Bruno Marchal wrote:
> Hi David,
> Le 16-août-06, à 02:51, David Nyman a écrit :
> > Good to see this. First off some grandmotherly-ish questions:
> >
> >> 1) The computationalist hypothesis (comp),
> >>
> >> This is the hypothesis that "I am a digital machine" in the
> >> quasi-operational sense that I can survive through an artificial
> >> digital body/brain. I make it precise by adding Church thesis and some
> >> amount of Arithmetical Realism (without which those terms are
> >> ambiguous).
> >> To be sure this is what Peter D. Jones called "standard
> >> computationallism".
> >
> > I need to ask you to make this more precise for me. When I say I *am* a
> > digital machine, what is my instantiation? IOW, am 'I' just the *idea*
> > of a dmc for the purposes of a gedanken experiment, or am I to conceive
> > of myself as equivalent to a collection of bits under certain
> > operations, instantiated - well, how?
> Well, for a "comp practitioners", saying "yes to the doctor" is not a
> thought experiment.
> I will try to explain at some point why we cannot really know what is
> our instantiation, and that is why the "yes doctor" needs some act of
> faith, and also why comp guaranties the right to say NO to the doctor
> (either because you feel he is proposing a substitution level which is
> too high, or because you just doubt comp, etc.). Eventually you will
> see we have always 2^aleph_zero "instantiations".


I noticed that you slipped in "infinity" ("infinite collection of
computations") into your roadmap (even the short roadmap).  In the
"technical" posts, if I remember right, you said that at some point we
were leaving the constructionist realm.  But are you really talking
about infinity?  It is easy to slip into invoking infinity and get away
with it without being noticed.  I think this is because we are used to
it in mathematics.  In fact, I want to point out that David Nyman
skipped over it, perhaps a case in point.  But then you brought it up
again here with aleph_zero, and 2^aleph_zero, so it seems you are
really serious about it.  I thought that infinities and singularities
are things that physicists have dedicated their lives to trying to
purge from the system (so far unsuccessfully ?) in order to approach a
"true" theory of everything.  Here you are invoking it from the start.
No wonder you talk about faith.

Even in the realm of pure mathematics, there are those of course who
think it is invalid to invoke infinity.  Not to try to complicate
things, but I'm trying to make a point about how serious a matter this
is.  Have you heard about the feasible numbers of V. Sazanov, as
discussed on the FOM (Foundations Of Mathematics) list?  Why couldn't
we just have 2^N instantiations or computations, where N is a very
large number?


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