Once as a grad student I handed in a proof to a logician. The proof was a good proof—by the standards of mathematicians (the proof was of a probabilistic fact, and I had previously published a number of peer-reviewed articles in probability theory, so I knew what I was doing). The logician absolutely hated it and did not think it was a proof.
What a logician means by a "proof" and what a mathematician means by a "proof" are different. I think the difference is roughly this: A mathematician's proof is an informal argument that there exists a logician's proof.
2 comments:
A nice hint. Similar to your post(s) about differences btw mathematical and theoretical physics. So, logicians are the most exact herd? Well, not so fast -- philosophers of math and philosophers of logic is the right answer, I'd guess.
Here we see that exactness is context-relative. Pascal's mathematical minds (opposed to intuitive minds in Pensées, I) not exact enought for the logician.
I don't think Brower would agree with you, Alex!
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