...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. Kurt Gödel More Quotes by Kurt Gödel More Quotes From Kurt Gödel The more I think about language, the more it amazes me that people ever understand each other at all. Kurt Gödel language people thinking I don't believe in empirical science. I only believe in a priori truth. Kurt Gödel dont-believe believe Either mathematics is too big for the human mind or the human mind is more than a machine. Kurt Gödel machines mathematics mind All generalisations - perhaps except this one - are false. Kurt Gödel generalisation I am convinced of the afterlife, independent of theology. If the world is rationally constructed, there must be an afterlife Kurt Gödel afterlife independent world I like Islam, it is a consistent idea of religion and open-minded. Kurt Gödel islam open-minded ideas 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. Kurt Gödel development simple two The meaning of world is the separation of wish and fact. Kurt Gödel wish facts world All generalizations, with the possible exception of this one, are false. Kurt Gödel generalization exception 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. Kurt Gödel atmosphere body law But every error is due to extraneous factors (such as emotion and education); reason itself does not err. Kurt Gödel errors emotion doe Nothing new had been done in Logic since Aristotle! Kurt Gödel nothing-new logic done The physical laws, in their observable consequences, have a finite limit of precision. Kurt Gödel precision limits law The axiomatic method is very powerful Kurt Gödel very-powerful method powerful I don't believe in natural science. Kurt Gödel natural math believe 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. Kurt Gödel well-known mathematics development 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. Kurt Gödel principles views men Said to physicist John Bahcall. I don't believe in natural science. Kurt Gödel belief natural believe
