Saw an article talking about how we do not know why 2+2=4. Seems pretty simple to me. It has to do with representing counting and translation along a fixed ruler, with the observation that counting '2' from a starting point, and '2' from the new starting point - take you to a place on the ruler that is aka '4'.
If what you are missing in this account is an underlying ontology, seek no further than topic structures (dude!). The point is not that the two ledgers are identical ('2+2' is not the same as a direct '4') but the final state of the ledger is the same. In this version, we consider '1' to be a type with multiple instances.
There should be nothing surprising or deep about having a single name for a place ("4") and having different ways of getting there: direct counting versus repeated counting. Maybe it is a bit magical that we can do the counting in our head and always get the same results. On the other hand it looks like I am saying '2+2=4' is an empirical statement.
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