bayes theorem a form of affirming the consequent?

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Reply Mon 17 Aug, 2009 08:32 am
you may know this guy

P(A|B) = = P(A & B) / P(B) = P(B|A) * P(A) / P(B)

P(B|A) * P(A) is reckoned on the right-hand side of the equation, and is sort of equivalent to "A implies B" when its value is close to P(B) (i.e., the closer the ratio of P(B|A) * P(A) / P(B) is to one, the closer it is to true logical implication)

P(A|B) on the left-hand side asks, what is the probability of A given B, implying that the event B has been observed

so putting these pieces together, we've got

A implies B
B
therefore, A

hm, Bayes' theorem is a lot like affirming the consequent isn't it?

maybe I'll go easier on this fallacy in the future, ha
 
vectorcube
 
Reply Mon 17 Aug, 2009 11:59 pm
@odenskrigare,
odenskrigare;83761 wrote:
you may know this guy

P(A|B) = = P(A & B) / P(B) = P(B|A) * P(A) / P(B)

P(B|A) * P(A) is reckoned on the right-hand side of the equation, and is sort of equivalent to "A implies B" when its value is close to P(B) (i.e., the closer the ratio of P(B|A) * P(A) / P(B) is to one, the closer it is to true logical implication)

P(A|B) on the left-hand side asks, what is the probability of A given B, implying that the event B has been observed

so putting these pieces together, we've got

A implies B
B
therefore, A

hm, Bayes' theorem is a lot like affirming the consequent isn't it?

maybe I'll go easier on this fallacy in the future, ha


In is incorrect to think of bayes theory as being like material implication. They are fundamentally different notions.
 
odenskrigare
 
Reply Tue 18 Aug, 2009 12:01 am
@odenskrigare,
they are but they're comparable
 
vectorcube
 
Reply Tue 18 Aug, 2009 12:23 am
@odenskrigare,
odenskrigare;83954 wrote:
they are but they're comparable


No. Material implication operator is a binary relationship between propositions with truth values.


The probability of P(A) is such that A is an event. It does not have truth values.


P(A) is a number between 0, and 1, but it does not have true values.


One can model material implication and conditional probability using "counterfactual conditions over possible worlds".
 
odenskrigare
 
Reply Tue 18 Aug, 2009 12:41 am
@vectorcube,
vectorcube;83958 wrote:
No. Material implication operator is a binary relationship between propositions with truth values.


The probability of P(A) is such that A is an event. It does not have truth values


yes but if you're close to 0 or 1 you approximate truth or falsehood

I'm not saying they're the same

I'm saying they're similar in some respects

I actually managed to find a paper which says what I am saying backwards:

SpringerLink - Journal Article

affirming the consequent is a degenerate form of Bayes

I wish I could read the whole thing though, maybe I can find it under the UB library database but I feel too lazy to log in atm and even if I did I could get in deep **** if I just copy pasta'd the contents of the article, so I'd have to summarize, too

looks interesting though

I'd like to hear your thoughts first
 
 

 
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