Top 19 Quotes & Sayings by Kurt Gödel

The development of mathematics towards greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules.

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

Said to physicist John Bahcall. I don't believe in natural science.

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

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

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

All generalisations - perhaps except this one - are false.

I don't believe in natural science.

All generalizations, with the possible exception of this one, are false.

Nothing new had been done in Logic since Aristotle!

The development of mathematics toward greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules... One might therefore conjecture that these axioms and rules of inference are sufficient to decide any mathematical question that can at all be formally expressed in these systems. It will be shown below that this is not the case, that on the contrary there are in the two systems mentioned relatively simple problems in the theory of integers that cannot be decided on the basis of the axioms.

...a consistency proof for [any] system ... can be carried out only by means of modes of inference that are not formalized in the system ... itself.

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

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

The formation in geological time of the human body by the laws of physics (or any other laws of similar nature), starting from a random distribution of elementary particles and the field is as unlikely as the separation of the atmosphere into its components. The complexity of the living things has to be present within the material, from which they are derived, or in the laws, governing their formation.

The axiomatic method is very powerful

I am convinced of the afterlife, independent of theology. If the world is rationally constructed, there must be an afterlife

Ninety percent of [contemporary philosophers] see their principle task as that of beating religion out of men's heads. ... We are far from being able to provide scientific basis for the theological world view.

The physical laws, in their observable consequences, have a finite limit of precision.