Re: reductio ad falsum versus reductio ad absurdum

"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.

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

.