So, apparently the big online bruhaha is about math.
I ran into this on twitter today:
I’m not a mathematician, but I did take some advanced mathematics while in high school, and have a sufficient understanding of math to understand what, I think, is happening here.
What I think is happening here is two separate things. The first is a subtle point about the fact that we use a standardized mathematics which is somewhat arbitrary, and we could use a different kind of mathematics if we chose to. The idea is that the standard mathematics is often smuggled in as a part of a larger cultural program attached to a system of “Western” oppression. We’ll get to that later.
The 2nd thing is that some people on the Left/Progressive side of things, the super-woke, are picking a fight with logic and truth, as we can hear here:
Now, I don’t feel a need to address this because those who don’t understand that logic, rational thinking, and skepticism are the best tools we have to discern truth from untruth are not those who I feel like I’m ever going to reach. Because I’m not sure what other tool we could use to make distinctions between ideas, and make sense. If you don’t think that’s possible, then we have nothing left to talk about. If you straight up don’t care about truth, well….
If your whole project is that everything is about power dynamics (because “truth” is a Western lie), then you are just using the same tool that those “oppressors” have used which makes you no better than them. The key here is that those in power only utilize truth as a means, not as an end in itself. But if you don’t use it at all, then you will lose. So if you reject logic and the truth, and only seek to utilize the levers of persuasion, deception, compulsion etc to gain power, then you have become the monster you were fighting.
Because if and when your narrative becomes the dominant narrative or political source of power, you will be the same as they are now. Flipping who has the reigns of cynical power doesn’t make it any less cynical nor oppressive, it just switches who is the one in control. And if you claim that your narrative won’t be oppressive, then I suggest you learn some history, because I don’t believe you.
Some of you are already oppressive before the coup is complete, after all. If you actually gain real power, you don’t think this won’t get worse? Again, I don’t believe you. Have you read about the reign of Terror or the Cultural Revolution in China? Revolutions against entrenched power rarely avoid being the oppressor themselves. Hi, there, Polydelphia.
I’m interested in breaking that cycle of power and oppression, not handing the controls to someone else. If you don’t care about truth, then I don’t care if you are on the Left or the Right; we are at odds, and I will fight you (philosophically, ideally). The enemy here is authoritarianism, not whether you are woke or deplorable.
If you don’t know what code switching is, well, go read about it. The gist is that different dialects and cultural groups use different rules for language, and people who move in and out of different communities get used to speaking in different ways to different groups. A mild example is how a teacher might speak to their students in a different way than how they speak to their friends at the bar.
A more common, American, example is from this fantastic movie, Sorry to Bother You. Many Black Americans quite commonly switch between modes of speech depending upon who their interlocutors are. Here’s a clip for context:
You get it.
But what the hell does this have to do with math? Well, allow me to, once again, talk about Ludwig Wittgenstein. Ol’ Witty, as I call him in my head, was among the most important thinkers of the 20th century, and added a number of important ideas to philosophy, linguistics, and to the proper uses of fireplace pokers.
Among his more important ideas was that of language-games (also, see this). This is particularly important here because the concept of the language-game was created as part of a self-criticism of Wittgenstein’s earlier attempt to make language precise and purely logical, in his Tractatus Logico-Philosophicus (1921), of which his later Philosophical Investigations (1953, posthumously) was a criticism. The Philosophical Investigations includes the introduction of the concept of a language-game, which was a brilliant criticism of his earlier attempt to perfect language into a precise, logical, system.
In other words, Wittgenstein was so brilliant that he not only helped start a philosophical movement with hist first book (Logical Positivism, through inspiration of the so-called ‘Vienna Circle’), but he refuted it himself later with a better piece of literature, revolutionizing the philosophy of language in the process.
In short, the idea of a language-game is that when we use language, we are not building a logical structure but rather we are indicating things with sounds, symbols, gestures, etc and defining meaning through use. Words don’t literally represent reality in a precise logical way, it merely indicates things and we are able to do this in a number of ways which are sensible insofar as they are effective. Thus, there are different ways to indicate a thought, intention, etc which vary according to what rules we come up with. Those rules are somewhat arbitrary (although probably not infinitely so) and differ from language to language, group to group.
