No Platonism is necessary here; only the Simple Truth that taking the string “2 + 2” and applying certain rules of inference to it always results in the string “4”.

Wrong. The only "truth" is the actual getting "4" when someone applies those rules, and things like that you think that someone will get "4" when they apply the rules to "2 + 2".

The phrase "if A then B" generally just means something like "I tried putting A and not B into my idea of how the universe works, and it didn't make any sense".