15 Aug
2012
15 Aug
'12
3:20 a.m.
On 8/13/12 9:25 PM, Jay Sulzberger wrote:
I did suspect that, in some sense, "constraints" in combination with "forall" could give the quantifier "exists".
It's even easier than that. (forall a. P(a)) -> Q <=> exists a. (P(a) -> Q) Where P and Q are metatheoretic/schematic variables. This is just the usual thing about antecedents being in a "negative" position, and thus flipping as you move into/out of that position. The duality mentioned previously is just for the case where you don't have that handy "-> Q" there. How do we get the universal quantifier into a negative position when there's no implication? Why, we add an implication, of course. Even better, add two. -- Live well, ~wren