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3 replies to this topic

### #1 mmiguel1

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Posted 15 October 2010 - 11:16 AM

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?

Spoiler for Dare I?

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### #2 nash

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Posted 15 October 2010 - 06:40 PM

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.

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### #3 mmiguel1

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Posted 15 October 2010 - 07:03 PM

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.

So are you saying that the probability of anything given a contradiction is undefined?
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### #4 nash

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Posted 15 October 2010 - 07:09 PM

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
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