Fact Check 2+2 equals 4

10) must contend with two questionable consequences of their views: (1) Although the Earth and the Sun were around long before humans and other animals were, the fact that two plus two equals four was not.

In establishing the mundane reality ... 2 + 2 = 4, in De Neutralibus et Mediis Libellus (1652) Johann Wigand said: "That twice two are four; a man may not lawfully make a doubt of it, because that manner of knowledge is grauen [graven] into mannes [man's] nature." In the comedy-of-manners play Dom Juan, or The Feast with the Statue (1665), by Molière, the libertine protagonist, Dom Juan, is asked in what values he believes, and answers that he believes "two plus two equals ...

It provides a deeper dive into the process of increasing generalization and abstraction I referred to, starting with 2 + 2 = 4. He mentions how this process is somewhat validated by the fact that such “wild” results are found to be correct in physics. You can find the video here.

Description: Two plus two equals four. For more information, see "2+2=4 Trivia" on the Metamath Proof Explorer Home Page: mmset.html#trivia. This proof is simple, but it depends on many other proof steps because 2 and 4 are complex numbers and thus it depends on our construction of complex numbers.

Of course, numbers were discovered centuries before set theory, and historically they were "reversed engineered" back to the axioms of set theory. The proof of 2 + 2 = 4 shows what was involved in that reverse engineering, representing the work of many mathematicians from Dedekind to von Neumann.

Finally, there are two important successor-axioms we need to know to prove 2 + 2 = 4: A1: ∀x(x + 0) = x A2: ∀x∀y(x + sy) = s(x + y) So the proof that 2 + 2 = 4 is the following: ... (ss0 + ss0) = ssss0 by Transitive Equality on 5 and 7 ...

Accurate measures will repeatedly, positively indicate that adding two quarts and two quarts of water does not yield four. For cooking purposes, the difference may not be critical. For scientific purposes, the difference can be critical. Even for cooking, if the water is left to sit a while, ...

If you take two integers and use the standard addition law, then, yes, two plus two equals four. But there are many other things those numbers could stand for and many other addition laws, and depending on your definition, two plus two might ...

Opponents of this approach often claim that mathematics does not have room for creativity, sarcastically suggesting that this is tantamount to teaching that 2+2≠4. I’m here as a Ph.D. mathematician to prove that 2+2≠4. ... The National Review, for example, leads an article on “Woke Math” with a joke about what 2+2 might equal.