FOM: Refuting Hersh (cont)
Soren Riis
sriis at fields.fields.utoronto.ca
Mon Mar 23 20:36:03 EST 1998
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Refuting Hersh (cont)
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Dear Hersh,
Concerning the ontological status of mathematics could you please
answer the following questions:
Assuming the correctness of the Riemann conjecture what is the
most correct way of expressing the state of affairs?
(a) "It is a transcendental-abstract fact that Riemanns zeta function
have all its roots of the form z=1/2+ r im"
or
(b) "It is a social fact that Riemanns zeta function have all
its roots of the form z=1/2+ r im"
??
According to your view (b) seems to be the correct way of expressing
the state of affairs. Do you agree?
I would appreciate a serious answer to this question.
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According to your "philosophy" could you please answer in what sense
(1) Donald Duck exists. (2) The Mandelbrot set exists.
You will hopefully accept that there is a fundamental difference
between the two.
You might say that the Mandelbrot set is "reproducible" and have
"determined properties" etc. while Donald Duck fails on that account.
Suppose that a survey showed that amongst children, Donald Duck
is more determined and have more reproducible properties than the
Mandelbrot set? What would happen if everyone became children tomorrow?
Would Donald Duck then become mathematics, and the Mandelbrot set
become fiction?
In my posting [Riis; refuting Hersh by Hersh; 22/3-98] I took it for
granted you used "high degree of consensus" as indication for validity.
After all you defined mathematics (if I understand you right)
as that area of abstract human thought which is uniquely objective and
characterized by social consensus.
In attempting to refute my refutation you write:
> Another familiar example is the general belief by
> German people in 1933-1945 that they were a ""Herrenvolk""
> and should do as they wished with other ethnic groups.
> Again, there was a persecuted minority that
> disagreed. But the majority were wrong, the minority right.
The minority was certainly right. There is virtually universal
agreement about this. Thus according to your definition of mathematics,
it is a MATHEMATICAL fact that the German people were not a ""Herrenvolk""
(the statement that the "majority were wrong, the minority right" is
definitely an abstract statement which clearly transcend what
you can for example can measure by a rod).
Putting together various of your claims:
--------------------------------------------------------------
* Riemanns conjecture is an unsolved SOCIAL problem.
* It is a MATHEMATICAL fact that the German people were not a
""Herrenvolk"".
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As a kind of REALIST (and critical rationalist) I find your
ANTI-REALIST position completely unacceptable. In particular
in a time where the post-modernistic plague is spreading all
over the planet. I see the VANDALISM Harvey Friedman wrote about
(in a different context) as a special case of this dangerous
movement away from Science and critical RATIONAL thought.
This will most likely be my last FOM-posting in this absurd
discussion.
Soren Riis
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