2+2=5? A Postmodern Odyssey
Revisiting a Bizarre Great Awokening Sidebar
At the height of The Great Awokening, there was a Twitter kerfluffle when a Harvard grad in stats declared that 2+2=5 (or, at least, that it can).
He now has over 150k followers, and a ton, I’d guess half or more, came from the exposure he got from this little piece of absurdity. I had mostly forgotten about this until I started working on this post:
and found it a bit amusing that, after mocking 2+2=5 (as I show at the end of this post), I had posted a serious review of IAT/implicit bias work in which the title included “0≠0”(if you haven’t already, you’ll just have to read that post to see how I did that; I promise it will be worth it, at least if you can follow the math and stats).
Returning to Carr’s post, lots of Twitter, including academic Twitter loved it. But lots also hated it and there were all these dumb (and some sophisticated) justifications for it. Culture war stuff. To those who do believe that literally everything is socially constructed in the strong sense of there being no such thing as objectivity, it was received as vindication, coming from a statistician with math bona fides, in much the same way that Sokal’s original hoax paper on how quantum gravity is “socially constructed” (before it was revealed as a hoax) was received as vindication coming from a physicist. Actually, in my view, the two events have lots of similarities, with the main difference being that Sokal knew he was engaging in a hoax, whereas Carr …
Popular Mechanics had this to say:
This type of analysis, which was all over Twitter at the time, struck me as so dumb I could not believe it. Head-shakingly, face-palm sophomoric stuff, not counting that, even as a sophomore, I am pretty sure I would have cringed at it. And after the likes of academics and Popular Mechanics took it seriously, I could not help but wonder if they were just signaling their “anti-racist” bona fides by doing so.
Regardless, to many (like me), it was emblematic of an ascendant intolerant and authoritarian movement.
The Trivially True Completely Dumbass Way 2 + 2 can = 5
I mean, there are ways in which the 2+2=5 business can be trivially true. If you define words and numbers any way you please, well, then sure, it is “true.” Of course, any ridiculous claim can become trivially true this way. If you define “faster than light travel” as “sipping coffee” then I am traveling faster than light right now!
And the link to authoritarianism that comes with doing so is made clear here:
In addition to the whole analysis being at least authoritarian-adjacent, it was also emblematic of a certain move in left/far left circles of simply redefining words to advance some political agenda. “Diversity” comes to mind:
But there are many others, such as redefining “woman” to be something so complex a Supreme Court nominee felt she (? how do we know she is a she? it is so difficult….) had to defer to “biologists.” The bizarre complexification of this incredibly simple question was addressed in, of all things, an actual philosophy paper. What is bizarre is not that it was addressed, but that it was so necessary to address that doing so warranted a peer reviewed publication.
The abstract is a joy to behold:
When the intellectual classes act like they seriously believe something simple is overweaningly complicated, it becomes appropriate to explain the obvious in a peer reviewed philosophy journal. I can relate; a few years ago we too defended the obvious because it was no longer obvious to many in those same intellectual classes:
Note that it had to be published in The Journal of Controversial Ideas because:
Women being adult human females, the importance of impartiality and merit in science, and 2+2=5 might seem like they have nothing to do with each other. That would be completely wrong; they have everything to do with each other. All stem, at least in part, from the Humpty Dumptyism of postmodern-infected critical and subjectivist perspectives so eloquently highlighted and foreshadowed by Orwell’s and Arendt’s analyses of authoritarianism. Abandon objectivity and truth, then its easy to change the meanings of words — their meanings need not be anchored to anything real, because there is no objective reality. And if there is no objective reality, then words can serve one’s political agenda, and if changing their meaning can advance the liberation of the oppressed, we’ve all done a good day’s work, haven’t we?
Philosopher Matt Lutz took these issues head-on in a dense but brilliant post debunking the inherent subjectivist relativism of critical and postmodern perspectives:
In that post, you will find this:
What we care about in academic inquiry isn’t whatever-anyone-might-happen-to-mean-when-they-use-the-word-‘true.’ What we care about is truth - which is to say, truth as we understand it. And if you want to use the word ‘truth’ to talk about something else, then you may do so, but don’t expect us to care about your subject of interest. (By silly analogy: suppose some group decided to use the word ‘truth’ to mean ‘a giant bowl of lime jello.’ They’d be well within their rights to do so. But if they then declared themselves to be passionate about the pursuit of truth, we should understand their interests as being primarily concerned with dessert, and would be well within our rights to say that such a pursuit is not consonant with the university’s search for truth. We wish them the best in their quest for jello, but there’s no reason to allot tenure lines towards it just because they use the word ‘truth’ to describe their quest.)
Is Matt’s jello example silly? Well, sort of, intentionally so. But is it more silly than some of the justifications for 2 + 2 = 5? Look back at the Popular Mechanics excerpt. “+” is reinterpreted/redefined so that it does not necessarily mean “the sum of two quantities.” Instead, it can mean almost anything we like, such as “a male and a female of a species have sex.” Well, why not? Everything is “socially constructed” so we can make “+” mean anything we please!
