Christopher F. Rufo  ⚔️

So that's a situation where one might have expected 2+2=4 to be a very direct model for reality, but in fact it isn't. (Does that threaten the status of 2+2=4? Not if we do as I advocate and talk about the truth *within a system*.) 18/

I'll end by justifying my answer of "It's complicated" for the poll. The basic point of the question of whether 2+2=4.00 is that the numbers on the left-hand side look like integers and the number on the right-hand side looks like a real number. 19/

And while in elementary mathematics it's fairly harmless to think of the real number 2 as being "the same" as the integer 2, in higher mathematics that's very inconvenient for all sorts of reasons. And in fact, even non-mathematicians treat them rather differently: 20/

typically 2 the integer is used for counting, whereas 2 the real number is used for measuring. But in higher mathematics there's a technical sense in which integers *aren't* real numbers -- we say instead that they can be *identified* with real numbers. 21/

This matters a lot in computer programming too. So while there's certainly a sense in which 2+2=4.00, there's also a useful and sensible sense in which 2+2 and 4.00 are simply different kinds of objects (or "types", to use a more technical term) so can't be compared. 22/

In other words, it's complicated. PS I don't think @kareem_carr would disagree with any of this, except perhaps minor details.

Actually what I meant by that PS was something stronger -- I see what I've written above as an elaboration of part of what @kareem_carr has already said.