WHAT DOES THE NAME OF THE ALMIGHTY GOD ("JHWH") MEAN
IN EPISTEMOLOGY AND PROPOSITIONAL CALCULUS?
see
Patent "Method to Generate Self-Organizing Processes in Autonomous
Mechanisms and Organisms"
(last chapter) US6172941
EP1146406A1
Consequences for metamathematics, propositional calculus, epistemology and philosophy are:
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 [3] incompleteness theorem 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 Henkin's 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 metametatheories. 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". 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".
[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: An Eternal
Golden Braid" (page 17) ISBN 0-14-01-7997-6
[4] Douglas HOFSTADTER "Goedel, Escher, Bach" (pages 579, 580: "Tarski`s Theorem")
[5] Douglas HOFSTADTER "Goedel, Escher, Bach" (page 541: "Henkins Sentences")
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