Certainty of outcomes Vs possibility of outcomes?
I'm sill a little new to this whole wiki editing thing so i thought i'd better make it a discussion rather than put my foot in it by changing the page willy-nilly. Where you've written "if P is false, then P → Q is true." would it not be more accurate to say "if P is false, then P → Q may still be true."? after all, if (P), or (P and Q) are both false as per the last two rows in the table, we don't necessarily know that P → Q is true, just that it might be true and that we have insufficient data to rule it out. --Murphy 20:04, 7 November 2009 (CST)
- I think I know where you're going with this...
- Material implication explores the possibility of Q and ¬Q in the presence of P and ¬P.
- Logical implication explores the causative effect of P and ¬P on Q and ¬Q.
- The information and example is attempting to explain both material and logical implication in the context of material implication alone. Thus, the article as a whole could seem to be saying ¬P ⇒ (P ⇒ Q), which is false.
Material Implication Logical Implication P → Q P ⇒ Q P Q Valid P demands Q Valid P causes Q P ¬Q Invalid P prevents ¬Q Invalid P cannot cause ¬Q ¬P Q Valid ¬P allows Q Invalid ¬P is not the cause of Q ¬P ¬Q Valid ¬P allows ¬Q Invalid ¬P is not the cause of ¬Q ¬P allows either Q or ¬Q, but does not cause either.
- In either case, we've shown logically that ¬P cannot be used to establish either Q or ¬Q. Only P can.
- You could explain the difference between the two, and perhaps even include the chart/info I just wrote. Another level of confusion for the already confused creationists :) --Jaban 15:52, 8 November 2009 (CST)