Quotes About Undecidability

In contrast to the modern view that religious doubt is something to reject, fear or merely tolerate, doubt not only can be seen as an inevitable aspect of our humanity but also can be celebrated as a vital part of faith. Doubt has often been disparaged, or merely tolerated, because it is seen as leading to an inert state of undecidability in which nothing can be believed or acted upon. Yet in reality it is only in the midst of undecidability that real decisions can be made.

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.

Instead of countering Plato's argument, or approving it or modifying it, Derrida insists on its instabilities. It is inhabited at every turn by an undecidability that it cannot fully master.