Well, the deeper issue is “Must we rely on the Peano axioms?”
I shall not get into all the Godelian issues that can arise,
but I will note that by suitable reinterpretations, one can
indeed pose real world cases where an “apparent two plus
another apparent two” do not equal “apparent four,” without
being utterly ridiculous. The problem is that such cases are
not readily amenable to being easily put together into useful
axiomatic systems. There may be something better out there
than Peano, but Peano seems to work pretty well an awful lot.
Well, the deeper issue is “Must we rely on the Peano axioms?” I shall not get into all the Godelian issues that can arise, but I will note that by suitable reinterpretations, one can indeed pose real world cases where an “apparent two plus another apparent two” do not equal “apparent four,” without being utterly ridiculous. The problem is that such cases are not readily amenable to being easily put together into useful axiomatic systems. There may be something better out there than Peano, but Peano seems to work pretty well an awful lot.
As for “what is really true?” Well… . . . .