Language doesn’t require mathematical or formal-logical precision to function, and the attempt to create a language which is logically precise (or the similar goal of Bertrand Russel and Alfred North Whitehead around the turn of the 20th century, to perfect mathematics; Russell of course mentored Wittgenstein at the latter parts of WWI) is a fool’s errand, as Wittgenstein demonstrates after first attempting to do precisely that in his first work, the Tractatus.
But mathematics needs some level of precision to be meaningful. When I say that 2+2=4, I am assuming a set of meanings to each of the symbols in that string. Depending on what meanings they all have, that statement is either true, false, or meaningless. So we humans came up with a standardized set of meanings and functions for those symbols in order to have a shared mathematics which we can use to figure out problems related to physics, engineering, etc.
And if you have different arbitrary standards of math, it’s quite possible to code switch between them, if you wanted to. But what if you reject the premise altogether?
Different ways of knowing?
And this is where the people saying 2+2=5 come in, and say things like ‘if we had different meanings for those terms, 2+2=5 could be true.’ Sure it could. So what? ‘Well,’ they may say, ‘why is the dominant standard the standard?’
Why can’t we use different, non-Western and colonial ways of knowing?
What other ways? If you had another way of knowing, how would you compare it? what criteria would you use to compare them against one-another? Wouldn’t, say, practical knowledge, technology, and evidence be useful here? What if you also reject those?
Have you seen this?
This may be the fringe, but it is not that rare of a perspective. I run into worldviews such as this on occasion where I live. A rejection of skepticism, science, rationality, and logic are fairly common among those who are criticizing the Western/colonial system of oppression. We have to contend that this is part of the narrative being promulgated alongside anti-racist, anti-fascist, and anti-capitalist ideology (all of which I support in themselves). This is what I’m fighting against in the Left/Progressive world currently. This is why I still identify as a liberal, and am worried about some of the “woke” Left.
But, of course, not all of the Left agrees with this. Sometimes, Lefties are just trying to expand our worldviews about perspective, meaning, etc without actually throwing away logic and truth altogether. Sometimes there is just a point about how math is complicated and often can have different rules.
Listen, you are free to use whatever meanings, standards, or rules for whatever math you desire. You are free to use different “contexts” if you like. But what do you mean by different contexts? Do you mean that you are merely redefining the terms, or maybe just one of them? OK, feel free, but then you are just switching the code you are using to communicate. You don’t have to use the standard meanings, but then you are just sewing confusion by switching mathematical systems without declaring so.
The standards don’t exist to oppress you, they exist so we can share a common set of meanings so we know what other people are talking about. It’s merely a means to make communication possible. Switching the rules is not giving a finger to “the man”, it’s merely going to make you misunderstood. Further, the oppressor (what we used to call “the man”) isn’t oppressing you with logic; they are oppressing you with cynical levers of power and using logic as a tool because logic works at achieving goals because its logical. The goal for power is the source of oppression, not its efficient cause of rational thinking.
As I said above, language does not always require precision. If I’m hanging with my friends around my neighborhood, on the porch or otherwise, and they code switch into a different set of syntax or grammar, I can follow along because doing so becomes obvious in context. I can literally hear the difference in the language and grok the meaning in a number of ways they express it. But if they suddenly decided, in their head, that “tree” meant “trolley,” this is more than code-switching; it is arbitrarily swapping usual meanings to no purpose but to confuse.
If we all decided, perhaps as a private joke, that when I say “tree” I mean trolley, then this is our private code, our private language-game. Perhaps it has an origin in a joke or something that means something to us. To us, in such a circumstance, this would then makes sense and would be clear communication. But it has to arise in a context which this meaning becomes clear through use, not mere unstated fiat. That is, it has to arise organically from context, use, and agreement before its meaningful.
