Re: Natural deduction?


G. Frege wrote:
> On 09 Nov 2005 10:50:45 +0100, Torkel Franzen <torkel@xxxxxxxxxx> wrote:
>
> >
> > A fine example of the awful effects that a study of Copi's system
> > may have is given by the following derivation of N&P->O from N->O
> >
> > 1. N -> O [assumption (i.e., premise)]
> > 2. (N -> O) v ~P [from 1, Add.]
> > 3. ~P v (N -> O) [from 2, Com.]
> > 4. P -> (N -> O) [from 3, Impl.]
> > 5. (P & N) -> O [from 4, Exp.]
> > 6. (N & P) -> O [from 5, Com.]
> >
> > This is described as an elegant and simple derivation by Keith
> > Burgess-Jackson (co-author with Copi of _Informal Logic_).
> >
>
> Remindes me of the famous quote:
>
>
> "It is practically impossible to teach good programming style
> to students that have had prior exposure to BASIC: as potential
> programmers they are mentally mutilated beyond hope of
> regeneration."
>
> (Edsger Dijkstra)
>
>
> One might consider the following variant:
>
>
> "It is practically impossible to teach good proving style
> to students that have had prior exposure to Copi's system:
> as potential logicians they are mentally mutilated beyond
> hope of regeneration."
>
> (G. Frege)
>

Whether that analogy applies depends on what you think makes a system
of natural deduction good, IOW what one wants to achieve with one..

If one's aim is to use nd to formalize the inferences of informal
reasoning, then a system like Copi's would work best. If OTOH (as per

your analogy) one's aim is to train people to reason in a certain
'style' only, then a system like Gentzen's would clearly be better. .




> F.

.

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