> 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. Therefore, I don't see any reasonable way one can say that there is no mathematics (without quotes) apart from people.
> There is "what is," which possibly operates according to certain
> "laws" -- we don't know because that level of being is not
> commensurate with how knowledge operates.
> Knowledge operates by casting a kind of cognitive net over the given
> "data flow." The cognitive net is defined by culture. What it catches
> in the net, it calls "reality," "the laws of nature," etc., but it is
> always and by definition a partial view if you accept the thesis that
> the universe is dynamic/ever-changing.
The universe is indeed ever-changing. How do we know this? By scientific observation and the discovery of the laws of nature. But the laws of nature aren't changing (at any rate, that's the consensus of just about all the scientists I know about), and the mathematical relationships among numbers, shapes, etc., don't change. Our knowledge of these things does change, of course, and it is different in different societies. But once again, I come back to the distinction between our knowledge and what our knowledge is about. If you don't make that distinction, you are back with the idealism of the 19th century and
> The fact that this partial view can be used to make the billiard ball
> go into the pocket or the ariplane stay up in the sky, does not make
> our "science" "truer" than someone else's science in an absolute
> sense.
I don't know what you mean by "absolute." Unless you mean that our knowledge of reality is still quite imperfect, and we have a lot to learn. That's certainly true. But that doesn't mean that we know nothing, or that we don't know more than we did in the past. I'd sure rather be up in the air in a plane designed by someone with the current state-of-the-art knowledge of aeronautics than one designed by myself, since I know nothing about how to build aircraft.
> There have been any number of excellent critiques of
> universalist/absolute science in the 20th century, and they make for
> fascinating reading. I already mentioned Jacob Klein with respect to
> math,
I don't know him; does he argue that 2+2=4 can be false? If so, I like to see the argument; it would be fascinating.
> there's also Feyerabend of course,
Most philosophers of science don't think much of him, and neither do I.
> Cristopher Caudwell (The Crisis in Physics, Illusion and Reality),
I know the name, but haven't read anything by him. I don't think he has much stature in the philosophical world, though.
> and all the phenomenologists.
I don't know any phenomenologists who have this relativistic view of mathematics you are trying to uphold; Husserl certainly didn't, as far as I can tell.
Jon Johanning // jjohanning at igc.org __________________________ A sympathetic Scot summed it all up very neatly in the remark, 'You should make a point of trying every experience once, excepting incest and folk-dancing.' -- Sir Arnold Bax