Re: Robot Evolution



"Kent Paul Dolan" wrote:-

JE:-
WHY mathematics remains critically "incomplete"
supplies your answer.

No, it doesn't, ...

JE:-
I disagree. Please refer to the argument below.

snip relentless rhetoric<

JE:-
Do you know why?

Exquisitely.
Being a mathematician by training, I
long ago (1966 or so) read Goedel's proof, with
understanding, simply for the sheer joy of reading
it. You should make the attempt, it only involves
understanding simple arithmetic.

JE:-
No answer was provided (just rhetorical assertions).

Here is my answer:
Mathematics has always been critically incomplete because the propositions
of non mathematics which can make it complete are whatever constitutes
constant terms within the mathematics because only these can represent valid
EMPIRICAL frames of reference. Mathematics has no interest in what is and
what is not empirically based simply because all it does is logically
process each and every term no matter what they represent. Quite obviously,
each and very definition of an empirical constant term has to be imported
from outside of mathematics. IOW mathematics has to import any empirical
frames of reference. Without at least one, mathematics remains NON
empirically based. Without any constants at all, mathematics becomes reduced
to a tautology (just circular logic) so mathematics always remains
critically "incomplete". Being able to define what exactly represents an
empirical constant term within a mathematically based logic was and remains
entirely an act of human induction (no machine can make such an induction).
Circular logic (represented by reversible set intersection) becomes
transformed into vital contesting lines of logic (represented by
irreversible nested sets) depending on what was assumed to remain
empirically constant and what was not within each _different_ and therefore
_contesting_ lineal (not circular) assumption. Science (which always was and
will always remain empirically based) rigorously requires each and every
assumed constant term to remain empirically refutable allowing some frames
of reference to be discarded in favor of others but ONLY after testing
against NATURE in an entirely UNBIASED way. The net result: empirically
based reasoned arguments (theories) evolve in a Darwinian way where
refutation replaces natural selection. As one frame of reference replaces
another via Popperian refutation _absolutely lager_ outer nested sets
encompasses all the others expanding the truth domain of a theory of science
(the theory can explain more and more in a refutable way). These can modeled
as an expanding series of concentric circles representing expanding nested
sets. Each refutation (the edge of each nested circle) requires an even
better induction than the last where this critical scientific lineage of
human inductive inferences cannot be made by any known machine.

Regards,

John Edser
Independent Researcher

edser@xxxxxxxxxxxxxx







.

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