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1) Because there are no deterministic point of times, the status of a system can neither be
ascertained to be at a certain "point in time", nor "points in time" can be determined for a future
status. There is nowhere any type of determinism. Since the classical physics as well as the
quantum theory are based on the postulate that a system is in a certain status at a certain
"point in time" (in the first case as points of phase space, and in the other case as probability
distributions in phase space), neither theory can be completely consistent (see also THOMAS
BREUER / 1997)
[1].
2) Regarding WIGNER (1961)[2], an absolutely universally valid theory would have to be capable of
describing the origin of human consciousness. The auto-adaptation theory described herein
could be capable of this; the quantum theory cannot. (Wigner postulated that complex quantum
mechanics delivers a usable description of the physical reality only when there is no "subjective
sensing". The author holds the view that subjective sensing also exists in atomic and
subatomic structures).
3) Sequences of elapse times like TW and TW' are definable as strings of an axiomatic formal
system; albeit this system is a "time domain system" and not an arithmetic systems in the
usual sense of the classic number theory. Indeed, said formal system shows at least one
axiom and derives from it continuous strings of numbers through the application of a certain
algorithm. Regarding TURING, an axiomatic number theoretical system can be produced also
by a mechanical procedure, which produces "formulas and algorithms".For this reason, the
known logic theorems of GOEDEL, TARSKI or HENKIN are absolutely applicable on such a
model. GOEDEL`s incompleteness theorem
[3]
shows that each extensive number theoretical
model includes consistent formulations which cannot be proven with the rules of the model, and
which therefore are undecidable. This is valid also to metatheoretical models
and to meta-metatheoretical models etc.
For example, a self-referential metatheoretical sentence like the type of the Goedel formulation
<I am provable> is neither provable nor disprovable. A decision procedure for this proposition
leads to an infinite regress. TARSKI showed that a decision procedure for number theoretical
"truth"[4]
is also impossible, and leads to an infinite regress. Thus, a self-referential sentence of
the type <I am provable> is admittedly "true", but not "provable". It follows, that "provability" is a
weaker notion than "truth". HENKIN showed that there are sentences, that assert their own
provability and "producibility" in a specific number theoretical model and which are invariable
"true"[5]. A self-referential sentence based on Henkins theorem would be: <It exists a number
theoretical model in which I am provable>. Strings of quantized elapse times like TW and TW'
approach the domain of validity of HENKIN`s theorem. Applying Henkins logic, these strings
assert: <I will be produced to proved>. TW and TW's are therefore strings or sentences that are
produced in a specific formal model, which induces its own decision procedure on truth,
consistence, completeness and provability through continued self-generation (see also
description to Fig.10).
In contrast to self-referential strings or sentences of the Gödel or Henkin type, strings of elapse
times are never asserted to be "true", "consistent", "complete" or "provable" to a certain "point
in time", because within the "number theoretical model" in which they are produced, no "points
of time" exist. This model also prohibits superior semantics or metatheories or meta-
metatheories. It is plainly obvious that each formal system, each metatheory, each meta-
metatheory and each semantics, in which axioms, strings or sentences of any type are
formulated, is the result of continued autonomous adaptation (which is based on the
quantization of elapse times) and therefore a derivation of the model described in this work.
4) The cognition, that a specific formal system exists asserting absolute universal validity, from
which everything has been produced and to whom all other systems have to be subordinated, is
not new. Already in early antiquity, many years before PLATO and ARISTOTLE, the Hebrew
Scriptures (2. Moses 3: 14) let this <source of all logic> say from itself: "JHWH" (spoken:
Jahwe or Jehovah), that is about: "I shall be proved"[6]. This sentence asserts its own decision
procedure on provability, truth, completeness and consistence; through a specific formal
system, that it "induces to be".
5) There is no "cognition" without "recognition".
References:
[1]
Thomas BREUER (1997) "Quantenmechanik: Ein Fall für Goedel" ISBN 3-8274-0191-7
[2]
Eugene WIGNER (1961) "Remarks on the Mind-Body-Question",
see also: Roger Penrose:"The Emperor`s New Mind"/ ISBN 0-19-286198-0 (page 381)
[3]
Kurt Goedel "On Formally Undecidable Propositions in Principia Mathematica and Related
Systems I. (1931),
see also:
Douglas HOFSTADTER "Goedel, Escher, Bach" (pg. 17) ISBN 0-394-74502-7
[4]
Douglas HOFSTADTER "Goedel, Escher, Bach"
(page 579, 580: "Tarski`s Theorem")
[5]
Douglas HOFSTADTER "Goedel, Escher, Bach"
(page 541: "Henkins Sentences")
[6]
See WIKIPEDIA
(note: the engl. JHWH-web-site became removed by
some nerds in 2007.
So the link to this site
has been deleted too.)
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