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## Question

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] ?

## 3 answers to this question

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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

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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?

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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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