Similarly, if someone simply types “2+2=5” without any context, there is no attempt to indicate the code switch or standard alteration here. I have no way of knowing that you have switched to some alternate or non-standard mathematical system. If, hypothetically, this was a reference to some private joke, in-group code switch, or some obscure non base-10 mathematics we use together, then we’re fine because we understand what was meant.
Again, you are free to use whatever terms in whatever way you want, and utilize whatever mathematics, symbols, etc which you like. However, if your point is that we shouldn’t have to accept the dominant standardization, the dominant code, because that code is part of the western system of cultural oppression, well….
Then we need to have a conversation about that.
But before I do that, I want to make something clear; if the point in saying 2+2=5 is merely to draw attention to the fact that some standard exists and that it is arbitrary, and that it’s possible to see the world using different meanings and perspectives, then fine. I find that impractical, but there is not (necessarily) any philosophical or logical error happening in doing so.
Unless, of course, you just reject logic or truth altogether, as I made reference to above. In that case, we have nothing to talk about.
So, what might we have to talk about?
The West, oppression, and rational thinking
There is no doubt that “The West” has committed atrocities of many scales upon the world. This set of cultures does not have the monopoly on such atrocities, but perhaps it is leading the world in this category. Everything from colonialism to the slave trade has been written on the ledger of Western history and culture, among their many other crimes of history. I am aware of much of this history, and I think that this context must be kept in mind.
Yet this is too simplistic.
The West also has philosophers, scientists, and other intellectuals who opposed–with speeches, literature, revolutions, and other means of resisting–the political, cultural, religious, etc methods of oppressing, enslaving, and otherwise being dicks to people of many regions of the world, including its own people. Also, many other sets of cultures have also committed many atrocities of their own.
The West also doesn’t have a monopoly on such philosophies, literature, and efforts of resistance. No culture has a monopoly on any human behavior. So even if “The West” is winning in the category of awful, and currently holds the reigns of power and oppression, they didn’t invent it nor are they solely liable. But if the point is that “The West” is currently holding the reigns and is primarily responsible for the current awful, then we are largely in agreement.
But let’s assume, for a moment, that “The West” was solely responsible for the general awful, for argument’s sake.
That is, even if “The West” did hold a monopoly on all the colonialism, wage/actual slavery, genocide, environmental ruin, political corruption, etc, and all other times, places, and people were innocent victims of “The West,” this still wouldn’t address the fact that much of the philosophical history of the “The West” are not the foundation of this oppression and historical crime.
Remember, the people holding the reigns also oppress and dominate its own citizens. Hell, my ancestors (primarily Irish) were under the boot of the English for hundreds of years, and while certainly not ideal in themselves, the Irish were rarely if ever in positions of any power with which to oppress anyone. Yes, my skin color offers me advantages in many cases in the world, but much of the historical oppression has landed upon my ancestors as well, even if to a lesser degree than it did to some others. I can still be racist as Irish, but the oppression is not coming from me. (Whether I’m responsible if I don’t resist it and speak out againt such oppression is another question).
But further, there is a tradition of resistance to the oppression, corruption, and dominance from those in charge within “The West” as well. Giordano Bruno? The Enlightenment? Abolitionists? Such individuals, movements, and ideologies were opposed to the sources of power within “The West” itself. And they had to use the tools of logic, rationalism, skepticism, etc in criticizing its own set of cultures. It is part of the “Western” tradition to criticize itself, it’s just that such critics rarely had sufficient power to make change. And when they did manage to achieve change in power, the results were often mixed, if not downright awful. The same is true in the East.
Criticism, resistance, and revolutions against the crimes of “The West” have tried, using rational and martial tools, to stand up to such crimes, usually failing in the attempt. The tools of oppression are not logic, rational thinking, skepticism etc, even insofar as those tools are used for them (because you need to use these tools to do anything well).
