Another Challenge for the Critical-Race Theorists

Recently, I issued a challenge (here) to the critical-race theorists to explain how a procedure that is obviously racially neutral – having applicants for symphony orchestras audition behind a screen – is somehow part of systemic racism. No one has bothered to explain, of course. And now here is another challenge: explain what evidence there is that mathematics is racist. This is the claim of the Mathematical Association of America. See here. It is one thing to claim that books, especially textbooks, on math are racist, or that teachers of math are racist. It is quite another to insist that math itself is racist. If so, then that is sad news for non-whites because there is nothing we can do about it.

Or is there? Here we get into what is perhaps the nerdiest of nerdy topics, not just math, but the philosophy of math. For those who don’t know about this, there are at least three possible positions on the status of number, and they correspond to the three positions on the existence of universals.

There is the Platonic, or realist, position that numbers exist independently of us.

There is the conceptualist position that numbers are invented or created by us.

And then there is the nominalist position that numbers don’t exist at all and that “mathematics is a game played according to certain simple rules with meaningless marks on paper.” That’s a quote from the mathematician David Hilbert.

Virtually no one really cared about any of this until the current madness settled upon us, and now we have people insisting that math is racist because “mathematics is created by humans and therefore inherently carries human biases.” This isn’t very persuasive. First, we have to assume that it is created rather than discovered, and second, we have to assume that human biases get in the way, somehow. But even if math is created rather than discovered, how do biases creep in? This isn’t really explained. If I say that the derivative of 2x is 2 or that of sin x is cos x, am I somehow biased? Are these statements somehow biased? These are about as far from anything related to skin color or ethnicity that I can imagine. I don’t see any reason for believing that the truths of calculus would be any different if “created” by non-whites rather than by Newton and Leibniz since it’s reasonable to think that they would create calculus in the same way Newton and Leibniz did. For that matter, think of how poorer the world would be if the French had reacted to the invention of calculus by saying it was an Anglo-German plot against the French? We would have missed out on Legendre, Lagrange, L’Hopital, Laplace, Cauchy, Fourier, Poincare, and so on.

Anyway, those who assert that math is racist claim that mathematical entities are invented and not discovered, so they take the conceptualist position. Not many actual mathematicians believe this, since they are realists. They believe that they are discovering truths about independently existing entities, not about human inventions. But the mathematician Leopold Kronecker declared that God made the integers and all else is the work of man (as it’s usually quoted). Of course, we can declare that fractions and irrational numbers and imaginary numbers are all somehow invented, but it’s hard to detect any difference here between integers and any of these others. They are all abstract entities. And if real numbers are real entities that we discover, then why not other entities, such as vectors, tensors, fields, rings, groups, and topologies?

Kronecker’s quote, incidentally, is repeated by a character in Dorothy Sayers’s Gaudy Night (p. 34 in my edition). I have never understood what it is doing there since it seems to have no relationship to what was being talked about. Anyone?

Anyway, what are we supposed to do if math is racist? If the realist view of numbers is correct, then there is nothing we can do. Bad luck for those of the wrong race, but they will just have to live with it. Suppose, then, that numbers are invented. Are we supposed to invent non-racist math? And what would that be like? Will the proofs be less rigorous? Will they come up with different results for derivatives or maybe even dispense with the concept altogether? Well, I for one don’t want to drive across bridges designed by engineers using some crazy, nonstandard math.

All of this seems like it is poorly thought out. I say, stick to saying that maybe some math books or teachers are racist and be done with it. Oh, and why not just admit that some ethnic groups in America don’t do well on math tests for no reason other than they aren’t interested in the subject?

Comments

[Kevin Kim]

Back in grad school, when I was inadvertently marinating in postmodernist thinking (a hypnosis that took years to snap out of), I heard talk of "rationalities," plural, and "logics," plural. Among the PoMo thinkers I had to read, there were some who contended that rationality itself was a tool of Western oppression to be wielded against non-Western people (they had to argue this case rationally, of course). Rationality, after all, led to the creation of the technologies of war that resulted in mass death. Therefore, according to PoMo thinking, rationality is inherently toxic. Just as certain people on the right blame communism/socialism for over 100 million deaths in the 20th century, postmodernists blame rationality for millions of deaths in the 20th century. So "math is racist" is the latest rhetorical salvo in an ideological conflict that's been going on for quite a while. Much of this nonsense wafts out of academe and into the general populace, infecting minds as it permeates the masses.

