It seems to me (though I would be *extremely* glad to be proven wrong here) that in mathematics we often blindly assume that the theorems we attempt to prove/disprove are either true or false. Such an assumption is implicit in every proof by contradiction. We eliminate the possibility of the theorem being false (by deriving a contradiction), and thus conclude that the theorem is true since that is the only other option. But this is not a trivial assumption. The theorem could very well could be neither true nor false (like the liar paradox, for instance). How do we justify this assumption?