Bruno Marchal wrote:
> Le 23-août-06, à 13:32, 1Z (Peter D. Jones) wrote (in different posts) :
>
> >
> > There are many interpretations of the box and diamond.
> > Incompleteness introduces ideas if necessity and possibility based
> > on provability (or provability within a system). But there are,
> > and always were, ideas of necessity based on truth rather than
> > provability.
>
>
> I agree (so what?)
So all mathematical staments are still necesary-qua-proof
even if they are possible-qua-provability. So contingent truths -- like
"matter doesn't exist" -- don't belong in Platonia.
> >> Since the failure of logicism, by Godel's theorem, we can argue that
> >> numbers does not necessarily exist. Numbers does not come from logic
> >> alone. If you want them,
> >
> > to exist
> >
> >> you have to do a ontological commitment.
> >
> > ..and if you want to play with them as a formal
> > system, you don't.
>
>
> I am not sure I follow you (terminological) nuance between "wanting
> something" and "wanting something to exist".
All you have to assume or adopt in order to *do* arithmetic --
beyond logic -- is additional axioms.
> The move toward formalism does not work for any theory of formal
> system. This is a consequence of Godel's incompleteness.
GIT means there are theorems which cannot be proven within
*a* formal system. It does not mean there are theorems which
cannot be proven with *any* formal systems. Every mathmetical
proof procedes from axioms and rulesof inference. A claim
to have peeked into Plato's heaven doesn not count as proof.
> I don't believe the formalistic philosophical position can even make
> sense of notion like "yes doctor".
That depends on what you mean by "yes doctor". As far
as most people are concerned , "yes Doctor" is about the ability
of silicon to emulate organic matter. Most people woul not assent
to being killed here, in the sublunar wolrd, on the basis that they
would still survive
in Plato's heaven.
> Still less about arithmetical truth,
> unless you formalize all this in second order arithmetic or in set
> theory, but then you need to rely on informal intuition at that level.
"Informal intuition" still doens't require Platonic objects.
There are several non-Platonic theoires, formalism is not the only one.
> > Hence the need for a metaphysical account of
> > matter-as-Bare-Substance to complement the
> > physicst's account of matter-as-behaviour.
>
>
> I have not the slightest idea of what could be
> "matter-as-bare-substance".
> Does "matter-as-bare-substance" possess a mass?
Not necessarily.
> Does "matter-as-bare substance" violate Bell's inequality?
Not necessarily.
> Does such questions make sense, when you add that such bare matter has
> no property of its own?
> Especially when you put some consciousness in it.
If I put consciounsess on it, it is no longer bare.
However, there is no *contradiction* in the idea -- and hence no *hard*
problem.
> It seems to me that
> you are trying to use a "metaphysical notion" just to put in there all
> remaining unsolved fundamental questions.
So are you: the difference is that I know I am,
and I know I must. No amount of mathematics will dodge the
metaphyiscal question. If I am in Plato's heaven, then Plato's
heaven must exist in the same way that I exist ,
whatever that is.
That is the metaphysical quesiton which has not been addressed.
> > For a formalist, there is nothing to numbers except definitions (axoms,
> > etc),. The numbers themselves do not have to exist. So there is
> > still no necessary ontological commitment in CT.
>
>
> OK. In that sense comp does not make any ontological commitment at all.
That is what I have been saying all along!
> "as if" will always be enough, even for the comp-electrons and protons.
> Are you formalist? Could you develop your notion of bare matter in a
> formalistic theory of physics?
If I am formalist about mathematics, that doesn not mean I have
to be formalist about physics. Prima-facie, there is a difference
between
maths and physics.
In physics, you have to *look* -- in maths, you don't.
> What about the "interpretation" of such a theory.
> Note that formalist have no problem with the lobian interview, which
> can indeed be seen as the formal counterpart of the UDA reasoning, but
> I am not sure any mind/body questions addressed in that enterprise
> could make sense to a formalist philosopher.
> I agree with Girard (french logician, discoverer of linear logic) that
> "formalism" in logic is just bureaucracy: it is more harmful than
> useless, imo.
I am nor exaclty a formalist. I am using formalism as an
example of a non-Platonic approach . There are others.
The important point is that nothing is ontologically guaranteed by
comp or CT or AR -- but, for your conclusions, something needs to be.
> >> I said something along such line some times ago. I can provide a
> >> (short) explanation. The reason is the Hilbert-Polya conjecture
> >> according to which the non trivial zero of the complex Riemann Zeta
> >> function could perhaps be shown to stay on the complex line 1/2 + gt,
> >> if it was the case that those zero describe the spectrum of some
> >> quantum operator.
> >
> > The *spectrum* of a quantum operator is not observer-dependent.
> > What is observer-dependent, according to some, is the particular
> > value on the spectrum that is actually observed.
>
>
> Sorry I was (much too much short). We can come back latter on this
> difficult subject. It is a bit out of topics for now.
OK.
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/
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Received on Thu Aug 24 2006 - 20:27:55 PDT