Not wanting to go off topic.
But 2+2=6 isn't something I would consider illogical.
What do you mean by the symbol, "2"? Maybe this symbol represents three units. So then 2+2= three units + three units = six units which can be represented by the symbol "6" (If you'd like).
What I mean is that in your mind you can decide for yourselves on what these "Symbols" represent in Mathematics.
Saying 2+2=6 is correct since the statement is ambiguous if we consider that Mathematicians haven't agreed on these symbols.
However, saying "Two units + Two units = Six units is incorrect.
Of course, there is nothing called "True symbolization of a concept". Humans always have to create Symbols for different ideas. However if someone asks me, 2+2=6? I would simply say I don't know. I would need him to state, "We are following the numerical symbols that mathematicians have agreed on."
**Warning: Don't give this answer in a test ^^.. I have learned that the hard way because I was simply mad at the teacher so I further replied like so."