...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 Copy Share Image
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… — Kurt Gödel Copy Share Image
...a consistency proof for [any] system ... can be carried out only by means of modes of inference that are not formalized in the… — Kurt Gödel Copy Share Image
Either mathematics is too big for the human mind or the human mind is more than a machine. — Kurt Gödel Copy Share Image
The more I think about language, the more it amazes me that people ever understand each other at all. — Kurt Gödel Copy Share Image
The physical laws, in their observable consequences, have a finite limit of precision. — Kurt Gödel Copy Share Image
I am convinced of the afterlife, independent of theology. If the world is rationally constructed, there must be an afterlife — Kurt Gödel Copy Share Image
All generalizations, with the possible exception of this one, are false. — Kurt Gödel Copy Share Image
In any non-trivial axiomatic system, there are true theorems which cannot be proven. — Kurt Gödel Copy Share Image
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