[Fis] The new axioms

Sat Feb 10 16:28:05 CET 2024

Dear Gordana, Marcus and Colleagues,
Thanks a lot for your comments on my humble post.
I will reply to both of you, but I don't think now is the time to veer off
into a GIT discussion.
Let's be consistent and respect Stu and Carlos by continuing the discussion
on the points they raise.
My post was exactly in this direction.

I'll answer Markus first, because my answer has to be the size of "a book"
and can't fit in one comment.

Dear Markus,
There are now two different printed editions of the GIT monograph, but both
are bibliographic rarities.
We hardly need to go back more than 30 years when they appeared.
But there is a summary article from a later time that was intended to give
a brief and informal account of the main ideas.
Here is a link to it
https://urldefense.com/v3/__http://www.foibg.com/ijita/vol14/ijita14-1-p01.pdf__;!!D9dNQwwGXtA!T--mSBwvdh6msFJ6TKGdvxE4pEGhAyILMEm5KxzcI2iq_CZ3b1084zwB4QPprGg0HMw9UI5CNUTwPeKWEM8$ 
Of course, to this day there are some clarifications, but the essence of
the theory has not changed.

Dear Gordana,
I use the term "reflection" in its classic philosophical sense.
It is perhaps most visually illustrated by Plato in his parable of the
cavemen.

Shadows on the wall! - As a popular song says.

I have already noted in this discussion list that for me Plato provided a
perfect model of the human brain.
All we perceive are "shadows on the wall"!

For convenience, I'll recall here the GIT basic definition of "reflection":
******

*Entity *

In our examination, we consider the real world as a space of entities. The
entities are built by other entities, connected with relationships. The
entities and relationships between them form the internal structure of the
entity they build.

*Interaction *

Building the relationship between the entities is a result of the contact
among them. During the contact, one entity impacts on the other entity and
vice versa. In some cases the opposite impact may not exist, but in
general, the contact may be considered as two mutually opposite impacts
which occur at the same time. The set of contacts between entities forms
their interaction.

*Reflection *

During the establishment of the contact, the impact of an entity changes
temporarily or permanently the internal structure and/or functionality of
the impacted entity. In other words, the realization of the relationships
between entities changes temporarily or permanently their internal
structure and/or functionality at one or at few levels.

The change of the structure and/or functionality of the entity, which is
due to the impact of the other entity we denote with the notion “
*reflection*”.

The entities of the world interact continuously. It is possible, after one
interaction, another may be realized. In this case, the changes received by
any entity, during the first interaction, may be reflected by the new
entity. This means that the secondary (transitive) reflection exists. One
special case is the external transitive self-reflection where the entity
reflects itself as a secondary reflection during any external interaction.
Some entities have an opportunity of internal self-reflection. The internal
self-reflection is possible only for very high levels of organization of
the entities, i.e., for entities with very large and complicated
structures.

******

I asked ChatGPT to "understand" what I was saying. Here is the answer:

******

1.       *Entity:*

·        The real world is viewed as a space of entities.

·        Entities are constructed by other entities and are interconnected
through relationships.

·        The internal structure of an entity is formed by the entities and
relationships that build it.

2.       *Interaction:*

·        Relationships between entities result from contact between them.

·        Contact involves mutual impacts; one entity influences the other,
and vice versa.

·        Contacts collectively form the interaction between entities.

3.       *Reflection:*

·        When entities interact, the impact of one entity temporarily or
permanently changes the internal structure and/or functionality of the
impacted entity.

·        This change is termed "reflection."

·        Entities continuously interact, and the changes from one
interaction may be reflected in subsequent interactions.

·        Special cases include transitive reflection (changes from one
interaction reflected in a new entity) and external transitive
self-reflection (entity reflects itself during external interaction). Some
entities may also have internal self-reflection, limited to highly
organized entities.

In summary, this definition explores the dynamics of entities in the real
world, emphasizing their interconnectedness through relationships, the
impacts of interactions, and the resulting reflections that alter the
internal structure and functionality of entities. The concept of reflection
extends to transitive reflection, external transitive self-reflection, and
internal self-reflection in specific cases.

******

Finally, here is the main thesis:

There are infinitely many reflections.
Some of them are recognized by the subject, others are not.

Those recognized by him are information for him, and the rest, not
recognized - data.

With respect,
Krassimir

На сб, 10.02.2024 г. в 14:13 Marcus Abundis <55mrcs at gmail.com> написа:

> 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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