[FOM] Arnon Avron's reply to me
martin at eipye.com
Wed Oct 24 00:41:44 EDT 2007
In reply to what Arnon seems to have thought I said, he wrote:
"Wrong, *certainty* in mathematics is not just a matter
of social activity".
Here is what I said:
"There are two further points I'd like to make.
One is that, in the last analysis mathematics is
a social activity,"
Note that I said nothing about "certainty" in this sentence, and I
surely didn't use the delimiting word "just"; the use of that word by
Arnon is what leads him to a very long diatribe in which I am seen as
an ally of "post modern" relativism. I find this particularly ironic
because I engaged in some spirited polemics with Reuben Hersh on FOM
years ago in which I accused him of much the same offense.
Who could deny that mathematics is a social activity? But to say that
is not to say that there is anything in the least arbitrary about the
propositions that the mathematical community comes to accept as true.
The process by which this happens is complex and could be the subject
of a long essay One would need to discuss the role of intuition (see
Euler's summation of the reciprocals of the perfect squares) as well
as how new methods of proof gain general (though often not immediate
and not universal) acceptance.
Arnon has told us repeatedly that it is very important to him that
certain theorems are known to him with certainty. His latest message
goes sufficiently far afield that this concern of his is seen as a
bulwark against Nazi ideology.
He is of course welcome to this belief and to draw the line beyond
which theorems are "uncertain" wherever he thinks it is appropriate.
He is certainly free to reject the consensus among the experts that
FLT is now truly a theorem despite the transfinite methods on which
the proof seems to rest. But he needs to understand that (as he has
been told repeatedly on this list) his views are not universally
held, and that his concept of "certainty" remains highly subjective.
Visiting Scholar UC Berkeley
Professor Emeritus, NYU
martin at eipye.com
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