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Logical Limbo (Posted on 2002-08-12) Difficulty: 4 of 5
Prove that either

a) this problem is solvable

or

b) this problem is unsolvable

See The Solution Submitted by Cheradenine    
Rating: 3.2000 (15 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Solvable or not | Comment 8 of 33 |
(In reply to re: Solvable or not by Cheradenine)

That is where I am having trouble as well. We know that in the set of all possible statements, the set of statements provably true is a discrete subset of the set of true statements, and by reflexion, the set of all statements provably false is a discrete subset of the set of false statements. This means that there are statements (both true and false) whose truth value is unprovable.

Nick used the word paradox to descibe the dead ends in his "proofs" of "b can be proved" and "neither a nor b can be proved" but they are not truly paradoxes, they just point out that the solution, if there is one , lies along a different branch. The entire question is (or might be shown to be) a paradox if the third branch also dead-ends, as I suspect it will. I can't at the moment think of a way to approach this branch.
  Posted by TomM on 2002-08-13 02:38:02

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