Different math in physical multiverses or black holes?

Question

Are there thoughts that different physical multiverses or black holes have different math, I.d. physical events follow the mathematics that is not discovered yet, whose logic may be different from current first order logic, nonclassical logics or any other logics that admit already known algebraic (boolean and different) semantics?

Answer 1

Logic by itself does not apply to our universe, you also need physics. For example, if you had two sheep and four sheep and wanted to know how many sheep you had in all, you would have to use physics to map sheep to integers, logic to deduce $2+4=6$, and then physics again to map $6$ back to sheep. The idea that physical objects can be mapped to integers for counting is perhaps the first physical law that people learn.

In this light, it is not exactly clear what it would mean for an alternate universe to "not follow logic." If in the alternate universe two and two made five, you could get that to work with the same math we have now: all you would have to do is have a different physical law of counting, that said that sheep in a field should be mapped on to something other than integers, and sheep composition should be something other than addition. If nothing in our present knowledge of math would suffice, you could just invent something new.

Are there any systems that can be conceived of that cannot be constructed at all? Sure, one of them is a list of instructions that would allow you to, by following them, determine whether or not a computer program will eventually stop running. However, if we lived in a universe where the laws of physics "solved that problem," we could still make the non-constructive observation that doing such-and-such a thing will cause the universe to deliver us the answer to the Halting problem. Doing so would pose no threat to logic, because that would just mean the universe was at least one step above a Turning machine on the hierarchy.

Granted, the fact that I can't think of any situation that would force us to abandon logic is not proof of the claim that there is no such situation. Still, the constructive power at hand is great - perhaps great enough to handle any situation we could conceive of.