# The Liar Paradox

twhitehead
Science 06 Mar '09 10:19
1. 06 Mar '09 10:19
In the March 09 Scientific American there is an article ("Impossible Inferences"ðŸ˜‰ about incompleteness theorems and claims that it is impossible for an entity inside the universe to learn everything about how the universe works.

It also talks about predicting the future and presents the question:
"Will your answer to this question not be 'yes'?"
It claims that nobody can correctly answer the question and therefore the future is unpredictable.

I disagree. I think that it is impossible to truthfully answer the question with a 'yes' or a 'no' but that is not equivalent to being unable to predict the future. If you simply don't answer it, that is predictable.
2. 06 Mar '09 10:20
The future is most likely not completely predictable, but that's not due to that silly paradox, of course.
3. DeepThought
Losing the Thread
06 Mar '09 11:10
You just answer a different question. This goes back to the ancient world. Epimenides, a Cretan, once stated: ¨All Cretans are liars.¨ since he was a Cretan if he was telling the truth, then as a Cretan he must be a liar. Of course it doesn´t work as provided there is one Cretan who is not Epimenides who is truthful he can make the statement and still be lieing. It´s easy to generate this stuff, language allows you to make grammatically correct statements that never-the-less generate contradictions.

The same is true in mathematics. Russel´s paradox works as follows. Consider the set U which is the set of all sets. Since U is a set it must contain itself. This is a little wierd, but doesn´t generate a contradiction. However, now consider the set V which is the set of all sets which do not contain themselves. Now V is a set, if it does not contain itself then it fulfills the criterion for membership of the set. If it does contain itself it does not fulfill the criterion for membership of the set. So a contradiction is generated.
4. 06 Mar '09 13:58
I brought it up here because I thought it odd that mathematicians would seriously think that it is evidence that the future cannot be predicted. I wondered if I was missing something.