Let me respond to some of your comments:
>>>I believe the rules of chess are what is left when you destroy all the chess boards and all the chess pieces.>The reason the rules of chess exist is because someone who was sentient thought them up. That could have been done in the presence or the absence of boards and chessmen, but it is unlikely that the rules got invented without someone making a board and a set of chessmen and trying the rules out.>>Of course, there are other sets of rules that work, e.g. checkers. But even if no other set of rules could work, that would still not be a sufficient reason for the rules of chess to exist.>>The fact is that there is not a single set of mathematical rules. You can adopt a wide variety of definitions and axioms as the 'rules' and develop completely independent branches of mathematics from each of those starting points.>>Nor can the rules of mathematics cause the existence of phenomenal reality any more than the rules of chess can manufacture a chess board.>The scenario that makes the most sense to me and which seems the simplest and most straightforward, is that some sentience thought about, and eventually developed some systems of mathematics, which no doubt included the system of arithmetic of natural numbers (and in my opinion, a finite set of them), and then proceeded to somehow construct phenomenal reality in conformance with this arithmetic mathematical system.