Feeling like David Hilbert?

Remember the big brouhaha back in the late 19th and early 20th century about the foundations of mathematics? There was one radical school of thought, the Intuitionists, who insisted on constructive proofs. They held the method of "indirect proof", i.e. suppose what you wish to prove is false, and then show that a contradiction results, to be invalid, and disagreed with the "law of the excluded middle", that any given proposition is either true or false.

This was pretty controversial stuff, and David Hilbert wrote the following famous line about it: taking the principle of the excluded middle from the mathematician is the same as denying the telescope to the astronomer, or the boxer the use of his fists.

As a programmer brought up on imperative languages, I have to wonder whether those of similar training feel about pure applicative languages the way Hilbert did about intuitionism.