>> Even if you write it down on a piece of paper,
>> an equation is still ideal and eternal, and this is
>> what's supposedly governing matter.
>Here comes the most horrible sentence of the day.
>Lexicalists, generative grammarians, Marxists,
>bourgeois liberals, anarchists, and postmodernists may
>wish to avert their eyes:
>Depends upon the what the equation, independent of its
>representation, represents, no?
The key word in the sentence quoted above is "supposedly." I do not believe that anything is governed by equations, which are simply creations of the human mind, constructed so as to describe things. Mathematics is language, not eternal truth given from on high. Equations are conceived of as ideal and eternal in the context of Newtonian, mechanistic science, which is what my above statement was about. I was *not* describing my own belief. What I was trying to get at is that Platonism permeates modern science, particularly physics.
I can't agree with the conclusion that the status of an equation depends on what it represents. *All* equations, regardless of what they represent, are descriptions. They have no self-existence. They do not exist except to the extent that we imagine them.
>To illustrate what I mean, here's a question about
>mathematical objects: did the transfinite cardinals
>(the numbers that describe different orders of
>infinity) exist before Cantor "discovered" them?
No. And they will no longer exist if we forget about them. To put the matter more plainly, 2 + 2 did not equal 4 until somebody created the concepts of "number," "addition," and "equal."
>Here's another one: did the derivative exist before
>Newton and Leibniz? What can we make of the fact that
>infinitesmals weren't a decent foundation for the
>calculus? Or that with contemporary set theory, we
>can now *make* infinitesmals that are a decent
>foundation for calculus?
It's certainly possible to come upon a correct idea even though you didn't actually have the conceptual foundation for it properly in place. A lot of our knowledge comes from intuitive leaps, with the details filled in later.