Re: Newbie logic questions
- From: Chris Menzel <cmenzel@xxxxxxxxxxxxxxxxxxxx>
- Date: Mon, 19 May 2008 06:52:17 +0000 (UTC)
On Sat, 17 May 2008 06:15:08 -0700 (PDT), priscila
<priscila.gutierres@xxxxxxxxx> said:
I am studing math logic and i found something I think its very
strange.
Why if p is false and q true, p => q is true? it seems very strange
this assertation for me.
Suppose I told you: If you water my plants while I'm gone, I'll take
you to dinner when I get back. Under what conditions, upon my return,
can you say that I lied, that what I said was not true? Obviously I
lied if you in fact watered my plants but I didn't take you to dinner as
promised. But what if you didn't water my plants and I took you to
dinner anyway, just because I like you? Does that make me a liar?
Pretty clearly not; hence, what I said remains true.
I think that one false proposition can't imply a true one.
Well, there are much stronger notions of implication than the truth
functional notion of material implication discussed above, notably,
entailment, where p entails q iff, *necessarily*, p->q. Thus, it is not
enough to count "p entails q" true if p just happens to be false and q
just happens to be true. We have to consider what q's true value would
have been under any conditions in which p would have been true.
You can find a lot more about the issue you are raising by googling
"paradoxes of material implications".
.
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