Re: reductio ad falsum versus reductio ad absurdum

adamgolding@xxxxxxxxx writes:

> the => means |-, here?

We don't need to take => to refer to provability in any formal calculus.
Just read G=>A as "A follows from G". The rule

G,A => B
--------
G => A->B

then allows us to conclude, given that B follows from G together with
A, that A->B follows from G.

> so, by this line of thinking, saying that CP is
>
> (P |- Q) |- (P -> Q)
>
> makes a lot of sense to me--although i gather from the responses that
> there is something wrong with this--although i don't quite gather
> what--is there something formally/techincally wrong? is it false?

To make good sense of the above, you need to specify the language
you use and how |- is to be understood.

> >
> > ~A => Q ~A => ~Q
> > -------
> > => A
>
> Allen & Hand call the above rule "Impossible Antecedent", and they lump
> all the rest under RAA...

"Impossible Antecedent" is not standard terminology. But the
important thing is that indirect proof is not constructively
valid, but constructive reductio is.

> ok, so with RAA often being used as an umbrella term, 'constructive
> reductio' makes it clear that one means the one with no premises.

Here I don't see what you have in mind.

> there another specifying term in somewhat common parlance to specify
> the other kind, i.e. not constructive reduction, not impossible
> antecedent, but the one i called 'reductio ad falsum' ??

Not that I know of.

.