[FOM] Truth and existence
Alex Blum
Alex.Blum at biu.ac.il
Sat Jul 16 16:31:43 EDT 2011
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'.
Alex
----- Original Message -----
From: "Richard Heck" <rgheck at brown.edu>
To: "Foundations of Mathematics" <fom at cs.nyu.edu>
Sent: Saturday, July 16, 2011 12:46 AM
Subject: Re: [FOM] Truth and existence
> 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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