Part of the problem is postmodernism's resistance to the idea of universals. Using the disparaging term "totalizing metanarrative" to describe universals, postmodernists argue that any attempt at describing anything in a general way, i.e., teasing out general principles, is inherently oppressive because it disrespects specific historical context, and in PoMo, absolutely everything is radically contextualized and subjectivized. The very claim that human beings might have "a nature" is disputed (this is what led Steven Pinker to write his anti-PoMo monograph _The Blank Slate_). Rational pursuits like math and logic stink of totalization because their insights apply everywhere and to everyone, regardless of context. 2+2=4 is an apodictic truth to be feared because it obtains whether you happen to be black, white, yellow, Asian, German, or Martian. The PoMo rebellion against totalization is what leads to the social balkanization we see: intersectionality is an ideology predicated on identity politics, which itself is derived from PoMo thinking: I have my reality, and you have yours. The ironic result is cultural segregation: whites can never understand the black experience, and vice versa, and if blacks want to flourish in a university, then there must be black-only spaces for black students and black teachers—the very segregation that people like Martin Luther King had fought against. Far from seeking a healthy "e pluribus unum" unity, people in this camp seek an absurdist plunge into a perverted notion of diversity.

The whole thing is quite sad, and to my mind, it's the result of wholly unnecessary stupidity. But if stupidity is congenital and therefore incurable... what can be done? Maybe it's not stupidity so much as what thinker Bernard Lonergan called "scotosis," i.e., willful intellectual blindness.

[John Pepple]

Thanks for the great reply. I had never heard of totalizing metanarratives before. However, I had heard of the pomo mistrust of science, math, and logic, which is why I always sneer when the Democrats say that people on the right are science deniers. That is simply to ignore the people on their own side who are doing the same.

[Charles N. Steele]

I just gave a doctoral lecture on the idea of universals and the postmodern attack on it, although I did it from the standpoint of methodology of economics. Arguing that principles of logic, math, etc. are arbitrary is self contradictory and the sort of stupidity that only a person with no worries about the next meal can afford, i.e. a word game played by bored first-world academics. We could dismiss it as mere stupidity except that it undercuts man’s capacity to think, and that’s our one means of survival, to say nothing of preserving civilization.

BTW I don’t understand Kevin Kim’s “Just as certain people on the right blame communism/socialism for over 100 million deaths in the 20th century...” Is there some doubt being expressed here about the existence of gulags, killing fields, the Holodomor, China’s ‘Great Leap Forward’ famine, etc.?

Rationality did not kill millions in the 20th Century. Leftists operating under the influence of leftist ideology did, so I don’t get the “just as” remark.

[Kevin Kim]

Mr. Steele,

My apologies if I was unclear. I assume your point is that "rationality" is something carried around inside a person's head whereas people are the actors who do the actual killing. Ideas don't kill people: people kill people.

I think the PoMo folks who contend rationality is inherently deadly are coming from the same point of view as those who contend a gun is inherently deadly: while your focus might (rightly) be on the wielder of the gun as opposed to on the gun itself, the PoMo adherent's focus is less on the wielder and more on the gun itself—i.e., rationality—as an inherently deadly weapon.

Regarding this:

"Rationality did not kill millions in the 20th Century. Leftists operating under the influence of leftist ideology did..."

While I would agree with you, my very point was that PoMo adherents would not. They would say rationality, as instantiated in science, led to the deadly technologies employed in war. I find this PoMo viewpoint to be a misguided, even perverse, assessment of the situation, but my own point in saying "just as" is that

1. Conservative thinkers blame leftists (motivated by their leftist ideology) for over 100 million deaths, while at the same time,

2. Leftist thinkers blame rationality, which they see as inherently toxic (toxic, deadly, etc.), for millions of deaths resulting from the employment of rational (specifically, scientific) thinking.

In both cases, what's really going on is that Parties X and Y are both blaming people-plus-ideology for a massive amount of death. The difference is that the conservative side places more emphasis on the moral agency and culpability of the human actor (who acts according to ideology) while the PoMo/left side places more emphasis on the perceived inherent danger of rationality. Blame the gun, not the gun's user.

Again, to be clear, I personally don't buy into the PoMo/leftist worldview, so I don't accept (2), and I'd agree with you that (2) doesn't merit a "just as" equivalence. But it doesn't matter what I think: the actual reality is that many, if not most, PoMo thinkers think this way. To them, rationality is toxic, partly because of its totalizing tendencies, and partly because of (they'd contend) its inevitable gravitation toward war and the science that makes large-scale war possible.

Me, I'm more inclined to see PoMo and leftism as inherently toxic while rationality is merely a value-neutral tool that can be employed for the benefit or for the detriment of humanity. We can use rationality to build bombs, but we can also use it to build health-enhancing nanotech solutions.

[Charles N. Steele]

I get your point now. Thanks!