On 26 Aug 2015, at 12:06, Peter Sas wrote:
Personally my brain stack overflows at about 3 or 4 levels of being
aware that I am aware that ... I am aware. I think it would require
infinite memory to truly be aware of an infinite number of steps in
such a recursive relation.
Maybe the infinite hierarchy doesn't have to be thought/remembered
in full. Royce notes that the simple intention to be completely self-
aware is enough: the infinite hierarchy is logically implied in the
intention. Oskar Becker has a slightly different approach: he says
that as soon as one notices the endlessness of 1, 2, 3.... etc. one
is already beyond the natural numbers and has reached the first
transfinite ordinal (small omega=N) which collects all the natural
numbers into one set. And then of course one can continue: omega+1,
omega+2...etc. Noting the endlessness of that series one has grasped
the next transfinite ordinal (omegaxomega). And so on... Becker
notes that Cantor's generation principles can be recast as
principles inherent in the structure of self-awareness. I think
that's a strong point.
That is very well known in recursion theory (alias theoretical
computer science).
We can both collapse the infinite regression, by using the second
recursion of Kleene, which I often explain with the diagonal Dx =
T(xx) ==> DD = T(DD) methode to get self-reference.
Then this can be used to define properly the constructive ordinal. The
first non constructive ordinal, which is also the set of all
constructive ordinal is omega_1^CK (for Church and Kleene). Then
reflexive machine can name ordinal beyond omega_ 1^CK, but using a non
recursive naming procedure. Machines and humans suffer from the same
limitation there (provably so if we assume computationalisme).
On the other hand, if there is an absolute self-awareness grounding
reality as such, then maybe it must have infinite memory... I don't
know, this account is still too undeveloped to say anything more
specific in it.
The entire machine's theology completely rest upon the fact that we
can collapse infinite regression. It is truly amazing, but the
technical idea is very simple. It is a variant of Cantor
Diagonalization. So even the physical reality appearance is a product
of that collapsing of level. The first person view, technically,
uncollapse it and build constructive names: it is a logic of an
unamebale subject which extends itself. It is a bit solipsist,
nationalist and dangerous ... for the others.
What about when a being is not contemplating its self-awareness and
merely living in the moment? Is it not conscious at those times?
In my view one cannot live in the present without self-
consciousness. Maybe this is lame argument, but I think this is
suggested by the similarity of the words "present" and "self-
presence"... I would say: the self-presence of the absolute self-
awareness is just what the present is... It is difficult to explain
this, but intuitively it feels right to me... And then there are is
also the claim that there is no (phenomenal) consciousness without a
measure of self-awareness... Kant originally advanced this idea, but
many present-day cognitive scientists accept it as well...
I kind of agree. Consciousness needs a reference to oneself, but that
reference has not to be conscious. Then self-consciousness is the same
+ one loop of self-reflection more.
RA is conscious, but PA is both conscious and self-conscious. RA is
just a typical Universal Machine, and PA is a typical Universal
Machine able to know that she is universal (I call them Löbian, as
they are characterized by a theorem in arithmetic due to Löb).
I still don't know if PA is not already a bit delusional. His soul is
already "falling", maybe.
Bruno
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