[Fis] The new axioms

[Marcus Abundis]

Greetings,

Missing in this study of Limits of Formal Systems (ways of managing diverse
abstractions), and even back to Yixin’s Paradigm Shifts and to Stu’s notes,
is the matter of simple-to-complex material reality. Gordana partly frames
the issue as Multi-Level Analysis (too much like Multidisciplinary
approaches?) and Dynamical approaches (differed from Agent views?)—where it
is easy to agree a need for New Mathematical approaches and more.

And now we have Krassimir’s (most of which I agree):
< Have you asked yourself the "simple question“: "Why are there so many
theories in mathematics with corresponding systems of axioms?“ >
—Here, the reason is NOT mathematic or axiomatic, but Simple-to-Complex
Material Reality, where HUMAN-logical gaps persist. It is our own
`impoverished logic’ (a psycho-logical problem) that leaves us with
mathematical issues, having failed to FIRST correctly view the full
problem(s). If we take modeling as a discipline, one must first find a
proper intuitive fit BEFORE proceeding to mathematic models—the lesson of
Einstein's famous thought experiments.

PRIMALLY AXIOMATIC Simple-to-Complex Material Reality has many INNATE
Material Paradigm Shifts, we imperfectly map via Logical Paradigm Shifts
(re Yixin). Not until we have perfect knowledge of the cosmos and LEVEL
TRANSITIONS, will `all such issues’ dissipate (re Kant’s das Ding an sich.

To debate which CURRENT mathematic view might be a `better tool’ (re
Category Theory, etc.) is too much like `dueling pathologies’, blind to our
own personal flaws. This all brings the Limits of Formal Systems back to a
central matter of a need for New Mathematical approaches. But to imagine
new approaches we must FIRST confront our own logical gaps (psych-logical
poverty). This dates back even further, long before Shannon, to Korzybski’s
`confused levels of abstraction’.

So when Krassimir states
< thousands of articles pointing out how one formal system or another
CANNOT be applied to modeling . . . But writing such articles is pointless.>
— It is hard to disagree, except I would start by looking BENEATH living
matter, as living matter itself cannot exist in a vacuum, always in a
context of eternal adaptations. To ignore STIPULATED adaption (adaption to
what exactly? = context) as a central aspect of Simple-to-Complex Material
Reality AND Life is equally pointless. A firm grasp of ensuing Functional
Material Levels is thus an ESSENTIAL first step in confronting Limits of
Formal Systems.

But then, still — Krassimir — when various `axiomatic offerings’ are
already known to you and us, why are we NOT critically examining those
offerings . . . as part of discussing and truly exploring the current
topic Limits
of Formal Systems. For example,

— Kun Wu’s view (1991—earliest I can find) of subject object modeling seems
to head in an interesting direction but also seems excessively complex, and
essentially pantheistic.

— Terry Deacon’s teleo-dynamics (2011) seems deeply flawed with a purely
thermodynamic base that he initially transcribes to homeodymanics, while
entirely ignoring a much broader established homeostasis roles.
Theromdynamics works ONLY as a bare/incomplete trope.

— Mark Burgin’s GTI is entirely without semantic/subjective roles (per his
own admission).

— Stu Kauffman and his engine block coconut crusher/paper weight `thinking’
. . . well he never answered my posts, so I am unsure what to make of it.
But *I* would be embarrassed by such an offering, with NO functional depth. He
also seems to repeat/encourage Terry's thermodynamic error.

— Pedro every so often offers 10 (or so) informatic principles, but I have
never seen a fully developed model. Still, I have seen enough to know he
often insists it `ALL evolves around Life, and only Life’ (as *many* do in
FIS) and seems to forget Life must continually adapt to `something’.

— Joe Brenner’s LIR I have also looked at and it seems hopelessly dualistic
and thus cannot account even for Nature’s creativity, let alone human
creativity.

— Krassimir’s GIT, certainly makes very promising `sounds’, but I have
never seen a fully developed model, despite many requests.

— and then there is of course my own S-O modeling/Natural Informatics
offering, which I will not repeat . . . and there are likely many others I
have forgotten about or just never heard of.

I hope this somehow helps `get the ball rolling’ in exploring further *firm
critical thinking* around Limits of Formal Systems . . . assuming that is
the aim of this session(?)

Marcus
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