I'll admit that I didn't want to go into all of that on this thread. I have said as much, however, in recent posts on the philosophy forum. See https://www.physicsforums.com/showpost.php?p=2446381&postcount=3.While I applaud kote for his intentions, and for having made this thread, I must take issue with the following:
That depends on how you define the symbols "2,4,5", and also, what your "+"-operation is meant to convey.
There might well exist well-defined "+"-operations that from some point of view are justified as being a "sort-of-plus"-operation, called +' in which 2+'2=5.
Maths is a set of logical games where we make up what are the valid rules for one particular game. Results are game-dependent.
I have no issue with anyone bringing up "sort-of-plus" operations. It's different when everyone agrees we are talking about the normal mathematical definitions of the symbols.
You can find people loudly proclaiming that P=P is not necessarily true within the rules of normal propositional logic. Something like that might have been a better example.
...want to fight about it on the philosophy forum?