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)
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:I think I know where you're going with this...
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:'''Material implication''' explores the possibility of Q and ¬Q in the presence of P and ¬P.
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:'''Logical implication''' explores the causative effect of P and ¬P on Q and ¬Q.
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: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.
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:{| class="wikitable"
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| colspan="2" |
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| colspan="2" | '''Material Implication'''
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| colspan="2" | '''Logical Implication'''
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|-
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! colspan="2" |
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! P → Q
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!
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! P ⇒ Q
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!
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|-
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| P
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| Q
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| '''Valid'''
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| P demands Q
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| '''Valid'''
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| P causes Q
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|-
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| P
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| ¬Q
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| '''Invalid'''
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| P prevents ¬Q
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| '''Invalid'''
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| P cannot cause ¬Q
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|-
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| ¬P
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| Q
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| '''Valid'''
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| ¬P allows Q
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| '''Invalid'''
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| ¬P is not the cause of Q
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|-
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| ¬P
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| ¬Q
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| '''Valid'''
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| ¬P allows ¬Q
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| '''Invalid'''
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| ¬P is not the cause of ¬Q
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|-
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| colspan="6" style="text-align: center; font-size: 80%" | ¬P allows either Q or ¬Q, but does not cause either.
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|}
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:You could explain the difference between the two, and perhaps even include the chart/info to what I just wrote.
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: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)
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