> My main problem with the whole concept is that it seems to require one to
> abandon the *extremely* useful notion of "reductio ad absurdum." That is, I
> can't prove A simply by proving ~ [~A] (i.e., assuming ~A and showing that
> leads to a contradiction. Seems too much to give up.
No, you just introduce another tool for looking at problems, you don't
have to give up the old ways since they apply in their own domain. After
all, we still use the real numbers after we have learned about the
complex numbers, don't we?
Besides, RAA is not universally accepted (the Intuitionists don't use it)
and often just a convenient and natural trick - which sometimes don't
work.
-----------------------------------------------------------------------
Anders Sandberg Towards Ascension!
nv91-asa@nada.kth.se http://www.nada.kth.se/~nv91-asa/main.html
GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y