Quotes from Kurt Gödel

I like Islam, it is a consistent idea of religion and open-minded.

The meaning of world is the separation of wish and fact.

I don't believe in natural science.

I don't believe in empirical science. I only believe in a priori truth.

The more I think about language, the more it amazes me that people ever understand each other at all.

I don't believe in empirical science. I only believe in a priori truth.

The meaning of world is the separation of wish and fact.

Our total reality and total existence are beautiful and meaningful . . . . We should judge reality by the little which we truly know of it. Since that part which conceptually we know fully turns out to be so beautiful, the real world of which we know so little should also be beautiful. Life may be miserable for seventy years and happy for a million years: the short period of misery may even be necessary for the whole.

Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F.

The result of our previous discussion is that our axioms, if interpreted as meaningful statements, necessarily presuppose a kind of Platonism, which cannot satisfy any critical mind and which does not even produce the conviction that they are consistent.

Bemerkung: Sonderbarerweise sind auch die Tatsachen, welche wir absolut sicher wissen (2 + 2 = 4, ich heiße Kurt) aus Begriffen zusammengesetzt, die wir nicht vollkommen verstehen (und die sehr kompliziert sind). 2 Erklärungen dafür: 1.) Das Einfache in der Welt sind die Tatschen und nicht die Begriffe. 2.) Diese sicheren Tatschen sind so, dass sie bei einem sehr weiten Spielraum von möglichen Interpretationen für Begriffe gelten.

Either mathematics is too big for the human mind or the human mind is more than a machine.

There is a difference between a thing and talking about a thing.

But, despite their remoteness from sense experience, we do have something like a perception of the objects of set theory, as is seen from the fact that the axioms force themselves upon us as being true. I don't see any reason why we should have less confidence in this kind of perception, i.e., in mathematical intuition, than in sense perception.

Time-travel is possible, but no person will ever manage to kill his past self. Godel laughed his laugh then, and concluded, The a priori is greatly neglected. Logic is very powerful.

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.

But every error is due to extraneous factors (such as emotion and education); reason itself does not err.