This is not the roadmap. I think aloud in case it helps (me or someone
else).
Le 21-juil.-06, à 15:01, I wrote
> This can be made precise with the logics G&Co, but for this I should
> explain before the roadmap George has suggested (asap).
My problem. How much should I rely on Plotinus?
When people asks me for a non technical version of my saying, Plotinus'
Enneads are quite close to that. You should not take his examples
literally, but only its logic and the difficulties he encouters.
I must think. Strictly speaking, math is what makes the explanation
easier. In a nutshell I could perhaps try to put it in this way:
One (among many) possible description of the comp ontology of a comp
TOE, is just:
Classical logic +
the (recursive) definition of addition and multiplication.
This gives Robinson Arithmetic (RA), one of the weakest theory
possible. RA can prove that 4 + 5 = 5 + 4, but is already unable to
prove that this is true for any number n. RA cannot generalize. It can
prove that the sum of the first ten odd numbers
1+3+5+7+9+11+13+15+17+19 = 10 * 10, but RA cannot prove that for any n
the sum of the n first odd numbers gives always the perefct square n *
n.
Yet, RA has enough existential provability ability so as to be able to
represent the partial recursive functions, and from a recursion
theorist point of view RA can be seen as a universal machine, and RA's
theorem codes the generation of a universal dovetailing.
(Technically RA is able to prove all true sigma-1 sentences, those
which are like ExP(x) with P decidable).
Now if I stop here, I would fall against a critic David Deutsch once
made against Schmidhuber's "computationalist view of everything". It
would be quasi trivial.
So I add an epistemology: this concerns what richer machine's can
prove. Those richer machines are emulated all the time in the sequence
of simple existential proposition proved by RA.
Then I do what Everett did for quantum mechanics: what can prove the
lobian machine whos histories are generated by RA, or any DU, or just
the sigma1 truth).
(To understand this you need to understand the difference between
computation or emulation, and proof). Many people are wrong about
this. For example the (very rich) theory ZF can prove that the (rich)
theory PA is consistent. PA cannot prove that. But PA can prove that ZF
can prove PA's consistency. The main reason fro that, is that the fact
that you can emulate Hitler's brain (in platonia) does not entail you
will get Hitler's belief. This can be related to Dennett and Hofstadter
correct (assuming comp) rebutal of Searles in the book "Mind's I".
Even RA can prove that ZF can prove that PA and RA are consistent! But
RA and PA and ZF can hardly prove that they are respectively consistent
(no theories which can talk about addition and multiplication can prove
their own consistency, but richer lobian machine can prove many things
on simpler lobian machine, including what is true about the simpler
machine that the simpler machine cannot prove).
The lobian machine, my epistemology, is thus richer than the TOE comp
basic ontology (given by RA or the UD). A typical lobian machine is
given by the theory (or its corresponding theorem prover program if you
prefer) PA (Peano arithmetic). It is given by
-Classical logic
-the (recursive) definitions of addition and multiplication
-The infinity of induction axioms (read "A" "for all") like
[P(0) and An(P(n) -> P(n+1))] -> AnP(n)
This provides PA with incredible introspective abilities, enough for
enabling it to discover its limitations and the geometry of those
limitations. and eventually to correctly infer, from the logic of
provability (note the "v) the logic of "probability" (note the "b")
bearing on the collection of all their consistent extensions. And more.
At least enough for discovering two, and then 4, 8, 16, ...
plotinian-like hypostases (person notions), including the one which
justify matter, both in the UDA sense, and in the plotinian sense (a
"slight platonist correction of Aristotle theory of matter actually (I
begun the reading of Aristotle at last).
Note that the first primary hypostasis, truth, could aptly be called
the zero person point of view. That could perhaps be related with
Nagel's "point of view of nowhere". It is really here that Plotinus
contradicts the more Aristotle, which first hypostasis, seems to be a
1-person, especially in the treatise (5.6) which has been abridged out
in the pengwin paperbook Ennead (I guess a coincidence because that
point is well explained in many other ennead's treatise, so it is
normal to abridged this one for making possible to put the enneads in
your pocket without demolishing the pants).
I must think, the subject is difficult and goes over many disciplines,
Bruno
http://iridia.ulb.ac.be/~marchal/
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