FOM: extra-terrestrial math etc.

[Michael Thayer]

Vaughan answers Neil
[...]
NT> I want to maintain that EVEN THIS wacko philosopher of
NT> mathematics would quite rightly assert the NECESSITY of the
NT> claim that 7 plus 5 makes 12.
>
VP>You say *the* necessity.  How would you compare it to the necessity of
VP>the following link?
>
VP> When 7+5 no longer makes 12, 8+6 will no longer make 14.
>
VP>You might prefer to judge them equally necessary because both are
VP>absolutely necessary, or perhaps you view the separate necessities of
VP>the linked facts as so absolute that it makes the link vacuous.  But to
VP>me, the link is more necessary than either fact alone.  Which to my
VP>mind makes 7+5=12 not the most necessary fact in the world.


It seems to me that Vaughan's example connection is just the sort that would
allow us to
translate the alien mathematical system into ours.

Neil's truths would then be those which were accepted as proven in both
systems.

Thus I would say that both are fundamental, but in different ways.

Michael