Isn't this a wittgensteinian problem? ie how you interpret language is inherently subjective. But regardless of what language you use, or how you intend to bind the terms to reality semantically, apriori truth is still apriori truth. It's the only basis of objective "truth" we have access to. Throwing that out the window feels like tossing the baby out with the bath water.
Imo, this just comes down to the fact that most people would consider "standard" to be a floating signifier. I don't think the idea that mathematical concepts changing definitions when you change axioms is at all controversial in itself.
Imo, this just comes down to the fact that most people would consider "standard" to be a floating signifier. I don't think the idea that mathematical concepts changing definitions when you change axioms is at all controversial in itself.