Re: Help with a problem

On Wed, 23 Nov 2005, George Dance wrote:
> William Elliot wrote:
> > On Wed, 23 Nov 2005, Robert Zimmerman wrote:
> > > Chris Menzel <cmenzel@xxxxxxxxxxxxxxxxxxxx> wrote:
> > >
> > > > On Wed, 23 Nov 2005 04:49:35 GMT, Robert Zimmerman <rfz1@xxxxxxxxxxxx> said:
> > > > > I'm am learning logic from Copi's book (as a hobby). There is an
> > > > > advanced problem:
> > > > >
> > > > > With the rules of inference, prove the validity of:
> > > > >
> > > > > A
> > > > > therefore B v ~B
> > > > >
> > > > > I am horribly stuck. Any help would be appreciated. I'm losing sleep.
> > > >
> > > > What rules of inference do you have available?
> > >
> > > The "19 rules of inference" from Copi's book "Intro to Logic" (that's
> > > the short answer). i.e. mp, mt, hs, ds, cd, etc etc.
> > >
> > Huh? mp is MP, modus ponens?
>
> Yes. mp is modus ponens, mt is modus tollens, hs is hypothetical
> syllogism, cd is constructive dilemma, etc., etc. Those are all
> standard abbreviations for standard nd rules.
>
Dang if I ever learn them, nor have they been of any notice in the texts
I've studied. However, locating mothers 87 year text book "Essentials of
Formal Logic", I find some mentions of Modus ponendo tollens and Modus
tollendo ponens. That's about all so far. Have you see mpt and mtp
before?

> > Here's natural deduction proof with classical negation
> > leaving reasons, rules and references for the reader.
> >
> > assume ~(p v ~p)
> > (p v ~p) -> f
> > assume p
> > p v ~p
> > f
> > p -> f
> > ~p
> > p v ~p
> > f
> > ~(p v ~p) -> f
> > p v ~p
>
>
.