[FOM] Truth and existence

[Richard Heck]

On 07/15/2011 03:33 AM, Alex Blum wrote:
> Arnon writes:
> >
>> I am sorry, but I do not see the difference between the claim that
>> one can believe in the objective truth of arithmetic without also
>> believing in the existence of numbers, and the claim that
>> one can believe in the objective truth of the stories of the Greek
>> mythology without also believing in the (past) existence of the Greek
>> gods.
>> I certainly miss something here.
>
> Numbers do not enter into real or putative causal relations, the Greek
> gods do.
>
I'm fairly sure Arnon's question was not "What differences are there
between numbers and Greek gods" but rather: What *relevant* differences
are there between numbers and Greek gods? The fact that Greek gods
putatively enter into causal relations looks like a good reason to think
their existence, and facts about them, can be verified or refuted in
certain ways, whereas facts about numbers cannot be verified or refuted
in those ways. It does not, prima facie, look like any kind of reason to
think that one can believe existential claims about numbers---e.g., that
there is a prime number between 5 and 10, that every polynomial has a
complex root, etc---without believing that there are numbers.

And yes, I've already read Carnap.

Richard


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