[FOM] Truth and existence

[Richard Heck]

On 07/16/2011 04:31 PM, Alex Blum wrote:
> To Arnon and Richard,
>
> If numbers have no causal effects, their non existence may not be
> missed in giving an account of the world. I presume physics does not
> assume that numbers exist. Greek mythology without the Greek gods
> cannot be true. One might argue that one cannot do arithmetic without
> assuming that numbers exist. But this only says that 'If you do
> arithmetic then you have to assume that numbers exist', but not that
> 'If you do arithmetic then numbers exist'.
>
Physics assumes the truth of much of mathematics, or so it would
certainly appear. If so, then physics makes and uses existential
mathematical claims all the time, and so assumes that numbers exist.

It has been argued, of course, by Hartry Field that one could give a
complete account of the world without using mathematics, but, when I
last checked in, the general view was against. But that was not the
issue, as I understood it.

Of course nothing follows about the existence of numbers from our
mathematical practice. Nor, however, does it follow from the fact that
anyone does biology that viruses exist. What is true is only that
viruses exist if the claims of biology are true. So if you believe the
claims of biology, then you ought to believe that there are viruses. And
we are insisting that numbers exist if the claims of arithmetic are
true. So if you do arithmetic, you ought to believe that there are
numbers. There is no disanalogy here.

And, I might add, Carnap would not have seen one, either. Metaphysical
claims, for Carnap, were all on a par, whether they were about numbers
or viruses or quarks.

Richard

-- 
-----------------------
Richard G Heck Jr
Romeo Elton Professor of Natural Theology
Brown University