Undecidability Quotes

Talk can neither be verified nor falsified in any rigorous sense. This is an open secret which hermeneutics and aesthetics, from Aristotle to Croce, have laboured to exorcise or to conceal from themselves and their clients. This ontological, which is to say both primordial and essential axiom (or platitude) of ineradicable undecidability needs, none the less, to be closely argued. (George Steiner)
Only someone who (like the Intuitionist) denies that the concepts and axioms of classical set theory have any meaning could be satisfied with such a solution, not someone who believes them to describe some well-determined reality. For in reality Cantor's conjecture must be either true or false, and its undecidability from the axioms as known today can only mean that these axioms do not contain a complete description of reality. View quote
Kurt Gödel