For example, consider a simulated world where you control the code. Can you make it so that 2+2 in that simulation is sometimes 4, sometimes 15, and sometimes green? I don’t see why not.
I think you’re conflating the physical operation that we correlate with addition and the mathematical structure. ‘Green’ I’m not seeing, but I could write a computer program modeling a universe in which placing a pair of stones in a container that previously held a pair of stones does not always lead to that container holding a quadruplet of stones. In such a universe, the mathematical structure we call ‘addition’ would not be useful, but that doesn’t say that the formalized reasoning structure we call ‘math’ would not exist, or could not be employed.
(In fact, if it’s a computer program, it is obvious that its nature is susceptible to mathematical analysis.)
I think you’re conflating the physical operation that we correlate with addition and the mathematical structure. ‘Green’ I’m not seeing, but I could write a computer program modeling a universe in which placing a pair of stones in a container that previously held a pair of stones does not always lead to that container holding a quadruplet of stones. In such a universe, the mathematical structure we call ‘addition’ would not be useful, but that doesn’t say that the formalized reasoning structure we call ‘math’ would not exist, or could not be employed.
(In fact, if it’s a computer program, it is obvious that its nature is susceptible to mathematical analysis.)