Outer universe with different math—We’re a simulation inside a different universe that runs on different math where 2+2!=4, but the math inside our universe is consistent. This is the same as 2+2=4 for most purposes. This is imaginable, I think...
Active demon—there’s a demon that controls all your inputs, in a way that’s inconsistent with any reasonable mathematics, but you can’t tell. This is the least likely, and if it were true I wouldn’t even consider myself a person.
Math is flawed—the whole concept of arithmetic, or all of mathematics, is inconsistent and it’s impossible to construct a system where you can actually prove 2+2=4. This doesn’t necessarily mean two apples and two apples makes four apples—it just means the apples behave like they do for other reasons than arithmetic. This is conceivable.
There are also like 3 different ways 2+2!=4.
Outer universe with different math—We’re a simulation inside a different universe that runs on different math where 2+2!=4, but the math inside our universe is consistent. This is the same as 2+2=4 for most purposes. This is imaginable, I think...
Active demon—there’s a demon that controls all your inputs, in a way that’s inconsistent with any reasonable mathematics, but you can’t tell. This is the least likely, and if it were true I wouldn’t even consider myself a person.
Math is flawed—the whole concept of arithmetic, or all of mathematics, is inconsistent and it’s impossible to construct a system where you can actually prove 2+2=4. This doesn’t necessarily mean two apples and two apples makes four apples—it just means the apples behave like they do for other reasons than arithmetic. This is conceivable.