<p>On Aug 15, 2012 3:21 AM, "wren ng thornton" <<a href="mailto:wren@freegeek.org">wren@freegeek.org</a>> wrote:<br>
> It's even easier than that.<br>
><br>
> (forall a. P(a)) -> Q <=> exists a. (P(a) -> Q)<br>
><br>
> 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.</p>
<p>Most of this conversation is going over my head. I can certainly see how exists a. (P(a)->Q) implies that (forall a. P(a))->Q. The opposite certainly doesn't hold in classical logic. What sort of logic are you folks working in?</p>