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
Your post is long, and I would like to comment Russell still today.
Will read the rest of your post tomorrow. perhaps we should try to
write shorter post on very specific points. It would help, if only the
mail boxes :)
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