Yes, yes yes, this is of course fine to reject the axiom I agree. But the metaphysics is where it actually gets good (I only did a maths degree and am leeching the metaphysics of it out of my system with posts like these lol).
I mean I think this is a plausibly reasonable account of when mathematical objects exist I guess, kind of a “structuralism” flavour to it, I’m actually somewhat sympathetic. I didn’t think of that objection!
Though I will note this is only one example of a potential object with perfect-essential necessity. I’ve linked the formalization which comes up with a logical model of these axioms (including all the necessity, perfect-essential necessity, etc) in a different thread on your original comment, if you’re curious!
If you’d like to stop back-and-forthing about metaphysics, seems reasonable. I’m sure we’ll make lots of progress if we keep going debating our priors about this! \s
Yes, yes yes, this is of course fine to reject the axiom I agree. But the metaphysics is where it actually gets good (I only did a maths degree and am leeching the metaphysics of it out of my system with posts like these lol).
I mean I think this is a plausibly reasonable account of when mathematical objects exist I guess, kind of a “structuralism” flavour to it, I’m actually somewhat sympathetic. I didn’t think of that objection!
Though I will note this is only one example of a potential object with perfect-essential necessity. I’ve linked the formalization which comes up with a logical model of these axioms (including all the necessity, perfect-essential necessity, etc) in a different thread on your original comment, if you’re curious!
If you’d like to stop back-and-forthing about metaphysics, seems reasonable. I’m sure we’ll make lots of progress if we keep going debating our priors about this! \s
Yeah I think it might be more productive, if I wanted to make progress on this, to look at the math rather than the metaphysical back-and-forth.
Indeed!