Bruno,
there is a lot of wisdom in your post. Your last sentence, however, may
apply to that wisdom as well I am afraid.

"...I have to assume that [such] truth are not dependent of me,..." -
nor on anything else we may know of. I stay clear of 'truth' which is
applied in whoever's theory - as 'his' truth.
I am in trouble with the "Church Thesis", it seems to be anchored in the *math
of functions* and applied to *comp.science*. (BTW "recursive functions"
pointing back to themselves? a restriction into what has been known
(already)?  I may have the wrong idea (if any) about the Ch-Th of course.)
It may be 'fundamental' in - what I consider - a segment of the totality.

I can accept the 'universal machine' as not restricted to mathematical comp,

it definitely should not apply those binary-slanted algorithms. I consider
it as
some analogue 'think-tank' beyond our present terms. Whatever I would try to
characterize it with, is MY restriction to its unlimited capabilites. So I
don't.

Bruno, is your own restriction  concentrated to 'physics' with 'math' as in:
("All theories in physics use at least that arithmetical fragment....")?
I love your extension of 'metaphors' (bosons) into galaxies and brains. They
certainly are, included into our presently valid "perceived reality" of
figments.

"Scientists do not commit themselves ontologically...."
Most - (especially the conventional ones) do. I find it a restriction of the
total into the so far experienced portion - even  to the *adjusted format of
those* - serving as the 'entirety this 'ontology' is based on.  I would love
to device an ontology for the 'totality' - that would explain lots of
questionmarks we still have in our ignorance (the how-s, why-s, and the
other 1000 to be modest).
I am not sure about the 'excluded middle' since that is excluded from a mere
segment we consider 'them all' while the entire set may include quite
another *middle*. (My usual objection against statistical conclusions and
probabilities of course, that are mere illusions of our human ways of
anticipatory thinking).

I intended this reflection to be 'positive' to your ideas, as considered
them in more ways than just 'arithmetically based' (numbers?).

John





On Fri, Sep 4, 2009 at 5:12 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:

>
>
> On 04 Sep 2009, at 19:21, Flammarion wrote:
>
> > ...  Bruno has been arguign that numbers
> > exist because there are true mathematical statements asserting their
> > existence. The counterargument is that "existence" in mathematical
> > statements is merely metaphorical. That is what is being argued
> > backwards
>
>
>
> I have never said that numbers exists because there are true
> mathematical statements asserting their existence.
>
> I am just saying that in the comp theory, I have to assume that such
> truth are not dependent of me, or of anything else. It is necessary to
> even just enunciate Church thesis. A weakening of Church thesis is 'a
> universal machine exists".  In the usual mathematical sense, like with
> the theorem asserting that 'prime numbers exists.
>
> I just make explicit that elementary true arithmetical statements are
> part of the theory. You are free to interpret them in a formlaistic
> way, or in some realist way, or metaphorically. The reasoning does not
> depend on the intepretation, except that locally you bet you can 'save
> your relative state' in a digital backup, for UDA. And you don't need
> really that for the 'interview' of the universal machine.
>
> All theories in physics uses at least that arithmetical fragment. But
> fermions and bosons becomes metaphor, with comp. May be very fertile
> one. Like galaxies and brains.
>
> Scientist does not commit themselves ontologically. They postulate
> basic entities and relations in theories which are always
> hypothetical. I am just honest making explicit my use of the non
> constructive excluded middle in the arithmetical realm.
>
> You get stuck at step zero by a bullet you are ntroducing yourself, I
> 'm afraid.
>
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
>
> >
>

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