Friday, July 13, 2012

On the necessary existence of the elephant in the room

There is a philosophical view which says that mathematics is a way of evolutionary signaling, i.e. an elaborate way of demonstrating fitness (in this case, intelligence) to one's potential mates. This may very well be true but there is an elephant in the room that it does not address. Which is: while the purpose of doing mathematics may be an accident of evolution, its content cannot. It is possible to conceive of a world in which this function of doing mathematics is not plausible, or even a world in which natural selection does not exist at all; however, it is not possible to conceive of a world in which theorems of mathematics are false. Provable propositions are true in every possible world. Inasmuch as mathematics contains theorems about certain modes of reasoning, it follows that there is a realm of human thinking which cannot be an accident of evolution.

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