"The development of mathematics toward greater precision has……" — Kurt Gödel
"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
★
★
★
★
★
0.0 avg (0 ratings)
10 Quotes by Kurt Gödel
Kurt Gödel has 10 quotes on this site.
A few more worth reading:
More All Quotes
This quote is filed under All Quotes,
one of 128,558 quotes in that category. Here are a few more:
-
Total loyalty is possible only when fidelity is emptied of all concrete content, from which changes of mind might naturally…
— Hannah Arendt
-
No cause is left but the most ancient of all, the one, in fact, that from the beginning of our…
— Hannah Arendt
-
The ultimate end of human acts is eudaimonia, happiness in the sense of living well, which all men desire; all…
— Hannah Arendt
-
The new always happens against the overwhelming odds of statistical laws and their probability, which for all practical, everyday purposes…
— Hannah Arendt
-
Where all are guilty, no one is; confessions of collective guilt are the best possible safeguard against the discovery of…
— Hannah Arendt
-
We have almost succeeded in leveling all human activities to the common denominator of securing the necessities of life and…
— Hannah Arendt
-
I keep my friends as misers do their treasure, because, of all the things granted us by wisdom, none is…
— Pietro Aretino
-
We must all make peace so that we can all live in peace.
— Jean-Bertrand Aristide
-
The spirit of Ubuntu, that once led Haiti to emerge as the first independent black nation in 1804, helped Venezuela,…
— Jean-Bertrand Aristide
-
As we all know, many people remain buried under tons of rubble and debris, waiting to be rescued. When we…
— Jean-Bertrand Aristide
-
Wise people, even though all laws were abolished, would still lead the same life.
— Aristophanes
-
A friend to all is a friend to none.
— Aristotle
See all 128,558 All Quotes »