Talk:Implication

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 &not;Q in the presence of P and &not;P.


 * Logical implication explores the causative effect of P and &not;P on Q and &not;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 &not;P &rArr; (P &rArr; Q), which is false.


 * {| class="wikitable"

! colspan="2" | ! P &rarr; Q ! ! P &rArr; Q !
 * colspan="2" |
 * colspan="2" | Material Implication
 * colspan="2" | Logical Implication
 * P
 * Q
 * Valid
 * P demands Q
 * Valid
 * P causes Q
 * P
 * &not;Q
 * Invalid
 * P prevents &not;Q
 * Invalid
 * P cannot cause &not;Q
 * &not;P
 * Q
 * Valid
 * &not;P allows Q
 * Invalid
 * &not;P is not the cause of Q
 * &not;P
 * &not;Q
 * Valid
 * &not;P allows &not;Q
 * Invalid
 * &not;P is not the cause of &not;Q
 * colspan="6" style="text-align: center; font-size: 80%" | &not;P allows either Q or &not;Q, but does not cause either.
 * }
 * Invalid
 * &not;P is not the cause of &not;Q
 * colspan="6" style="text-align: center; font-size: 80%" | &not;P allows either Q or &not;Q, but does not cause either.
 * }
 * }


 * In either case, we've shown logically that &not;P cannot be used to establish either Q or &not;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)


 * I think i kind of get it, but even by that definition of material implication (as in not a causal link), isn't the truth of the statement (&not;P allowes &not;Q) a completely separate issue to the truth of the original statement that (P → Q).


 * As far as i can see, (&not;P allows &not;Q) would be similar to (&not;fruitbowl allows &not;apple) which isn't necessarily false, but it doesn't really tell us anything about the truth of the statement (fruit bowl → apple). I just don't see how based on (particularly in row four) insufficient data, you can't make a definitive claim about the truth of statement (P → Q) one way or the other.


 * Likewise in the logical implication side of your table, the last two rows don't necessarily invalidate the statement that (P ⇒ Q). In row three, perhaps in this case Q was in this case caused by X, but that doesn't necessarily mean Q can't also caused by P (when p occurs). And in row four we have the same problem. Insufficient data to say one way or the other. You could could make the same statement as in the material implication. (&not;P allows &not;Q), but that doesn't necessarily tell us whether (P ⇒ Q) is actually true or false.


 * I guess what I'm getting at is that if we've shown logically that (&not;P cannot be used to establish either Q or &not;Q. Only P can), then how can we make any True, false, valid, or invalid claims about the statements (P → Q) or (P ⇒ Q) based on the last two rows of the table. Shouldn't they read "insufficient data" or "unknown" or something (@_@?) Sorry, i don't mean to be an ass or anything, I'm just not quite seeing it.--Murphy 17:12, 8 November 2009 (CST)


 * If I can summarize what you're thinking:


 * If '&not;P &rArr; Q' is false, that doesn't speak about 'P &rArr; Q'. So if &not;P don't we automatically lose the ability to speak about 'P &rArr; Q'?


 * My answer is that we ARE asking what you think we should be. You could rewrite the table like this:


 * {| class="wikitable"

! colspan="4" | Logical Implication !P !Q !Question !Answer
 * true
 * true
 * Does +P &rArr; +Q?
 * yes
 * true
 * false
 * Does +P &rArr; &not;Q?
 * no
 * false
 * true
 * Does &not;P &rArr; +Q?
 * no
 * false
 * false
 * Does &not;P &rArr; &not;Q?
 * no
 * }
 * false
 * Does &not;P &rArr; &not;Q?
 * no
 * }


 * But that's not necessary. P and Q are containers for values, not values themselves. "Does P &rArr; Q?" means "Does the value of P in this case imply the value of Q in this case?" It does not dictate the values as positive.


 * I totally mistook what you were getting at there, but I think that point (logical versus material) needs to be addressed.--Jaban 21:40, 12 November 2009 (CST)