Re: In the empty domain:

From: Jim Spriggs (jim.sprigs_at_ANTISPAMbtinternet.com.invalid)
Date: 02/21/05 

Date: Mon, 21 Feb 2005 15:55:40 +0000 (UTC)

Paul Holbach wrote:
>
> > Jim Spriggs wrote:
> > > Owen wrote:
>
> > > Ax(Fx) -> Ex(Fx) is tautologous, for all domains,
> > > including the empty
> > > domain.
>
> > If you're interested in logic in which the domain
> > of quantification may
> > be empty, you should consider free logic.
>
> Even in free logic all formulas of the type "Ex(...x....)" are false
> due to there being nothing in the empty domain by definition.
>
> Furthermore:
> "The label 'free logic' is shorthand for 'logic free of existence
> assumptions with respect to its general and singular terms, but whose
> quantifiers are interpreted exactly as in classical first order
> predicate logic'."
> [Lambert, Karel (1997). /Free Logics/. Sankt Augustin: Academia. (p.
> 35)]

Absolutely! My point was merely that, since FOL doesn't consider empty
domains, Owen might like to look at logics which do. Will those that do
serve his purpose? I know not.

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