[FOM] FOM - reply to Haney and others
giovanni sambin
sambin at math.unipd.it
Sat Feb 4 04:05:05 EST 2006
At 12:15 -0800 27-01-2006, Ehlert-Abler wrote:
>The question of foundations is not so much, "What is basic in mathematics?"
>as, "What causes mathematics in the first place?"
>
> Two main answers are commonly available.
> 1) Mathematics is wholly arbitrary, a product of the mind. It has its
>ultimate source in human biology and sociobiology.
> 2) Mathematics is not arbitrary, but is more found than made.
>
> For several reasons, the first answer is wrong. We can't arbitrarily
>decide, for example, that "2+2=5", or that "pi=3". More profoundly, if
>mathematics is an indirect product of human evolution, which is driven by
>selective advantage, then there is an equation that explains why people can
>do equations, i.e., because selective advantage is expressed by an equation.
>Solution 1 is circular.
The argument above is incorrect, in two points:
1. Nobody would say that, since art is a product of the mind, then it
is wholly arbitrary. Ehlert-Able applies the same argument to
mathematics: if mathematics is a product of the mind, then it is
wholly arbitrary. This means that he is making some other
assumptions, which should be made explicit.
2. More profoundly, even giving the very rough statement "selective
advantage is expressed by an equation" for granted, what's wrong with
circularity? In this very moment, we are using our brains to try and
explain how they work. We have no other way to do it, unless by
principles of faith.
I will not buy the book.
Giovanni Sambin
More information about the FOM
mailing list