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

From: Paul Holbach (paulholbachSPAMBAN_at_freenet.de)
Date: 02/22/05 

Date: 21 Feb 2005 22:43:31 -0800

> robert j. kolker wrote:
> > Paul Holbach wrote:

> > "For all x, if x is a triangle, then x has three sides."
> >
> > This is an analytic truth, which in no way
> > implies the existence of triangles.

> If x is Cerebus, then x has four legs.
> Since Cerebus is a dog and dogs
> have four legs (barring accidents of course) it follows.
>
> So it is analytically true that Cerebus has four legs.

No, it isn´t.

First of all, "Cerberus" is not a predicate/concept like "triangle" but
a proper noun.
So you cannot simply substitute it for a predicate constant such as
"F".

What you may do is create the predicate "identical to Cerberus":

"For all x, if x is identical to Cerberus, then x has four legs."

But this alone doesn´t suffice, because we still have to specify what
kind of thing Cerberus would be (if it existed):

"For all x, if x is identical to the dog called 'Cerberus', then x has
four legs."

This sentence may be regarded as true, there being no need for the
existence of Cerberus.

Regards
PH

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