Bruno Marchal wrote:
> I think my discussion with Pete is terminological. When I say "numbers
> exist", Pete seems to think I believe in some magical realm were
> numbers exist in I don't know which sense. But when I say number exist,
> I just mean that the proposition "numbers exists" is true independently
> of myself. I know since a long time that the word "platonist" is
> slightly ambiguous when used by "modern" mathematician, and that is why
> I prefer to say "realism" instead of Platonism.
This is the heart of the disagreement. Of course I agree that 'numbers
exist' is true independent of myself, but for me this just means that I
believe that such 'mathematical objects' - abstracted from other
putative features of what-exists - are instantiated in what-exists
independently of any instantiation of myself. That's all. And I
challenge you to show that this is insufficient for any actual
mathematics that is, has been, or could be practised.
I also prefer to say 'realism', in this case in place of
'Aristotelianism'. And this is the parting of the ways. If we choose to
be 'realist' about numbers, we also choose not to explain them further.
If our 'realism' relates to observables - e.g. my primitive 'figure/
ground reflexivity' - then we have OR (observable arithmetic) derived
from its instantiation in a posited differentiable what-exists. I've
chosen the latter because my intuition favours starting from what is
reflexively manifested. This is clearly not mandatory. But choose we
must, and what is then 'explicable' follows ineluctably from this.
perhaps we should try to
> write shorter post on very specific points. It would help, if only the
> mail boxes :)
I'm trying!
David
> Le 22-août-06, à 23:03, David Nyman a écrit :
>
> > But this suggests to me that comp, in the 'instantiation-free' AR+CT+YD
> > sense, *cannot* be correct, precisely because it makes 'existential'
> > claims for the 'axiomatisation of indexical existence in a 3rd-person
> > way'. The key issue here is surely the distinction between 'existence'
> > and 'truth' as Peter specifies in his post to me.
>
> Comp makes only the assumption that there are numbers (although
> technically it is just about the number 0, and its successor).
>
> The 'axiomatisation of indexical existence in a 3rd person way' is
> "derived from that.
>
> This is a key point.
>
> I think my discussion with Pete is terminological. When I say "numbers
> exist", Pete seems to think I believe in some magical realm were
> numbers exist in I don't know which sense. But when I say number exist,
> I just mean that the proposition "numbers exists" is true independently
> of myself. I know since a long time that the word "platonist" is
> slightly ambiguous when used by "modern" mathematician, and that is why
> I prefer to say "realism" instead of Platonism.
>
> My ontic theory is really no more than Robinson Arithmetic (Q).
> Well to be sure I have more cute ontic theories, like the
> SK-combinators, or like a unique equation for an universal diophantine
> polynomials, etc. Some are more useful than others in some context, but
> they are all equivalent with respect to the derivation of physics from
> numbers.
>
> Your post is long, and I would like to comment Russell still today.
> Will read the rest of your post tomorrow.
>
> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/
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Received on Wed Aug 23 2006 - 10:51:50 PDT