FOM: Effective Bounds in Core Mathematics

Fred Richman richman at
Sun Jun 25 08:27:48 EDT 2000

Harvey Friedman wrote:
> Constructivists should also bear in mind that the truth of these four
> theorems is completely accepted by the mathematical community.

I'm not completely sure I understand the point of this statement. In
their professional lives, constructivists constantly run into
reminders that their criteria for justifying theorems differ from
those of the mathematical community at large. There is little danger
that they would stop being aware of this situation. 

So the only purpose I can see to the statement is to suggest that the
complete acceptance of these four theorems by the mathematical
community should give constructivists pause as to their denial that
these theorems have been proved, as indeed it should. In this forum,
however, that sociological card is an ungentlemanly one to play. I
would respond to it were I sure that it had been played.


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