Does 2 + 2 Always Equal 4?

Christians are found of arguing that 2 + 2 always equals 4. They make this argument to support their claim that there are "absolute" truths that (like their "God") necessarily exist, which we can all know and must in essence all abide by. But they make this argument without ever actually considering its further implications, other than they think it supports their "beliefs" about God, religion, absolute ideas of right and wrong, and so on. The trouble, of course, is that, like everything in life, it is never as simple as that.  And here's why. 

First, David A. Gershaw has shown how sometimes, 2 + 2 does not equal 4. He did this by pointing out that there are four types of measurement scales: nominal, ordinal, ratio, and interval (or NORI). As he went on to explain, it is only in the last two categories that we find 2+2=4, but not in the first two. In short, while nominal classifies players on a football team, ordinal classifies and ranks those players by height or weight, for example. 

But an interval scale combines qualities of both the nominal and ordinal scale with equal intervals. The problem is that an interval scale includes arbitrary zeros, which Gershaw illustrates by pointing out that 20^oC is not twice as hot as 10^oC.  And ratio scale has all the qualities of nominal, ordinal and interval, plus absolute (true) zero. 

Additionally, Clfford Levy pointed out that "when we realize why 2+2 is not always 4, we start thinking critically." In an article for the New York Times, Clifford quotes Georgievich Bogin, who runs a school called the New Humanitarian in Moscow who points out:

"While two apples and two oranges add up to four pieces of fruit, two cats and two sausages only add up to two well-fed cats. And if you take two drops of water in a saucer and add two more drops of water, you really only get, one big fat drop of water. It is this ability that allows us to then answer the riddle of how many of 10 birds are left on a tree after a hunter shoots one."

Second, is a rounding problem, that illustrates the bias of "near enough," discussed by David Hand in his book, The Improbability Principle. Hence, if by "2" we mean any real number that rounds to "2," and by "5" we mean any real number that rounds to "5," then 2.4 + 2.4 = 4.8. And while we would round 2.4 to 2, we would round 4.8 to 5. But this may just be splitting hairs, of course. 

Third, there is a difference between "beliefs" and "knowledge," which the Christian often conflates as easily  and as often as they conflate their "beliefs"with "infallible truths." And along with this conflation, the Christian further implies, without a shred of evidence to support such an implication, that a mathematical truth such as 2+2=4 somehow "proves" or at least suggests that "truths" exist which are altogether external to the human mind, even though numbers are a purely human invention (since we do not see aardvarks or amoebas doing accounting or quantum physics). 

As Rene Descarte pointed out, in the realm of pure ideas, the self-evident idea that 2+2=4 may in fact have no reality outside the human mind. And while Ayn Rand's hero John Galt posits in Atlas Shrugged the idea that "the noblest act you have ever performed is the act of your mind in the process of grasping that two and two make four," we still have the question of free will.

Fourth, the question of "free will" is something the Christian often claims to be a champion of even as they often falsely accuse all atheists of being nothing but a bunch of deterministic materialists (even though Jean Paul Sarte was an atheist who believed free will was only possible outside of the bondage of a belief in a "God").  

Fyodor Dostoyevsky, for example, proposed that it is the free will to choose or reject the logical as well as the illogical that makes mankind human. He added: "I admit that two times two makes four is an excellent thing, but if we are to give everything its due, two times two makes five is sometimes a very charming thing too."

And fifth, the Christian who offers this mathematical axiom as evidence for the soundness of their religious "beliefs" only ever overlooks the fact that it is not the atheist who denies that 2+2 can equal 4, but the theist, whose religious belief in a "God" amounts to demanding that 2+2 equals whatever God and their Bible tells them it equals! A "miracle," after all, is something that defies the laws of nature and even mathematics.

This is why Mikhail Bakunin called religious faith a “philosophical vinegar sauce," which combines, as he put it, “the most opposed systems” of philosophies with a complete and contemptuous ignorance of natural science, until “two times two make five” and proves “the existence of a personal God."[i] In other words, it is not the relativist or the atheist who argues 2+2=5, but the theist who insists that 2+2 = God. 

In fact, the same devotion that the Christian holds for their "beliefs" about their God and their "religion" are no different from that which Nazi Reichsmarshall Hermann Goring held for Adolf Hitler, with Goring declaring as adamantly for his own "beliefs" in Nazism as any Christian being fed to the lions in Rome,  that "If the Führer wants it, two and two makes five!" 

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[i]. Marx, Karl, & Engels, Friedrich, 2003. The Communist Manifesto and Other Revolutionary Writings. Dover Publications. p. 199.