Undecidable Quotes

We, the garden of technology. We, undecidable. ~ John Cage

Science in its everyday practice is much closer to art than to philosophy. When I look at Godel's proof of his undecidability theorem, I do not see a philosophical argument. The proof is a soaring piece of architecture, as unique and as lovely as Chartres Cathedral. Godel took Hilbert's formalized axioms of mathematics as his building blocks and built out of them a lofty structure of ideas into which he could finally insert his undecidable arithmetical statement as the keystone of the arch. The proof is a great work of art. It is a construction, not a reduction. It destroyed Hilbert's dream of reducing all mathematics to a few equations, and replaced it with a greater dream of mathematics as an endlessly growing realm of ideas. Godel proved that in mathematics the whole is always greater than the sum of the parts. Every formalization of mathematics raises questions that reach beyond the limits of the formalism into unexplored territory. ~ Freeman Dyson

There is some relationship between the hunger for truth and the search for the right words. This struggle may be ultimately indefinable and even undecidable, but one damn well knows it when one sees it. ~ Christopher Hitchens

Explanation is always incomplete: we can always raise another Why-questions. And the new why-questions may lead to a new theory which not only "explains" the old theory but corrects it.
This is why the evolution of Physics is likely to be an endless process of correction and better approximation. And even if one day we should reach a stage where our theories were no longer open to correction, because they are simply true, they would still not be complete - and we should know it. For Godel's famous incompleteness theorem would come into play: in view of the Mathematical background of Physics, at best an infinite sequence of such true theories would be needed in order to answer the problems which any given (formalized) theory would be undecidable.
Such considerations do not prove that the objective physical world is incomplete, or undetermined: they only show the essential incompleteness of our efforts. But they also show that it's barely possible (if possible at all) for science to reach a stage in which it can provide genuine support for the view that the physical world is deterministic. Why, the, should we not accept the verdict of common sense- at least until these arguments have been refuted? ~ Karl Popper

I do not deny the power and the beauty of reductionist science, as exemplified in the axioms and theorems of abstract algebra....But I assert the equal power and beauty of constructive science as exemplified in Godel's construction of an undecidable proposition.... ~ Freeman Dyson

Technology is crucial to civilization why? Because it helps us make our fate. We don't need God or miracles or the flight of the bumble bee. But it is also crouched and undecidable. It can go either way. ~ Don DeLillo