Re: Exception to the rule? (Tarski´s T-scheme)

From: Paul Holbach (paulholbachSPAMBAN_at_freenet.de)
Date: 06/23/04 

Date: 23 Jun 2004 08:01:55 -0700

> Aatu Koskensilta <aatu.koskensilta@xortec.fi> wrote in message news:<
> aEaCc.2565$se1.423@reader1.news.jippii.net>...
> > Acid Pooh wrote:

> > Wait... you couldn't prove AxP(x) -> ExP(x) without assuming that
> > something exists? It seems like it would be vacuously true in the
> > case that nothing existed.

 
> AxP(x) is vacuously true in case there are no objects, but ExP(x) is
> obviously false, so AxP(x) -> ExP(x) does not hold in case nothing exists.

If ~ExE!x, then for every formula of the form "Ex(...x...)", 0 e "Ex(...x...)".
Existential generalization is not possible in the empty domain.

PH

Quantcast