[FOM] Math vs. Logic
Dana Scott
dana.scott at cs.cmu.edu
Thu Mar 1 12:57:40 EST 2012
The current March 2012 issue of the AMS Notices (p. 366) has the appended
letter. In this Turing Year should we not try to make logic more relevant?
And should we not try to make the teaching of logic more interesting?
(I broke the letter into paragraphs for readability.)
> Response to Quinn
>
> This is a response to the article “A revolution in mathematics? What
> really happened a century ago and why it matters today”, by Frank Quinn,
> that appeared in the January, 2012 issue of the Notices.
>
> My mathematics colleagues almost never think about mathematical
> logic (see: “The ideal mathematician”, Philip J. Davis & Reuben Hersh,
> http://people.maths.ox.ac.uk/bui/ideal.pdf, for what is simultaneously
> the funniest and most profound description of mathematicians!!).
>
> Mathematical logic is almost never taught in mathematics departments —
> it’s taught in computer science departments and philosophy
> departments — and, when it is, it is taught in a purely technical way
> with no concern for history or philosophy.
>
> Mathematicians still live in Cantor’s paradise — or even Eilenberg’s
> paradise — in spite of Russell’s paradox; they simply learn not to make
> certain moves that lead to trouble (as long as the referee doesn’t
> complain, what, me worry?). The various formalizations for avoiding
> Russell’s paradox also prevent one from making certain moves which are
> usually safe and powerful. So mathematicians work informally and have
> always done so; there is almost no trace of mathematical logic in most
> of the history of modern mathematics!!
>
> I’m not saying that mathematicians are aware of what I just said; most
> are totally unaware of these issues and simply working in a successful
> research tradition.
>
> — David A. Edwards
> University of Georgia
> dedwards at math.uga.edu
> (Received December 14, 2011)
Dana Scott
Berkeley, CA
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