And that is the crux, here. To practically achieve any goal, whether oppression, liberation, or mere theory you must use, to some extent, rational thinking. It is merely a tool to be used for building or destroying; harming or helping; killing or healing. To irrationally conflate logic and rationality with oppression is to misunderstand the role that such tools have played throughout history, and is a failure to understand their power and importance as tools to resist and stand up to power.
The foundations of oppression are not logic nor truth. Fear, tribalism, greed, and other human flaws are the source of these things, and because logic, rational thinking, etc work in finding ways to achieve the ends of such ignoble flaws, they are necessarily part of the recipe. But remove greed, fear, and all the rest of those things which drive us apart, and you have no ideology at all; merely helpful tools which are impotent in themselves. That is, if you seek to resist oppression and win, you need to use the tools of rational thinking or you will almost certainly lose.
Yes, the systems of oppression, whatever they are, cynically utilize logic in the greedy grab for power, influence, deception, and ultimately control. But to reject one of the tools it uses, merely because it uses it; to employ resistance against such cynical control while rejecting its most powerful tools–logic, rationalism, and skepticism–is to make the exact mistake they are hoping you will make; you are falling into their trap. They see you rejecting truth, logic, and rationality and don’t have to say or do anything, because that’s how they gained that control to begin with. They denied you education, knowledge, and understanding and so they took power from you. When you reject it on your own you are scoring an own-goal. You are helping them dominate you.
You are not punching up, you are punching yourself in the face.
Power wants you weakened, confused, and impotent. It wants you screaming, irrational, and fueled by blind rage. This is how it manipulates you.
If you really want freedom of oppression, you need the strongest tools at your disposal. Those tools are clear, rational, logical, powerful thinking.
It means breaking your chains of tribalism that take the form of traditions, in-groups, nations, religions, racial identities, and even viewing love and sex in terms of property (which has been one of the intentions of this blog, over the years). The more you insist upon the boxes that are placed upon us as defining us, from the outside, the less free you are. If you really want to break free from oppression, you need to reject the limitations placed upon you; you need to deconstruct and possibly reject the framing of who we are, as humans, according to them.
But this doesn’t mean rejecting humanity’s greatest tools. So-called “Western” logic is not Western. It is a universal set of ideas discovered and improved by many cultures, throughout history, which have allowed us to build greater things, envision better ideas, and overcome previous mistakes. Just because most of us, in the West, talk more about Plato and Aristotle rather than Confucius, Averroes, or Avicenna is more of an historical accident than anything else.
In fact, the reason that we are talking about Aristotle at all has a lot to do with the fact that during the “dark ages” of European history, The Islamic cultures and empires carried the torch of intellectual history, expanded upon it, and gave us those very mathematical symbols we use now.
Remember, 2, 4, and 5 are Arabic numerals, ultimately derived from much older Indian symbols. 2+2=4 isn’t Western; it’s a set of symbols that are influenced from many contributions from many cultures, and have existed for hundreds of years before “The West” even had fever dreams about colonizing anyone except itself.
When the European powers colonized, invaded, and committed genocide with the help of gunpowder, remember that the West didn’t invent gunpowder. The fact that the West uses gunpowder doesn’t necessarily mean that we shouldn’t ever use it to resist further oppression, does it?
If you agree with my rhetorical point, then you should also agree that we need to utilize logic, rational thinking, etc. And if we’re going to insist upon 2+2=5, utilizing other “contexts,” then we are merely going to divide ourselves into more tribes, and soon we will not be able to communicate, let alone resist oppression. Like the story of the Tower of Babylon in the old Hebrew Bible, we will be cast in different directions, speaking with different kinds of mathematics and contexts of logic, and the oppressors will have no meaningful resistance against them because we can’t coalesce around the powerful tools which many have rejected because they saw them as “Western.”
Even the most evil, most corrupt, and most problematic oppressors use the best tools because the best tools work. To reject their tools is to reject your own power to resist their power.
That is precisely what those in power want us to do. Freedom requires using the best tools we have, and 2+2=4 is the basis for that power.