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MY UNIVERSITIES 2. HIDEOUT BRIEFINGS
Introduction
67 years passed since a 14-16 youngster who is supposed
to have been me, held in precarious Warsaw hideouts
conversations which molded his ideas. Time has blurred
many details and, as I worked the rest of my life on
concerned issues, my concurrent views may stain the
bygones. I'll try to keep them as clean and true as
quotes from memory may possibly be.
As I said in the "Context", thanks - if I dare to say -
to the AB-Aktion, I had the unbelievable fortune to be
briefed in philosophy by Tatarkiewicz and Kotarbinski,
in mathematics by Pogorzelski, in Logic by Lukasiewicz's
student "Dziwny" -some activists were only known by
pseudonyms-, and by "Daniel", a Jewish origin Jesuit
- another Dirac if the SS did not hang him - in Relativity,
and in Einstein's "Physical Reality".
DANIEL
(D1)Relativity
I shall not give here the technical details of Daniel's
briefing on Relativity, but mention his idea that it
reposes 90% in intuition and that the 10% of maths are
there to express intuitions in exact and simple way.
He explained me the derivation of the Special Relativity
in a few days with maths restricted to the Pythagoras
theorem and the derivation of the General with help of
the purely intuitive mental experiment of the Rotating
Disk - in one day. The 10% of maths did not seem to me
at first so simple, due to the confusion of difficulty
with simplicity. Maths may be difficult to learn, like
any new language, but once learned, becomes the simplest,
concise way to express complex contents.
Be that as it may, the necessary minimum of calculus,
partial differential equations, vector and tensor calculi
was difficult enough and I would have not made it out
without Pogorzelski. Now, this wizard - like the Aliance
Francaise courses speaking only French from the first day-
talked maths to me as if I were his peer and, believe it
or not, it soon started to crystalize into more and more
clear, transparent and indeed simple forms.
In short, between Daniel and Pogorzelski I have been
briefed sufficiently to be subsequently accepted by
Infeld to his Relativity research team.
(D2)Einstein's Physical Reality (PhR)
Second issue I learned from Daniel was Einstein's
Physical Reality (PhR), which became my principal
interest, leading through 67 years to my concurrent
view of the "Second Enlightenment". The latter is, of
course, incomparably more extensive and detailed than
a hideout briefing and may retroject its shadows deforming
the recollections. Yet, I'm certain that Daniel asserted
following points:
(D21)Immanency of the PhR encompassing mental percepts or
events and abstract constructs justified exclusively by
their capacity to coordinate events.
(D22)CD (Continuum/Discreteness) Polarity with continuum
preponderance, underlying all PhR's constructs and the
entire concurrent physics, and intuited as continuous
time flow, chopped by discrete events into discrete
periods.
(D23)Covering Principle embodying (D22) and stating that
distances and periods may be expressed - also in mental
experiments - only with physical rods and clocks, where
"physical" means conforming with principles of concerned
physical model. Thus the Covering Principle using rods
conforming with the Lorentz Transformation underlies the
Rotating Disk mental experiment, deriving the General
Relativity.
As corollary of (D22) Daniel mentioned that whole mathematics
is founded in geometry's continuum. On my timid objection
that maths is supposed to be founded in the discrete set
theory, he answered something like **I can't say anything,
as I never met the set theory, don't intend to, and avoid
walking its way**.
That being a bit cryptic, I repeated it to Pogorzelski,
asking for the key (see (P) below).
TATARKIEWICZ
Daniel's was surprised by Tatarkiewicz's knowledge of the
PhR and even more by his competence in Relativity.
"It's advisable to know what one is talking about",
answered Tatarkiewicz.
The PhR sparked his several comments:
(T1)Immanency of the PhR versus Cogito,
(T2)CD Polarity versus Cartesian dualism,
(T3)Einstein's lapsus.
(T1)Immanency of the PhR versus Cogito
At the first glance Descartes' view was entirely
sceptical and marked by universal uncertainty, by doubt
about all one may think. Yet, he cannot be called a sceptic,
because his uncertainty was not negative, he did not doubt
just for the sake of doubting, but under this pervasive
uncertainty sought some certain bedrock. Paradoxically, he
found it through his very doubt.
Indeed, doubting implies necessarily thinking. What I think,
the theme of my thinking, may be erroneous or illusory, but
I am absolutely certain that I am thinking.
This assertion turned epistemology upside down, showing that
foundation of knowledge does not reside in the transcendental
outer world, but in the immanent awareness of the subject.
