Re: Existence of mathematical entities (Re: Successor Axiom: on what grounds TF?)

From: Paul Holbach (paulholbachSPAMBAN_at_freenet.de)
Date: 02/23/05 

Date: 22 Feb 2005 15:10:23 -0800

> Mitch Harris wrote:
> > Paul Holbach wrote:

> > Certainly not!
> > The topic <referential vs. irreferential singular terms>
> > is independent
> > of the topic
> > <realist vs. anti-realist philosophies of mathematics>.

> What do you mean by "certainly not"? That's pretty much what Eray
> said, existence does not follow/does not depend on reference. So are
> you disagreeing with him or not?

Let ">->" symbolize the relation of reference:

("a" >-> a) <-> Ex("a" >-> x)

In words:

"a" refers to a iff there is something x such that "a" refers to x.

That is to say, the reference relation holds if and only if both
relata, the singular term and the referent, exist. There is no such
thing as genuine reference to nonexistents.

Regards
PH

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