[Fis] Formal Theory of Reflections

[Krassimir Markov]

Dear Colleagues,
Let me inform you about publishing the second part of the Formal Theory of
Reflections (FTR).
Now it is available in full.
Links to the papers with FTR:
Part 1: https://urldefense.com/v3/__http://www.foibg.com/ijita/vol31/ijita31-03-p01.htm__;!!D9dNQwwGXtA!SDDWI9aWWdou9iqE-647WbroCXDPH82nTmFoOUhiIJvdqCZDAFrEPuJ-ft0Kfr1LdcR3v-KEAkDR0W9yRng$ 
Part 2: https://urldefense.com/v3/__http://www.foibg.com/ijita/vol31/ijita31-04-p01.htm__;!!D9dNQwwGXtA!SDDWI9aWWdou9iqE-647WbroCXDPH82nTmFoOUhiIJvdqCZDAFrEPuJ-ft0Kfr1LdcR3v-KEAkDR2k9D4U8$ 
An abstract of the FTR is given below:

Formal Theory of Reflections
Abstract
In the beginning, we traced the concept of reflection in extensive detail
across Western philosophy from Plato and Aristotle through Stoicism,
scholasticism, early modern philosophy, Kant, and phenomenology; across
Buddhist, Daoist, Yogācāra, Advaita Vedānta, and Sāṃkhya thought; across
Neoplatonic, Sufi, Hermetic, and Kabbalistic traditions; across the
idealist–materialist debate; and across modern cognitive science,
predictive processing, embodied cognition, neuroscience, and information
theory.
We then formalized reflection as the category Refl, with reflections as
objects and contacts as morphisms, characterizing the identity morphism as
reflection's null case and distinguishing it from self-reflection proper —
a non-trivial endomorphism that may be either direct or transitive,
depending on whether it factors through an intermediate reflection. We
established Refl's basic properties, theorems, and cross-domain
applications, extended it with functors, natural transformations, and a
hierarchy of reflection levels, and introduced explicit temporal dynamics —
throughout grounding the formalism in two recurring examples, a lake
reflecting sunlight and a solar eclipse observed through several
instruments.
We raised the question: what distinguishes the subject from any other
reflecting entity within the Formal Theory of Reflections? The answer is: a
subject is an entity that compares — that relates an incoming reflection to
reflections already held in memory, through an operator of its own, and
acts on the result.
We built this capacity for a single subject, grounding the once-informal
notion of comparison in a precise, gestalt-derived, three-valued adequacy
measure, and showing the resulting criterion to specialize, without
revision, into the independently developed affective-cognitive cycle of the
human case. Further we showed that because this capacity is internal to
each subject, nothing can pass between two subjects directly — only through
contacts mediated by a shared environment — and that the resulting chain of
mutual adjustment, rather than any single transmission, is the right unit
for understanding how subjects come to share, imperfectly but usably, one
another's reconstructions. We showed that populations of such subjects,
coordinated under shared rules rather than a common processor, can
themselves satisfy an analogous criterion — collective memory, distributed
comparison, distributed decision, connected into a cycle invariant under
the replacement of any individual member — and illustrated this with a
case, the ant colony, chosen precisely because it shares none of the human
institutional apparatus that might otherwise make the claim seem merely
metaphorical. We extended the same criterion across substrate, to the
artificial subject, showing what it would structurally mean for an Infotron
to compare, identifying a genuine disanalogy with the biological case that
has no clean precedent anywhere and raising, without resolving, the
question of whether this disanalogy marks a new level of reality (the
Infotronic level) or an elaboration of the social one already established.
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