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I do agree with thougths expressed in his speech especially about science and human sciences. Mathematicians still have no proper definition of number, many basic theorems of scientific world have no proof, they have been just accepted and used. Human sciences tried to emulate natural sciences with very mixed results - when they try to apply such methods to humanity many important things, like faith, drop out in approximation of used methods, like cutting exponential curves in their most important but indefinite part. But many scientists and parrots from ordinary public do not say about faults of their theories and methods and THEY JUDGE.
And you say this on the basis of what? Those whom the Gods wish to destroy They first make mad. — Euripides
I suggest Naive Set Theory by Paul Halmos and On Numbers and Games by John Conway. Those whom the Gods wish to destroy They first make mad. — Euripides
As you know, the internal consistency of a logical system complex enough to contain the arithmetic of natural numbers [without tautology] cannot be proved from within the system. That is, the internal consistency of any theory of the logic of numbers cannot be proved without appeal to external principles.
Russel and Whitehead did their work on the definition of number 30 years before this fact was discoverd by Gödel. Not only Russell's philosophical approach to the logic of Mathematics, but also David Hilbert's were shattered by Gödel, Turing, Post [hey, I can even quote a Russian mathematician here] and others in teh 1930's and 40's.
I don't know what you mean by tautology.
Now, if you think that the fact that mathematics is based on unproven principles is a new insight, I suggest you take a look at Euclid and Aristotle, for whom it was clear already 2000+ years ago that axioms and postulates were accepted without proof and were not ashamed of it. Those whom the Gods wish to destroy They first make mad. — Euripides
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