law of excluded middle

Can a mathematical object be said to exist if you can't construct it?

If you can prove that a statement can't possibly be false, does this mean it's true?

If you like mathematics because things are either true or false, then you'll be worried to hear that in some quarters this basic concept is hotly disputed. In this article Phil Wilson looks at constructivist mathematics, which holds that some things are neither true, nor false, nor anything in between.