Jon Johanning wrote:
>
> On Jan 1, 2005, at 1:42 PM, joanna bujes wrote:
>
> > There is no "mathematics" apart from people.
>
> Sorry, but I just can't understand this sort of statement, which I know
> is quite fashionable in postmodern circles. Take away the quote marks
> -- I don't see why they in your sentence -- and we are talking about
> numbers, shapes, etc. There is a lot of controversy among philosophers
> of mathematics about just what their ontological status is, but I am
> sure they were around before people were. The universe was here long
> before we were, and it operated according to mathematical laws.
The universe was here before people existed. But it didn't operate according to mathematical laws, it just operated, period. Laws (unlike Plato's Forms), however, exist only in human brains; they represent our collective effort (never complete, never exact) to understand that operating of the universe. No human brains, no laws, mathematical or otherwise. It has been a long time since I read the _Anti-Duhring_, but as I understood it at the time, Engels held to this position: i.e., he held that the belief in the non-mental existence of laws led to idealism. The universe is extra-mental; laws are mental.
Carrol
P.S. I don't know if this is relevant or not. The ratio of the circumference to the radius of a circle is _not_ equal to any value of pi that has ever been expressed. And in fact the mathematician's circle does not exist in extra-mental reality; it is only an ideal abstraction from the 'circles' we see in the world. Mathematics only approximates the real world; but the real world is not an approximation to itself. It merely is.