the idea that “2” exists as an abstract idea apart from any physical model
It’s this one.
Note that “Platonism false” does not imply “physicalism true”. Numbers just might not be real entities at all, as in Formalism.
Now suppose that as the game board evolves, the AI discovers Peano Arithmetic, derives “2 + 2 = 4”, and observes that this corresponds to what happens when it puts 2 apples in a bag that already contains 2 apples (there are apple-like things in the AI’s simulation). The fact that the AI derives “2 + 2 = 4″, and the fact that it observes a correspondence between this and the apples, has to be entirely determined by the rules of the Game of Life and the initial state.
If the AI discovers transfinite maths or continuum mechanics, that fact is also entirely determined by rules of the Game of Life and the initial state. And neither of them can apply to a GoL universe—they are not “physics”.
Now, at this point, you need to choose between stipulating that the non-physical maths is false because it is non physical (finitism); or accepting that Platonism and physicalism are both false.
If the AI notices how deep and intricate math is, how its many branches seem to be greatly interconnected with each other, and postulates that math is unreasonably effective
But it’s not maximally effective: maximal effectiveness would mean that any mathematical truth is a physical truth.
You’ll note that it doesn’t matter if we replace the Game of Life by some other similar game where the board is a continuum
If the physical universe is any way a subset of the mathematical “universe” , you have the same problem.
Note that “Platonism false” does not imply “physicalism true”. Numbers just might not be real entities at all, as in Formalism.
If the AI discovers transfinite maths or continuum mechanics, that fact is also entirely determined by rules of the Game of Life and the initial state. And neither of them can apply to a GoL universe—they are not “physics”.
Now, at this point, you need to choose between stipulating that the non-physical maths is false because it is non physical (finitism); or accepting that Platonism and physicalism are both false.
But it’s not maximally effective: maximal effectiveness would mean that any mathematical truth is a physical truth.
If the physical universe is any way a subset of the mathematical “universe” , you have the same problem.