FOM: extra-terrestrial math etc.
Vaughan R. Pratt
pratt at cs.Stanford.EDU
Sun Nov 2 14:50:04 EST 1997
ALL THIS is compatible BOTH with a realist/platonist view AND with
certain idealistic brands of intuitionism or constructivism.
The dimension of intuitionism/constructivism vs. classicism has
historically been less than orthogonal to that of realism/platonism
vs. idealism. The recent completeness theorems for constructive
mathematics are now beginning to untangle this messy situation and make
their orthogonality clearer. There are two such compatibilities, one
per dimension, and they are not only independent but of an entirely
I want to maintain that EVEN THIS wacko philosopher of
mathematics would quite rightly assert the NECESSITY of the
claim that 7 plus 5 makes 12.
You say *the* necessity. How would you compare it to the necessity of
the following link?
When 7+5 no longer makes 12, 8+6 will no longer make 14.
You might prefer to judge them equally necessary because both are
absolutely necessary, or perhaps you view the separate necessities of
the linked facts as so absolute that it makes the link vacuous. But to
me, the link is more necessary than either fact alone. Which to my
mind makes 7+5=12 not the most necessary fact in the world.
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