2009/9/16 Flammarion <peterdjones.domain.name.hidden>:
> 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.
Yes, but 'flammable' and 'exists' are horses of different colours,
surely. You and Bruno are disputing whether mathematics is a formal
abstraction from physics or vice versa. But in either case this seems
to me fundamentally a question of methodological, not ontic, priority.
We cannot hope to have any final criterion for what is really real;
rather we search for the deepest theory we can find, one that can
explain whatever we are currently persuaded needs explaining, and in
terms of which we are able to subsume subsidiary theories. Then we
feel justified in saying that our theory describes what exists. Isn't
that about the size of it?
David
>
>
>
> On 16 Sep, 12:54, David Nyman <david.ny....domain.name.hidden> wrote:
>> 2009/9/16 Flammarion <peterdjo....domain.name.hidden>:
>>
>> >> 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 07 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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Received on Thu Sep 17 2009 - 00:52:17 PDT