human-being mind, immersed in
high level abstractions from the young age, loses an adequate perception
of the real World (as V.I.Lenin, for example). Today, that immersion
became into the dangerous illness of outstanding (!) minds of the modern
science (and above all, of its most abstract area - modern
meta-mathematics): "Too much formalization and symbolization in the
theory of mathematics is dangerous to the healthy development of the
science of mathematics" (Von Neumann).
The famous Continuum Problem is the first acupuncture point of all
illnesses of modern mathematics. The Great Hilbert understood that well,
since he called just the Continuum Problem as the First Problem in his
famous list (1900).
The famous G.Cantor set theory with its pretension to fall outside
limits of the Godlike finite Natural Numbers (that were created by the
Lord, by L.Kronecker) into chimerical transfinite areas is the second
acupuncture point of all illnesses of modern mathematics (the Queen of
all sciences, by Gauss).
At last the eternal Problem of Paradoxes - the main reason of the Great
Crisis in Foundations of Mathematics - is the third acupuncture point of
all illnesses of modern science (including the Mathematics as the Queen
of all sciences, by Gauss).
By means of the send down idea of Cognitive Visualization of the World
of scientific abstractions, it was allowed me to solve the Continuum
Problem, to prove mathematically that the famous "Infinitum Actu Non
Datur" by Aristotel is not an empty slogan, but it is the direct
consequence of rigorous mathematical theorems, and to solve completely
the Paradox Problem.
The enclosed Parable is the direct consequence of all that solutions.
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As is known, the famous Russel=92s letter to Frege with the =93 Barber =94
stood for the begin of the Third Great Crisis in Foundations of
Mathematics. I am sure that the Parable is the first step to get over
the Crisis on the way to the high Lord Wisdom.
PARABLE
(The Atheistic Proof of God=92s Being)
As is well known, the Lord destroyed the First Tower of Babel by
confounding languages.
Holy Bible. The First Book of Moses, called GENESIS. Chapter 11, says:
5. And the Lord came down to see the city and the tower, which the
children of men builded.
6. And the Lord said, Behold, the people is one, and they have all one
language; and they begin to do: and now nothing will be restrained from
them, which they have imagined to do.
7. Go to, let us go down, and there confound their language, that they
may not understand one another's speech.
8 So the Lord scattered them abroad from thence upon the face of all the
earth: and they left off to build the city.
In order to guard the mankind from its own arrogance, from its own pride
and from new Babels in the Future, the Lord this time confounded Truth
and False and gave the "Liar" {=93The Cretians are always liars=85=94, Ho=
ly
Bible, The Epistle of Paul to Titus, Chapter 1, 12} as His Omen and
Warning for human beings.
More than 2500 years, a narrow-minded, finite human being repeats over
and over again: "If I am a Liar, then =85 I am not a Liar; but if I am no=
t
a Liar, then =85 I am a Liar" or in the modern meta-mathematical formal
notation:
(A =3D=3D > not-A)& (not-A =3D=3D > A) (1)
3. And they said one to another, Go to, let us make brick, and burn them
throughly . And they had the Liar (1) for stone, and a formal inference
had they for morter.
4. And they said, Go to, let us build us a new Meta-mathematical
paradise and the new transfinite Tower of Babel, whose top may reach
unto heaven; and let us make us a name, lest we be scattered abroad upon
the face of the whole earth.
And they built the new G.Cantor Paradise, and the Meta-mathematical
Prophet of XX Century David Hilbert said: "Nobody will banish us from
the Paradise that was built for us by George Ferdinand Ludwig Philippe
Cantor!".
Alas, all they forgot the Lord Commandment (EXODUS, Chapter 20):
4. Thou shalt not make unto thee any graven image, or any likeness of
any thing that is in heaven above=85,
- and nobody from them could understand the following True Sense of the
Lord Omen.
ESOTRERIC REVELATION. The true Nature of any classical paradoxical
contradictory, in fact, consists of not the two habitual forms:
(A =3D=3D > not-A)& (not-A =3D=3D > A) (1)
or ((A) & (not-A) (2)
but of its Godlike (i.e. without-ending !) Infinity:
Z =3D=3D > not-Z =3D=3D > Z =3D=3D > not-Z =3D=3D > Z =3D=3D > not-Z=
=3D=3D > Z =3D=3D > =85
, (3)
and there are neither logical nor mathematical arguments and reasons,
neither in heaven above nor in the earth benearth, nor in the water
under the earth, in order to stop this infinite process (3) ever in the
future.
He that hath an ear, let him hear what the Spirit saith =85
"And God posted an angel with a flaming sword at the gates of Cantor's
paradise", for everybody might understand the True Sense of the
transfinite wonders therein.
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COROLLARY 1. Any Meta-mathematical proof produced in a framework of,
supposedly, the Reductio ad Absurdum method and based on the paradoxical
contradictory (1) is a non-finite (in D.Hilbert's sense) "proof" since
it contains, in reality, the infinite fragment (2), i.e., by D.Hilbert,
it is not a mathematical or logical proof, at all.
COROLLARY 2. The Geodel=92s proof of the incompleteness is based, as you
know, on such the argumentation (see Stephen C.Kleene, =93Introduction to
Meta-mathematics=94, N.-Y., 1952, paragraph 42, Theorem 28):
IF |- Ap (p) THEN =85 |- not-Ap (p), but IF |- not-Ap (p) THEN =85 |- Ap
(p),
that is the Geodel=92s proof contains the (1)-type construction.
Consequently, that proof contains, in reality, the infinite (2)-type
argumentation, and therefore can=92t be ever ended and proves nothing.
COROLLARY 3. The epochal Cantor=92s Theorem about the uncountability of
real numbers do so. The Theorem which is the only (!) tool and reason
that allow meta-mathematicians to proclaim the existence of different
infinties by their cardinal numbers.
A =96 Z.
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Sincerely yours,
Alexander Zenkin
P.S. =96 I am sure, that just Cognitive Scientific Visualization is the
best medicine from that dangerous illness (see my WEB-Site, below).
Because only cognitive (semantical) visualization of the World of
scientific abstractions can unite the left-hemispheric, rational-logical
thinking with the right-hemispheric, intuitive-visual thinking of young
human-beings, aesthetic of cognition with ethic of behavour, wisdom with
conscience, knowledge with belief for further generations.
P.P.S. All said above is published in about 200 publications in
mathematical, logical, and philosophical journals (see my WEB-Site), but
I would be thankful if you could publish the message in your conference
proceedings for that could be known by the people who understand that we
can do nothing without the belief in the high Lord Wisdom from which the
modern science is very far off.
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Prof. Alexander A. Zenkin,
Doctor of Physical&Mathematical Sciences,
Leading Research Scientist of Computer Center
of the Russian Academy of Sciences.
Ph.: (095) 337.2168; e-mail: alexzen@com2com.ru
WEB-Site: http://www.com2com.ru/alexzen
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