Since Descartes' Cogito, till our own days, knowledge and
science are deemed to be based on subjectivity. The old myth
of scientific objectivity rests in trash, where Cogito had
dumped it.
Crucial to the case is the foundation of contemporary physics,
to wit, Einstein's PhR, whose immanency embodies Cogito in our
concurrent context.
The actual formulation "Cogito ergo sum" ("I think, thus I am")
was meant as a rhetorically salient header of a this new,
revolutionary epistemology. The unfortunate "am" misguided many,
suggesting, on the face of it, some ontological implications.
Yet, already the choice of "think", rather than "feel", "sense"
or "experience" clearly indicates the cognitive and not
existential meaning of Cogito.
The final verdict has been pronounced by history. Cogito
is recognized as the cornerstone of concurrent epistemology,
but there are no Cogito-based ontologies. Cartesianist
ontologies deal with the dualist view of the mind-body problem
(see next paragraph) and are in no way concerned with Cogito.
(T2)CD Polarity versus Cartesian dualism
Dualist view seeing mind and body as two interacting, but
ontologically different substances goes back to Plato and
Aristoteles. Descartes made it to the backbone of his
ontology, distinguishing the body (res extensa) having
extension in space, but incapable of thinking, from mind
(res cogitans) having no extension and capable of thinking.
He also made a consequential step, associating mind with
awareness. Yet, an essentaial problem stayed pending, to wit
the mind-body interaction - how can material body act on the
immaterial mind and vice versa. Neither Descartes, nor his
Cartesianist followers could see how and where its solution
might be possibly sought.
Now, how does the contemporary thought look at the Mind-Body
or Mind-Brain problem?
================
Tatarkiewich shared Kotarbinski's view of specialization (see
below) of particular areas of philosophy and their affinities
with particular sciences. Thus, rather than talking about
philosophy in general he distinguished the domain of
"Philosophy of Mind" and its two aspects - speculative and
neurologic views.
Another view he shared with Kotarbinski was that of "reifying"
or illegal endowing abstractions with "existence" in the outer
transcendental world.
================
SPECULATIVE VIEW OF MIND reifies Mind and Brain either in a
"dualistic" approach of two different "substances", or in the
"monistic", of two aspects of a unique "physical substance"
- the brain. The choice is not based on any empiric evidence,
but on arbitrary, often snobbish beliefs. Dualism, because of
its religious affinities, is often considered not wrong - there
is no evidence -, but shameful, like a disgraceful disease.
Respectful gentlemen are monists and fancy calling themselves
"physicalists" undisturbed by ignoring the first thing about
physics.
NEUROLOGIC VIEW OF MIND, surprisingly adopts in Descartes wake
the "disgraceful" dualism. Modified, of course, as at his time
Neurology and neural structues of brain were unknown, but
boiling down to similar duality of conscious mind and "material"
brain. And the interaction stays as mysterious, as before.
Yet, science does not explain mysteries, but coordinates events
and facing two interacting referentials, searches covariant
transformations between them. Thus, the Relativity, considering
two relatively moving referentials, defines their covariant
Lorentz Transformation, without pretending to explain anything,
nor confusing transformation with causality.
Likewise, Neurology ascertains two sets of events - mental and
neural - incongruous within a unique referential and consequently
attributes them to two referentials - Mind and Brain.
Henceforth, one of the crucial tasks of Neurology consists in
researching mutual covariant transformations between Mind and
Brain. That's where science stops, short of explaining anything,
especially of explaining transformations in terms of causality.
The Continuum-Discreteness Polarity underlying Einsteins
Physical Reality offers a way to express the Mind-Brain
duality as a monist, truly physicalist Polarity of continuous
mental awareness and discrete neural events.
(T3)Einstein's lapsus
Einstein blamed Kant for having transferred some conceptual
bases of Natural Science (mainly time and space) from the
controllable domain of empiric adequacy into the inaccessible
heights of the Necessary Apriori.
Tatarkiewicz stood up for Kant who sincerely and rigorously
derived his view from his concurrent physics.
It's the Galilean Relativity which was based on absolute time
and space, and Einstein should have more justly blamed Galileo
and Newton. But, on the one hand, one does not see Einstein
blaming his masters on whose shoulders he always declared to
stand, and, on the other hand, they could hardly be blamed,
as nothing in their time could possibly call in question the
absolute time and space.
(P)POGORZELSKI ON FOUNDATIONS OF MATHEMATICS
Daniel is right - said Pogorzelski -, but establishments
are overwhelmingly irrational and dogmatic.
