# Talk:Implication

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(Certainty of outcomes Vs Probability of outcomes?) |
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− | ==Certainty of outcomes Vs | + | ==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. | 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. | ||

+ | |} | ||

+ | |||

+ | :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 :) --[[User:Jaban|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 (¬P allowes ¬Q) a completely separate issue to the truth of the original statement that (P → Q). | ||

+ | |||

+ | ::As far as i can see, (¬P allows ¬Q) would be similar to (¬fruitbowl allows ¬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. (¬P allows ¬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 (¬P cannot be used to establish either Q or ¬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.--[[User:Murphy|Murphy]] 17:12, 8 November 2009 (CST) | ||

+ | |||

+ | :::If I can summarize what you're thinking: | ||

+ | |||

+ | :::'''If '¬P ⇒ Q' is false, that doesn't speak about 'P ⇒ Q'. So if ¬P don't we automatically lose the ability to speak about 'P ⇒ 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 ⇒ +Q? | ||

+ | | yes | ||

+ | |- | ||

+ | | true | ||

+ | | false | ||

+ | | Does +P ⇒ ¬Q? | ||

+ | | no | ||

+ | |- | ||

+ | | false | ||

+ | | true | ||

+ | | Does ¬P ⇒ +Q? | ||

+ | | no | ||

+ | |- | ||

+ | | false | ||

+ | | false | ||

+ | | Does ¬P ⇒ ¬Q? | ||

+ | | no | ||

+ | |} | ||

+ | |||

+ | :::But that's not necessary. P and Q are containers for values, not values themselves. "Does P ⇒ 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.--[[User:Jaban|Jaban]] 21:40, 12 November 2009 (CST) |

## Latest revision as of 12:56, 15 January 2011

## 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)

- 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 (¬P allowes ¬Q) a completely separate issue to the truth of the original statement that (P → Q).

- As far as i can see, (¬P allows ¬Q) would be similar to (¬fruitbowl allows ¬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. (¬P allows ¬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 (¬P cannot be used to establish either Q or ¬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 '¬P ⇒ Q' is false, that doesn't speak about 'P ⇒ Q'. So if ¬P don't we automatically lose the ability to speak about 'P ⇒ Q'?**

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

Logical Implication P Q Question Answer true true Does +P ⇒ +Q? yes true false Does +P ⇒ ¬Q? no false true Does ¬P ⇒ +Q? no false false Does ¬P ⇒ ¬Q? no

- But that's not necessary. P and Q are containers for values, not values themselves. "Does P ⇒ 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)