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?)
>> 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".
The move toward formalism does not work for any theory of formal
system. This is a consequence of Godel's incompleteness.
I don't believe the formalistic philosophical position can even make
sense of notion like "yes doctor". 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.
> 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?
Does "matter-as-bare substance" violate Bell's inequality?
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. It seems to me that
you are trying to use a "metaphysical notion" just to put in there all
remaining unsolved fundamental questions.
> 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.
"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?
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 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.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Thu Aug 24 2006 - 05:22:18 PDT