[FOM] Arnon Avron's reply to me

[Martin Davis]

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.

Martin




                           Martin Davis
                    Visiting Scholar UC Berkeley
                      Professor Emeritus, NYU
                          martin at eipye.com
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                        http://www.eipye.com