# Talk:Implication

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(Whoops, i think i meant possibility not probability) |
(→Certainty of outcomes Vs possibility of outcomes?) |
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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. | 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. --[[User:Murphy|Murphy]] 20:04, 7 November 2009 (CST) | 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. --[[User:Murphy|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. | ||

+ | |||

+ | :{| class="wikitable" | ||

+ | | colspan="2" | | ||

+ | | colspan="2" | '''Material Implication''' | ||

+ | | colspan="2" | '''Logical Implication''' | ||

+ | |- | ||

+ | ! colspan="2" | | ||

+ | ! 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 | ||

+ | |- | ||

+ | | colspan="6" style="text-align: center; font-size: 80%" | ¬P allows either Q or ¬Q, but does not cause either. | ||

+ | |} | ||

+ | |||

+ | :You could explain the difference between the two, and perhaps even include the chart/info to what I just wrote. | ||

+ | |||

+ | :Another level of confusion for the already confused creationists :) --[[User:Jaban|Jaban]] 15:52, 8 November 2009 (CST) |

## Revision as of 16:52, 8 November 2009

## 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.

- You could explain the difference between the two, and perhaps even include the chart/info to what I just wrote.

- Another level of confusion for the already confused creationists :) --Jaban 15:52, 8 November 2009 (CST)