A Revolution in Mathematics? What Really Happened a Century Ago and Why It Matters Today (2012)
1 points by safinaskar
1 points by safinaskar
The physical sciences all went through “revolutions”: wrenching transitions in which methods changed radically and became much more powerful. It is not widely realized, but there was a similar transition in mathematics between about 1890 and 1930. The first section briefly describes the changes that took place and why they qualify as a “revolution”, and the second describes turmoil and resistance to the changes at the time
I agree with everything here, except for:
The author says that "true" should mean "impossible to contradict". As well as I understand "impossible to contradict" means "cannot be disproved", i. e. "one cannot prove 'not A' ".
Well, one can stretch the interpretation to «if you try to contradict, you get a contradiction». After all, «can't be that not A» is what you prove in constructive systems when you want a translation of a classical excluded-third result but can't prove it directly in a constructive way.
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