Guest Posted October 15, 2010 Report Share Posted October 15, 2010 If an event T is a tautology, then P[T] = 1 (e.g. T = I am myself) If an event C is a contradiction, then P[C] = 0 (e.g. C = an empty cup is full) What is the probability of a tautology given a contradiction? i.e. What is P[T|C]? So..... What is the probability that I am myself given that an empty cup is full? What would Bayes say? What is the probability that the universe exists given that the statement "this statement is false" is true? If the event p is a paradox, then what are: P[T|p] ? P[C|p] ? P[p|T] ? P[p|C] ? P[p|p] ? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 15, 2010 Report Share Posted October 15, 2010 as logic shows 'a contradiction implies everything'..So, to say (a&-A) --> (b v-b) is a tautology in itself. But so is the entailment (a&-a) --> (b&-b) The probability of a tautology given a contradiction is whatever, so there ios no contradiction to say that the probability of a tautology given a contradiction is 1 The same, though, holds true for the expression the probability of a tautolgy given a contradiction is 0 or 0,1.....0,2.....0.3 ....etc. ad infinitum Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 15, 2010 Report Share Posted October 15, 2010 as logic shows 'a contradiction implies everything'..So, to say (a&-A) --> (b v-b) is a tautology in itself. But so is the entailment (a&-a) --> (b&-b) The probability of a tautology given a contradiction is whatever, so there ios no contradiction to say that the probability of a tautology given a contradiction is 1 The same, though, holds true for the expression the probability of a tautolgy given a contradiction is 0 or 0,1.....0,2.....0.3 ....etc. ad infinitum So are you saying that the probability of anything given a contradiction is undefined? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 15, 2010 Report Share Posted October 15, 2010 So are you saying that the probability of anything given a contradiction is undefined? it is undefined... So logic dictates. Your question raises automatically what in logic is called 'the paradox of material implication', i.e. that from a contradiction everything can happen But because in fact no contradiction can hold, the theoretical paradox is cancelled Quote Link to comment Share on other sites More sharing options...
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Guest
If an event T is a tautology, then P[T] = 1 (e.g. T = I am myself)
If an event C is a contradiction, then P[C] = 0 (e.g. C = an empty cup is full)
What is the probability of a tautology given a contradiction? i.e. What is P[T|C]?
So.....
What is the probability that I am myself given that an empty cup is full?
What would Bayes say?
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