Irrationality persists, only dogma vary. Not so long ago
calling in question Mary's virginity or geocentrism would
ban you from all academies, if not land you on a stake.
Today you may say what you want about Mary, but woe is
me, if I call in question the set theory with all involved
fatuities like transfinities, Banach-Tarski paradoxes or
Goedel's theorems.
That's of course my strictly private opinion. If we live to
see a post-war establishment, it will ban me from all
Universities if I dare to call in question the sacrosanct
set theory.
"E pur si move" - and yet mathematics is based on geometric
continuum. It is simple and natural to discretize continuum
into numbers and to integrate differential equations into
discrete solutions, but it's impossible even to define sets
and numbers as purely discrete constructs, nor to ascent
from them to continuum without help of fatuous transfinities,
nor, for that matter, with their help. And most non-trivial
mathematical problems deal with infinity and continuum.
Poincare considered transfinite numbers as a "disease" and
Kronecker called Cantor a scientific charlatan. One either
plays with sets, or does mathematics, one can't have it
both ways.
Charlatans playing with sets and transfinities may be
brushed aside, but it's sad to see some great mathematicians,
dazzled by the established verbiage, lose time and effort
on this fools errand.
If you want to avoid being corrupted by the set theory, just
do sincere mathematics, and sets will never come your way.
(K)KOTARBINSKI
I saw Kotarbinski less than the others and my souvenirs
of him from the hideouts are muddled by his post-war
writings. I'll just jot down my recollections for what
they are worth.
(K1)Linguistic clarification
Natural language statements predicate properties on subjects.
Subject predicated by concrete, observable properties is
concrete and its name is a proper name. When it's predicated
by fictitious properties, it's fictitious and its name is a
pseudo-name. Only proper names and statements about them are
meaningful. Pseudo-names are meaningless.
Abstractions are pseudo-names and strictly speaking are illegal
subjects. Yet, when reducible to concrete, abstraction may be
a useful, often indispensable shortcut.
"Field" is an abstraction, but it may be reduced to a book of
concrete historic experiences about electricity and magnetism.
It would be unfeasible to quote the book at every instance and
without the shortcut "field" it would be impossible to formulate
physics.
The same word may be a proper- or a pseudo-name, depending on
the context. "Substance" of a piece of furniture, implying wood,
plastic, iron, etc. is a concrete, meaningful name. On the other
hand, "substance" defined by Spinoza as **that which is in itself,
and is conceived through itself; in other words, that of which
a conception can be formed independently of any other conception**,
is a meaningless pseudo-name.
While propounding linguistic clarification by restriction to
concrete terms, Kotarbinskie distanced himself from "realism",
which "reified" them, i.e. bestowed on them ontological
"existence". He particularly castigated reifying of pseudo-terms
and in particular such "human" universals as Christian, German
or Jew, which he saw as bedrock of wars and discriminations
including the Nazi oppression, which we were currently suffering.
"Auschwitz is based on reifying "human" universals and on concrete
discrimination against people on account of these pseudo-terms."
This phrase impressed me perhaps more than anything else I heard in
the hideouts.
(K2)Specialization
Kotarbinski saw "philosophy" as a universal, too general to be a
meaningful, proper term and prefered to talk about its branches,
such as ontology, epistemology, logic, ethic, etc. These branches
have stronger affinities with related branches of science than
among themselves, let alone with the general philosophy. We
have seen above the examples of ontology related to physics and
of the mind/brain inquiry - to neurology. Nobody can be competent
in all branches of the general philosophy, especially taking
into account that rigorous dealing with a branch requires the
competence in the related science. A "general philosopher" is
necessarily a dilettante.
(Dz)Dziwny on Logic
Like Daniel, Dziwny was killed shortly after our encounters.
He briefed me on Truth Tables and on the Propositional
Calculus (PC). According to him, the PC was binary Boolean
Algebra, extended to 16 operators and excellent for Turing
Machine algorithms, but nothing more. Changing binary 0-1 to
truth/falsity is illegal as these terms are undefined and
incompatible with Boolean calculus. As long as they stay
undefined and there is no rule of setting them, PC has
nothing to do with logic. On the other hand, the limitation
to two operands is unrealistic. We need operations on N operands,
or a N-dimensional calculus exploding the 2D 16 operators to
2**(2**N) getting astronomic for quite practical cases like
N=100. And, reality being fuzzy, instead of the binary "truth"
variable ranging over two values 0 and 1, we would need a
continuous "certainty" variable ranging over the sector 0-1.
I did not understand all of that, but got vague indications,
which allowed me to take up where he left and to define, after
years of work, the ERN logic.
