Dear Stephen,

At 13:44 29/04/04 -0400, Stephen Paul King wrote:



    But there is no such thing as a delay in Platonia, but that is not my
point.


It is good it is not your point because there are delay in Platonia,
at least in the sense I was using the word. A delay relative to a
computational state is the minimal number of step for the UD
to come back on that state or its continuations (roughly speaking).
By the "compiler theorem" this make sense, and it is just a (computable)
number. It has nothing to to with the subjective time we will
be able to "axiomatize" once we define the first person, and it has
nothing to do with the physical time which we will or will not
recover from the quantum logics (given by interviewing
the sound universal machine).


I am trying to see how you deal with the problem of intractible
computations - as implementable given infinite resources - and how it may be
possible for measures to be defined using them. I had not considered this
application but it is intriguing. You touch on this below.

> If complexity
> play a role it must be derived along with the measure on the comp
histories.

[SPK]

    Yes, but is this derivation on that can be taken to exist independent of
the first person aspect of comp histories?

    This may be one of my key difficulties. On one hand, I do not have a
problem with the idea of Platonic existence, re AR, of mathematical objects
but I do have a problem with the seeming lack of a clear explanation of how
the "flow of temporality " arises in the first person aspect.


But we have not yet arrive at this point. Wait for S4Grz. You *will*
be delighted :)    (We will see ...).





    It seems to me that what ever our theory of Everything is, it must
explain how it is not just possible to have a "flow of temporality"  a
priori; it must have a non-measure zero sampling in the class of all
possible relationships between numbers - or whatever notion of Ur-object
that one uses.

    I personaly eschew the notion of fundamental "objects" and use the
Heraclitian notion of Process and fundamental, thus I see mathematical
objects - numbers, etc. - as derivative of this notion of Process. I see
Hintikka's idea of proofs as game theoretical constructs as strongly hinting
at this idea...


It is really a matter of convenience, to take numbers, sets, or games.
But in general game theories, or set theories are richer and less simple than
elementary arithmetic. I don't think those dictinction are quite relevant.
You will tell me ... after I make enough precise the result I got and the
propositions I conjecture.
Do you know Conway game theory?  Where games are jkust a slight
generalisation of his concept of number?



> In "Conscience & Mecanisme" I do make a case that Bennett notion of
> depth could play a role in order to derive the "cosmological" aspect of
> physics. Even prior a-la-Schmidhuber could play a role. But the
> methodology I advocate although it could justify the prior if needed,
cannot
> rely on it at the start.

[SPK]

    I agree. We have to have the methodology itself as an a priori existent.
It is co-present in Platonia in your thinking, it seems to me. ;-)


This is a little bit too vague for me I'm afraid.




> >     I do not see how the mere a priori existence of solutions (Integers)
and
> >the relationships between them (also Integers), as a priori existing
numbers
> >is sufficient.
>
> We will discuss that after I succeed in explaining how the whole things
> work. All Right?

[SPK]

Sure! ;-)

> >BM:
> > > The comp reason why the soul or the first person is never captured by
any
> > > complete third person description is akin to the reason truth and
> > > knowledge are
> > > not arithmetizable (as opposed to provable and consistent).
> > > Godel's theorem & Co. makes universal machine a highly non trivial
type of
> > > being.
> >
> >[SPK]
> >
> >     Does not this statement, that  "truth and knowledge are not
> >arithmetizable", imply that the postulation of AR is insufficient?
> [BM]
> No. And giving that Godel's incompleteness is true for much more
> general things than machine, we can say not only that arithmetical
> truth is not arithmetizable, but mathematical truth is not
> mathematicalizable, physical truth is not physicalizable, and more
> generally [whatever]-truth is not [whatver]izable.
> So strictly speaking AR could be sufficient (the Pythagorean version
> of my thesis). For reason of simplicity I do not use it.

[SPK]

    Wait a minute! It is one thing to say that "[whatever]-truth is not
[whatver]izable" and it is another to say that [whatever]-truth is finitely
constructible or approximatable. The former deals with its existential
aspects and the latter deals with its meaningfulness and expressiveness. We
do not require absoluteness (truth, decidability or otherwise) in our
interactions to be able to have meaningfulness.

    But this is not problematic to me; I am interested in how physicality
MUST obtain, even if only in the first person sense. In fact, in my work I
anly assume first person physicality - there is no such thing as third
person or "objective" physicality. This is where our idea overlap
strongly.;-)

> >Let me
> >state this in a different way. How does Digital Substitution ( "yes,
> >Doctor" ) get coded into numbers without involving physical
implementation?
>
> [BM]
> But that's the point of the whole work. Now, if you have follow
> a little bit the literature on the mind body problem you surely know
> that nobody has succeed in explaining how a private mind can be attached
> to anything third-person describable, be it physical or mathematical.
> All what I say is that if we survive the digital brain substitution, then
any
> fundamental explanation of what matter *cannot* rely on anything
> like Aristotelian substances or even to anything *primitively* physical.
> With comp the mind-body problem is just two times more difficult in the
> sense that we must explain not only the mind but also the matter, and
> this from the mind. The UDA (alias the 1-8 reasoning) just show that:
> comp *must* explain matter by a mind theory. Wait perhaps I say
> more to Kory so that you can be made your objection more specific.

[SPK]

    I have been following your discussion with Kory (and all others)
closely.

    In an attempt to "put all my cards on the table" I will state that my
idea is a kind of process based mind-body dualism (based on Vaughan Pratt's
work http://citeseer.ist.psu.edu/pratt95rational.html), but one that becomes
very similar to Russell's "neutral monism" in the limit of "the Totality of
Existence", which I believe is the same as your Platonia, e.g. an
"asymptotically vanishing dualism. I do not see Platonia as being "mental"
or "mind", ala a new form of Berkeliean Idealism.


We can guess similarities indeed.  But (I told you this before) Pratt's
paper are hard, and the relation with mind and bodies is implicit, nowhere
does him really tackle the m/b problem.


Best Regards and bon week-end.


Bruno




http://iridia.ulb.ac.be/~marchal/




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