Truth Tracking Bullshit (8/4/26 Update)
The “words can mean almost anything we like so truth is lime jello” account is right as far as it goes, but something nagged at me about it. 2 + 2 = 5 is still about numbers and math. It is not about lime jello or space travel. If it was about lime jello or space travel it would be obviously ridiculous. Carr, the supportive Twitter academics, and Popular Mechanics appear to be providing some new deepity about math, not about lime jello, and this makes it appear as if those deepities are trenchant and should be taken seriously. They have a weird superficial plausibility, that, for folks who do not think about it too much, might be sucked in. Note that no one said “We are redefining the “+” sign to mean “two animals having sex that produces an offspring” It is implicit in “two animals can become three through reproduction.” This bizarre reinterpretation is hidden but there, if you think about it for more than 5 seconds. Note further that the statement “two animals can become three by reproduction” is, by itself, literally true. So what you really have here is this weird combination of things that are actually true camouflaging an absurd redefinition of “+.” So you do have an imposition of an absurd new meaning (lime jello!, i.e., “+ means sex!”) but it is hidden under a seemingly plausible analysis.
Philosophy to the Rescue, Again
Frankfurt, a Princeton philosopher, wrote the book on bullshit, aka “On Bullshit.” Its not completely obvious when you read it, which I have done, but the rumors have it that it was intended to be a broadside against postmodernism. Its a short book but he also has an excellent short version which you can find here.
The short version is this: Frankfurt defined bullshit, not as lying, but as being singularly unconcerned about truth as most of us who are Dickians conceive it:
Of course, he also wrote this:
Regardless, Frankfurt’s definition of bullshit actually describes any subjectivist perspective, including but not restricted to postmodernism, which denies the existence of objective truths. I mean, from their perspective, there are no objective truths so of course they are not concerned with them!
But this does not solve the problem that nagged at me. Carr, Popular Mechanics et al, were still constrained by something in that their justifications for 2 + 2 =5 did in fact refer to quantities, not lime jello or space travel. If they believe they can define words and concepts any way they please, why did they bother to make their examples seem relevant and trenchant?
2 + 2 = 5 as Truth Tracking Postmodern Bullshit
A 2024 philosophy paper by Cova updated Frankfurt’s analysis of bullshit and provides the answer. The core idea is “truth tracking bullshit.” He defines truth tracking bullshit as:
what seems or purports to make an interesting contribution to a certain inquiry but can be identified as failing to do so under closer inspection by a minimally competent inquirer.
Bingo! Bullshit, including but not restricted to postmodern/subjectivist bullshit, does not permit explicitly defining truth as lime jello, or “+” as “animals having sex” because that would make the absurdity of their arguments transparent, and, as such, undercut their own attempts to “make an interesting contribution” to the understanding of 2 + 2. But, as Cova correctly pointed out, all one needs is “minimal competence” to understand the absurdity of such redefinitions. Working backwards, then, if all one needs is minimal competence to understand its absurdity, and lots of people, such as those at Popular Mechanics and academia, embraced 2 + 2 = 5, what does that say about their competence?
2 + 2 = 5
Of course, in the subjectivist worldview, “+” can mean anything we please, its just that they want their analysis to appear relevant and interesting, so no lime jello. But it certainly can mean “if two animals reproduce then they become three so 1 + 1 can = 3.” This is very cute, has a superficial appearance of reasonable plausibility, and it takes some minimal level of competence to realize that, implicitly, they have absurdly redefined “+” to mean “two animals have sex.”
Hell, if those animals have twins, 1 + 1 = 4. Cats and dogs have whole litters, so 1 + 1 can = 5, 6, 7 or more! And hey, if they keep making babies, the sky is the limit! At breakfast at a cafe the other day, I heard someone say they had 21 brothers and sisters — not step, not blended families, from one dad and mom (well, at least that’s what she said; I did not investigate the genetic ancestry of the 22)! But why restrict this to humans? Popular Mechanics referenced a tweet involving “animals.” Sea horses, which reproduce with a single mother and father, can have 2000 babies! 1 + 1 =2002!
Regardless, I thought it might be fun to play around with 2+2=5 simply by having the terms mean something completely absurd that nonetheless tracked actual math. So, shortly after the various defenses of 2 + 2 = 5, I tweeted this, and, with over 100k views, it is one of my few tweets to have ever gone viral:
The responses were a hoot. Here are some of my favorites:
Is there some serious conclusion to all this nonsense? I hope so. I am rooting for broad spectrum rejection of postmodern “there is no such thing as objectivity” nonsense. And it does seem somewhat better now than 2020.
I’ll take what I can get. Hopefully, I will get this:
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I remember that moment in Twitter history! Growing up in post colonial India, I could not figure out what was colonial about science. That was dark phase of “social constructivism” ! Hope we are moving beyond that phase
The absurdity of it all . You could also say truthfully that One biological Male + One biological Woman could be 1+1 = 1 Singleton or 2 Twins or 3 Triplets or 4 Quadtruplets or 5 Quintuplets or 6 Sextuplets or 7 Septuplets or 8 Octuplets .