There are two possibilities for the abstract existence of math equations.... a mind or no mind...
Here's another possibility: the quest for an "explanation" of the fact that the multiplication table works is basically misguided, for the reason I've already offered: that once you've established that something cannot be other than the way it is, it is futile to seek any further explanation for why it is that way.
Now you say, just below, that it
isn't the case that the multiplication table couldn't be otherwise, that in fact "it could be otherwise or should be otherwise in a mindless universe," but I can't imagine what you mean when you say this. If it really makes sense to you to say that two times two "could be and should be" something other than four, then I'm afraid I just don't believe in even the hypothetical possibility of this bizarre universe, and I certainly can't follow you into it.
So I propose we leave things at this: if two times two
could be equal to something other than four, then the fact that they do equal four in our universe is something that requires an explanation; if they
couldn't be equal to anything else, than no further explanation is required for the abstract existence of math equations. Does that sound reasonable to you? Why not?
A mind has the most explanatory power as opposed to your no mind postulate.
Maybe it's worth backing up here and going over what's your basis, generally, for saying that one hypothesis has more explanatory power than another one. How would you fill in the sentence, "one hypothesis has more explanatory power than another if it can..."? Because I genuinely cannot say how "a mind made it come out that way" is an "explanation" for why two times two equals four. Let me try to say why:
Nobody has ever seen any person create anything from nothing. But we do know that people with minds do make physical objects from other things. So maybe it's not entirely unreasonable to claim that the right explanation for the existence of the sun and moon and earth is that they were created, from nothing, by an infinitely powerful person with an infinitely powerful mind. It's quite a stretch, but OK.
However, not only has nobody ever seen any person create a mathematical or logical truth or rule from nothing, nobody has ever seen a mathematical or logical truth or rule created at all. It isn't like saying "well, maybe we couldn't put this mountain into orbit, but if we were as strong as Superman we could do it"; we
do know about how force can be used to accelerate mass, and we could calculate how much force would achieve this goal. But we
don't have the slightest inkling how even to begin using a mind to make something true which wouldn't otherwise be true, e.g. how to use mind-power to make the square root of two a rational number, or make two times two something other than four.
So we really don't have any reason at all to believe that producing mathematical rules is the sort of thing that can be done by any mind, no matter how powerful. And that being the case, it makes no sense to say that "the existence of math equations is a fingerprint of a mind and any other postulate is inferior."
No; not only for the reasons given above, but because it generally makes no sense to talk of explanations "winning by default." If we were living in 2000 B.C. and I told you that the reason the earth didn't fall down was because it rested on a turtle, and you then proceeded to show how unreasonable this was (what did the turtle rest on?), it would be absurd for me to say "I see you have no explanations, so mine wins by default." A silly or empty "explanation" is not really an explanation at all, and it doesn't win anything. Or maybe, more precisely, if it does win anything, it just wins a game that accomplishes nothing and is not really worth playing.
Your double standard is you require explanations for counter proposal of a mind and yet claim you have no obligation to offer any competing explanations.
Of course I did (repeatedly) offer an explanation for why the multiplication table worked: because it couldn't possibly not work. I went on from there to say that
even if that wasn't a good explanation, there is no obligation for anybody (me or you) to give a "competing explanation" if the only "explanation" on the board was one that didn't make sense, and I didn't think yours did make sense. That's my single standard for all.