I just read an interesting paper by Stephen Hetherington that was entirely too long and complicated, my guess is that I can summarize what he said in about one page.
He notes that Cartesian argument can be broken down to this:
Let p= “You are wearing pants”
Let S(p)= It seems to you that p
Let K(S(p))= It is known to you that (S(p))
Let d= you are dreaming
- K(p)->K(~d) (definition of Cartesian skepticism)
- K(p)->K(~(S(p)&~p)) (definition of dream)
- K(p)->K(~S(p)v~~p) (DeMorgan’s Theorm)
Now a Cartesian skeptic will grant us that S(p) so we can get rid of one of those disjuncts in 3… so we are left with ~~p which, of course, reduces to p. So now our argument looks like this:
- K(p)->K(~d) (definition of Cartesian skepticism)
- K(p)->K(~(S(p)&~p)) (definition of dream)
- K(p)->K(~S(p)v~~p) (DeMorgan’s Theorm 2)
- S(p) (Disjunctive Syllogism 3)
.: K(p)->K(p)
And that seems trivially true.
There we go, a 15 page paper summed up in a couple lines… who needs professional philosophers?
I don’t think that this “shatters” a cartesian argument as the title of the article implies, but I thought it was interesting nevertheless.