Quotes & Sayings About Godel

All generalisations - perhaps except this one - are false. — Kurt Godel

That is, for a mathematical Platonist, what the C.H. proofs really show is that set theory needs to find a better set of core axioms than classical ZFS, or at least it will need to add some further postulates that are-like the Axiom of Choice-both "self-evident" and Consistent with classical axioms. If you're interested, Godel's own personal view was that the Continuum Hypothesis is false, that there are actually a whole (Infinity Symbol) of Zeno-type (Infinity Symbol)s nested between (Aleph0) and c, and that sooner or later a principle would be found that proved this. As of now no such principle's ever been found. Godel and Cantor both died in confinement, bequeathing a world with no finite circumference. One that spins, now, in a new kind of all-formal Void. Mathematics continues to get out of bed. — David Foster Wallace

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

The axiomatic method is very powerful — Kurt Godel

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 Godel

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

Kurt Godel's achievement in modern logic is singular and monumental - indeed it is more than a monument, it is a landmark which will remain visible far in space and time ... The subject of logic has certainly completely changed its nature and possibilities with Godel's achievement. — John Von Neumann

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

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

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 Godel

I don't believe in natural science. — Kurt Godel

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

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

In 1931, Kurt Godel proved in his famous second incompleteness theorem that there could be no finitary proof of the consistency of arithmetic. He had killed Hilbert's program with a single stroke.

So should you be worried that all of mathematics might collapse tomorrow afternoon? For what it's worth, I'm not. I do believe in infinite sets, and I find the proofs of consistency that use infinite sets to be convincing enough to let me sleep at night. — Jordan Ellenberg

It's specifically this Z = 2^(Aleph0) that he couldn't prove. Ever. Despite years of unimaginable doodling. Whether it's what unhinged him or not is an unanswerable question, but it is true that his inability to prove the C.H. caused Cantor pain for the rest of his life; he considered it his great failure. This too, in hindsight, is sad, because professional mathematicians now know exactly why G. Cantor could neither prove nor disprove the C.H. The reasons are deep and important and go corrosively to the root of axiomatic set theory's formal Consistency, in rather the same way that K. Godel's Incompleteness proofs deracinate all math as a formal system. Once again, the issues here can be only sketched or synopsized (although this time Godel is directly involved, so the whole thing is probably fleshed out in the Great Discoveries Series' Godel booklet). — David Foster Wallace

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

The meaning of world is the separation of wish and fact. — Kurt Godel

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

If we have dwelled on Godel's work at some length, is it because we see it in the mathematical analogy of what we would call the the ultimate paradox of man's existence. Man is ultimately subject and object of his quest. While the question whether the mind can be considered to be anything like a formalized system, as defined in the preceding paragraph, is probably unanswerable, his quest for an understanding of the meaning of his existence is an attempt at formalization. — Paul Watzlawick

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 Godel

Murphy's Law, that brash proletarian restatement of Godel's Theorem ... — Thomas Pynchon

Like most religious mathematicians from Pythagoras to Godel, Bolzano believes that math is the Language of God and that profound metaphysical truths can be derived and proved mathematically. — David Foster Wallace

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

Nothing new had been done in Logic since Aristotle! — Kurt Godel

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

But you can't prove God exists. And isn't that what all science is ultimately about? Proving theories about the universe?"
"Provability is not truth, Caro. Godel's incompleteness theorem tells us that, if we didn't already know it intuitively, which we do. — Anna Jarzab

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 Godel