You seem to make self-reference into something esoteric. Every Mars
Rover knows where it is, the state of its batteries, its instruments,
its communications link, what time it is, what its mission plan is.
Whether it is "formalizable" or not would seem to depend on choosing the
right formalization to describe what engineers already create.
Brent
On 4/15/2019 11:28 AM, za_wishy via Everything List wrote:
Hmm... the thing is that what I'm arguing for in the book is that
self-reference is unformalizable, so there can be no mathematics of
self-reference. More than this, self-reference is not some concept in
a theory, but it is us, each and everyone of us is a form of
manifestation of self-reference. Self-reference is an eternal logical
structure that eternally looks-back-at-itself. And this
looking-back-at-itself automatically generates a subjective ontology,
an "I am". In other words, the very definition of the concept of
"existence" is the looking-back-at-itself of self-reference. So,
existence can only be subjective, so all that can exists is
consciousness. I talk in the book how the looking-back-at-itself
implies 3 properties: identity (self-reference is itself, x=x),
inclusion (self-reference is included in itself, x<x) and
transcendence (self-reference is more than itself, x>x). And all these
apparently contradictory properties are happening all at the same
time. So, x=x, x<x, x>x all at the same time. But there is no actual
contradiction here, because self-reference is unformalizable. The
reason why I get to such weird conclusions is explored throughout the
book where a phenomenological analysis of consciousness is done and it
is shown how it is structured on an emergent holarchy of levels, a
holarchy meaning that a higher level includes the lower levels, and I
conclude that this can only happen if there is an entity called
"self-reference" which has the above mentioned properties. So as you
can see, there pretty much cannot be a mathematics of self-reference.
I will also present about self-reference at The Science of
Consciousness conference this year at Interlaken, Switzerland, so if
you are there we can talk more about these issues.
On Thursday, 11 April 2019 02:55:55 UTC+3, Bruno Marchal wrote:
Hi Cosmin,
It seems your conclusion fits well with the conclusion already
given by the universal machine (the Gödel-Löbian one which are
those who already knows that they are Turing universal, like ZF,
PA, or the combinators + some induction principle).
Self-reference is capital indeed, but you seem to miss the
mathematical theory of self-reference, brought by the work of
Gödel and Löb, and Solovay ultimate formalisation of it at the
first order logic level. You cite Penrose, which is deadly wrong
on this.
In fact incompleteness is a chance for mechanism, as it provides
almost directly a theory of consciousness, if you are willing to
agree that consciousness is true, indubitable, immediately
knowable, non provable and non definable, as each Löbian machine
is confronted to such proposition all the “time”. But this
enforces also, as I have shown, that the whole of physics has to
be justified by some of the modes of self-reference, making
physics into a subbranch of elementary arithmetic. This works in
the sense that at the three places where physics should appear we
get a quantum logic, and this with the advantage of a transparent
clear-cut between the qualia (not sharable) and the quanta
(sharable in the first person plural sense).
You seem to have a good (I mean correct with respect to Mechanism)
insight on consciousness, but you seem to have wrong information
on the theory of the digital machines/numbers and the role of
Gödel. Gödel’s theorem is really a chance for the Mechanist
theory, as it explains that the digital machine are non
predictable, full of non communicable subjective knowledge and
beliefs, and capable of defeating all reductionist theory that we
can made of them. Indeed, they are literally universal dissident,
and they are born with a conflict between 8 modes of
self-apprehension. In my last paper(*) I argue that they can be
enlightened, and this shows also that enlightenment and blasphemy
are very close, and that religion leads easily to a theological
trap making the machine inconsistent, except by staying mute, or
referring to Mechanism (which is itself highly unprovable by the
consistent machine).
Bruno
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