23 June 2005

Intellectual Warfare: Mathematics is Culturally Relative

Diane Ravitch has an editorial in the Wall Street Journal (June 20, p A14) entitled "Ethnomathematics." She specifically cites a new college textbook for Education majors, Rethinking Mathematics: Teaching Social Justice by the Numbers which as she puts it "shows how problem solving, ethnomathematics and political action can be merged." Ethnomathematics is based on the principle that students will learn better if they are taught math in the way it was developed by their ancestral culture. [Does this mean that students of mixed ethnicity must do each lesson more than once? Must Italian kids use Roman Numerals to do long division?]

First let me say that pure mathematics is a language, which if you stick to its grammatical rules, guarantees that the statements you generate are true. You can generate falsehoods by making mistakes in the application of mathematics to real world problems, but that is applied mathematics. Pure mathematics guarantees truth because it only talks about itself.

In that respect, it is a closed system, whose structure is independent of the cultural and historical processes by which it was discovered. In other words, contrary to some multiculturalists, mathematics is not the property of Western Civilization, nor is it linked with the values of oppressors. It simply is. Whether you like it or not.

Pure mathematics serves only one cause: Truth. That is to say, mathematics is the only opportunity that humans have to encounter Absolute Truth by means of unaided reason. Mathematical statements are true, because, within the confines of mathematics, you can prove them to be true. There is a corollary to this: the only reason to do mathematics is to get the right answer!

As such, I think mathematics has a positive moral value: One can experience the limits of human will and knowledge by encountering and exploring mathematics. But those who relentlessly politicize everything including mathematics, don't want to encounter limits to their will. Ultimately they are attempting to demolish the chief obstacle to their will by deconstructing the concept of Absolute Truth itself.

I have a question for such people. When Truth is overthrown, and all is relative, what limits will you respect when you are in power, and to what will you appeal when you are out of power?

Keep mathematics pure and simple, and emphasize that in mathematics at least, there is right and wrong. Teach ways to achieve social justice in Civics class, please. And in that forum, teach ways in which social justice advocates have depended on mathematical truth. Because seeking Justice without regard for Truth leads to Tyranny.


Anonymous said...

Hi! Your blog is very interesting, as is your site, VCBC, which calls me a fundamentalist although I don't generally think of myself that way. Regarding mathematics, though, have you heard of Gödel's Theorem? Kurt Gödel showed that any logic system derived from a set of basic axioms has the potential to contradict itself, or prove inconsistent. I haven't studied this theorem very much, but I believe it shows that Absolute Truth in the form of immaculate logic cannot be attained.

Scooper said...

I had Goedel's Theorem in mind when I referred to "the limits of human will and knowledge." Goedel's Theorem is a constructive proof that, given any finite non-contradictory, non-trivial set of axioms, one can always construct a statement whose truth or falsehood is undecidable in principle. This means that while you can still encounter Absolute Truth by doing mathematics, there are limits to what you can encounter by unaided reason. Goedel's Theorem means that it is Absolutely True that you can't know everything by the power of unaided Reason. You can indeed encounter Absolute Truth in mathematics, you just can't encounter all of it.