Sorry for the comment delay.
Le 23-oct.-06, à 16:49, David Nyman a écrit :
> Bruno Marchal wrote:
>>> As usual, the truth of a mathematical existence-claim does not
>>> prove Platonism.
>> By Platonism, or better "arithmetical realism" I just mean the belief
>> by many mathematician in the non constructive proof of "OR"
> Lest we go yet another round in the 'reification' debate, is it not
> possible to reconcile what is being claimed here?
> Bruno, I'm assuming that when you eschew 'Platonic existence' for AR,
> you are thereby saying that your project is to formalise certain
> arguments about the logical structure of possibility - and through
> this, to put actuality to the test in certain empirical aspects.
Yes. Although people are so often wrong on what "formalization"
consists in, that I prefer to say that I just interview a machine.
> Questions of how this may finally be reconciled with 'RITSIAR' (I hope
> you recall what this means) are in abeyance.
I don't recall what RITSIAR means. Nor BU.
> Nevertheless, some aspect
> of this approach may ultimately be ascribed a status as 'foundational
> existent' analogous to that of 'primary matter' in materialism.
I don't think so. This would lead to a reification of numbers, which I
think is just a little bit less meaningless than reifying matter. But
still fundamentally wrong.
> Alternatively, such a hypothesis may be shown to be redundant or
Not really. It is SWE which should be made redundant.
> Peter, as we've agreed, materialism is also metaphysics, and as a route
> to 'ultimate reality' via a physics of observables, is vulnerable to
> 'reification'. Might it not be premature to finalise precisely what it
> is that physical theory decribes that might actually be RITSIAR? You
> may be tempted to respond, Johnsonianly, that it is precisely the world
> that kicks back that is RITSIAR, but theoretical physics and COMP are
> both in the business of modelling what is not so directly accessible.
> This notwithstanding that we may believe one or other theory to be
> further developed, more widely accepted, or better supported
> empirically. Or is there some irreducible sense in which 'primary
> matter' could be deemed to exist in a way that nothing else can?
Note that "consciousness" can be deemed to exist in a way that nothing
else can. In particular "consciousness of numbers".
But "Primary Matter", Ether, Phlogiston, Vital Principle, .... I doubt
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