Talk:Implication

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m (Talk:Biconditional (if and only if) moved to Talk:Implication: finally moving this again -- vast majority of article is not about biconditional)
 
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::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.
 
::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 Q was in this case caused by X, but that doesn't necessarily mean Q isn't also caused by P. 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.
+
::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)
 
::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)
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:::If I can summarize what you're thinking:
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 +
:::'''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'?'''
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:::My answer is that we ARE asking what you think we should be. You could rewrite the table like this:
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:::{| class="wikitable"
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! 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.
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:::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)
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