FOM: Mathematicians' views of Goedel's incompleteness theorem(s)

[Vaughan Pratt]

If one were to poll the grieving relatives of a recently deceased loved
one for their reactions, it would become obvious that some reactions
should not be taken at their face value but be interpreted suitably.
Among these are denial of the loved one's death.

Of the four categories of responses reported by Prof. Davis to his
poll, the following representative would seem to call for
interpretation.

>"Although Goedel's theorems are now a significant part of the unstated
>metamathematical assumptions of research, they are relegated to a far back
>burner. If a number theorist is working, say, on the famous and as yet
>unsolved problem of whether there are an unlimited number of twin
>primes..., then the strong assumption underlying the work, even in our
>post-Goedelian period, is that the answer is either yes or no.  It is not
>assumed that on the basis of the traditional axioms of arithmetic we
	      ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>cannot decide for true or false.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Evidently the segment of the mathematical community represented by this
sample is still in deep shock after two thirds of a century.

--------

By way of calibration of Prof. Davis' poll it might be useful to have
three control polls.  One would ask mathematicians merely to assess the
relevance of Goedel's results to mathematics, another would ask
scientists to explain why most scientists do not find radioastronomy
relevant to terrestrial physics, and a third would ask them merely to
assess the relevance of radioastronomy to terrestrial physics.

Vaughan Pratt