Jon Johanning wrote:
>> 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.
>
What we call "laws of nature" are interpretations of what we think these
laws are. These interpretations vary with culture, with the development
of mathematics, with what we are willing to accept that a "number" can
be, with the domain to which they are applied, etc. Because they are
necessarily partial, it is not really accurate to call them "laws"
though doing so seems to comfort a lot of people.
>
>> 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.
Well, in base 3, the argument wouldn't be false, it would be nonsensical. Moreover, the truth of science isn't given by the verifiability of 2+2=4, which is true by definition. One possible "truth" of science has to do with what matters numbers can be applied to and to what effect. The idea that "mathematics" is the language of nature was born in the sixteenth century and has now become part of "common sense." But this does not make it true.
> there's also Feyerabend of course,
>
> Most philosophers of science don't think much of him, and neither do I.
Well, there we differ.
> 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.
Ah, we're talking about stature now? I thought we were talking about truth.
> 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.
Think about the following:
--Try to multiply 1,435,763 by 329,548 in Roman numerals. Do you think the notation system affects our notion of mathematical possibilities? If the answer is yes, what do we make of the essentialism you attribute to mathematics?
-- What kind of a mathematics do you think we could develop if we only admit integers as genuine numbers (the Platonic position).
-- What kind of mathematics do you think we could develop without 0?
-- What kind of mathematics will result if the reality of a number is given simply by our ability to represent something as a possible number. For example, what kind of number is x in the equation x = the square root of (-1)? Is it a number like 1, 2, 3 .... is a number?
-- What kind of mathematics results from the ability to calculate with orders of infinity? What if the mathematics at hand doesn't allow us to do that?
This is not relativism. It is the observation that mathematics is not a single thing....it is one or many collections of rules and precepts having to do with the classification and manipulation of numbers, shapes, collections, and spaces... which produce the most diverse results and realities. Some mathematical entities vary with culture, some vary with historical development, and I am arguing that there is no vantage point from which you could say this mathematical model is wrong, this one is right. Some are useful, some are not. Some may be useful later. Some are just pretty. Some models are not commensurate with other models.
And thank you to Carrol and others for being very clear on this subject.
See Godel on the "truth" of mathematics.
Joanna