Re: reductio ad falsum versus reductio ad absurdum


Torkel Franzen wrote:
> "futurist" <adamgolding@xxxxxxxxxxxxxxx> writes:
>
> > these two modes of reasoning seem fundamentally different to me, and
> > thus seem to deserve separate names in ND, which is supposed to model
> > natural reasoning, after all.
>
> But we use exactly the same rules in proving results of the form
> G=>~A and in proving results of the form =>~A.
>
> > PS however, i'm a little confused as to what distinguishes a
> > constructive from a nonconstructuve reductio
>
> Just examine the form of the rules. They are not the same.
>
> Constructive reductio:
>
> G,A => Q G,A => ~Q
> --------------------
> G => ~A
>
> Indirect proof:
>
> G,~A => Q G,~A => ~Q
> ----------------------
> G => A
>
>
> Constructive reductio always leads to a conclusion G => ~A. Indirekt
> proof yields a conclusion G => A where A can have any form.

does A have to be atomic in the first case?


> For example, you need to use an indirect proof to prove => pv~p.

if A is not atomic, couldn't you have any number of '~' symbols
'inside' the A? (i.e. in the wff that A represents?)

.