On 4/16/2019 6:10 AM, Telmo Menezes wrote:
On Tue, Apr 16, 2019, at 03:44, 'Brent Meeker' via Everything List wrote:
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.
I don't agree that the Mars Rover checking "it's own" battery levels
is an example of what is meant by self-reference in this type of
discussion. The entity "Mars Rover" exists in your mind and mine, but
there is no "Mars Rover mind" where it also exists. The entity "Telmo"
exists in your mind and mine, and I happen to be an entity "Telmo" in
whose mind the entity "Telmo" also exists. This is real self-reference.
Or, allow me to invent a programming language where something like
this could me made more explicit. Let's say that, in this language,
you can define a program P like this:
program P:
x = 1
if x == 1:
print('My variable x s holding the value 1')
The above is the weak form of self-reference that you allude to. It
would be like me measuring my arm and noting the result. Oh, my arm is
x cm long. But let me show what could me meant instead by real
self-reference:
program P:
if length(P) > 1000:
print('I am a complicated program')
else:
print('I am a simple program')
Do you accept there is a fundamental difference here?
I take your point. But I think the difference is only one of degree.
In my example the Rover knows where it is, lat and long and topology.
That entails having a model of the world, admittedly simple, in which
the Rover is represented by itself.
I would also say that I think far too much importance is attached to
self-reference. It's just a part of intelligence to run "simulations"
in trying to foresee the consequences of potential actions. The
simulation must generally include the actor at some level. It's not
some mysterious property raising up a ghost in the machine.
Brent
Telmo
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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