These discussions about whether 2+2=4 are confusing because 2+2 is 4 by definition of this operation of addition, and then we see in what cases real world phenomena are described by this operation. If you define 2+2 as anything but 4, then you're just describing a different operation. There are many operations where 2 and 2 give 5.

The problem, always, is that there's no causal connection between mathematics and reality. Suppose you try to force one and say that however many rocks you have in a cup when you combine two cups (each with two rocks), that is going to be THE operation of addition. Then asking what 2+2 has to be is asking how many rocks you can have in the final cup. Well, it's not logically impossible for rocks to follow a rule that every four rocks in a certain small area will make a new rock and increase their number to 5. It just happens, in our reality, that rocks satisfy Peano arithmetic (and don't resonate daughter rocks).