FOM: Comment on Julio Gonzalez Cabillon

[Moshe' Machover]

Julio Gonzalez Cabillon asks:

> Now, if one believes that mathematics is "socially constructed",

> (i) how can we explain Wigner's dilemma of "unreasonable effectiveness
> of mathematics in the natural sciences"? ...

> ii) how can we explain the unreasonable fitness of large portions of certain
> fields mathematics in *other* areas of mathematics"?

Perhaps a clue might be found by observing that humans, and human
societies, are themselves part of nature. Therefore, paraphrasing a famous
aphorism, we must conclude that if humans do make their own mathematics,
they do not make it as they please. They (and it) are constrained, through
their interactions with the rest of nature, by how the world is.

Long long ago there was a tribe in Africa whose socially constructed
mathematics said that 1 + 1 = 3. A hunter of that tribe came across 3
lions. He killed 1, then another 1; then sat down to rest under a tree,
whereupon the third lion ate him. That tribe is now extinct.

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