Jump to content
BrainDen.com - Brain Teasers
  • 0


Guest
 Share

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] ?

Link to comment
Share on other sites

3 answers to this question

Recommended Posts

  • 0

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

Link to comment
Share on other sites

  • 0

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?

Link to comment
Share on other sites

  • 0

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

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
 Share

  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...