This time I disagree with Eliezer...this experiment won't convince me that 2+2=3...wouldn't even convince me that physical maxim "everything goes somewhere" is wrong...I would find where the earplugs are (even if they sublimated). That still don't make that an "imutable belief".
There's nothing wrong in switching lexically 3 and 4 ( S(2) = 4; S(4) = 3; S(3) = 5 )...sounds unuseful, and don't attack Peano's axioms. That would make me believe in 2+2=3.
To stop believing in the integer numbers, it's needed to prove an inconsistency in Peano'...
Nice, but the difference with this "belief" is that you're talking about sensory "counting" (visual grouping), and I was talking about the numbers themselves, as models for games, other phenomena, etc., and not just as a "counting" tool.
In the 1+1=3 example, to define the cardinality, he/she used the Peano's axioms, didn't he/she?
I don't see the "visual sensory counting" as the only use for "2+2=4", that's why I don't think this experiment would refute such a priori content.
Another idea: let Ann be a girl w... (read more)