On 16 Sep, 12:54, David Nyman <david.ny...@gmail.com> wrote:
> 2009/9/16 Flammarion <peterdjo...@yahoo.com>:
> >> I find that I can't real say what the difference is supposed to be
> >> between numbers existing mathematically and numbers existing
> >> Platonically, other than that different labels are being used. What
> >> precisely is the latter supposed to entail that the former does not,
> >> and what difference is this supposed to make? Can you help, Peter?
> > Existing mathematically doesn't have any ontoloigcal meaning.
> > Both formalists and Platonists can agree that 7 exists,
> > since they agree Ex:x=7 is true, but only the latter think
> > 7 has Platonic existence.
> Yes, but I still don't see what difference the word 'ontological'
> makes in this context. Surely whatever world-conjuring power numbers
> may possess can't depend on which label is attached to them?
The knowabilitry of a claim about what powers numbers
have can only depend on what labels are correctly attached.
Petrol is not flammable just becaue I attached the label
"flammable" to it. Petrol *Is* flammable, and that
makes the label-attachment correct.
> If a
> mathematical scheme fulfils a deep enough explanatory role (a moot
> point I admit) isn't that 'ontological' enough?
If you are claiming that the *existence* of numbers
would explain somehting empierica;, that is an abductive
argument for Platonism. Other than that sayign "Numbers
explain" is too vague. Numbers are often used to
explain things about other numbers. So what,
says the formalist, none of them exist and such
explanations are nothing but moves in a game.
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