Only when people make posts while they are still writing their responses to previous posts... I don't know what you mean by "mathematics is empirical". That is a nonsense statement. "Empirical" is not a quality that a body of knowledge can possess. If you mean "mathematical truths can be known by empirical means", then yes, of course. If I put two things next to two other things and count them then I can learn that 2+2=4 empirically. However, I would deny that mathematical truths can be known only by empirical means. They are true by logical necessity and can be known intuitively. There's nothing particularly controversial about that. You seem to be denying the possibility of any kind of a priori knowledge at all. That seems almost impossible to believe - quite apart from being itself impossible to verify empirically. Well, I'll have to take your word for that as I don't know about it. But I don't see that it really makes any difference unless you explain in more detail. As you can no doubt tell, philosophy of mathematics is not my field so I don't want to digress too far down this road. I also note that I don't see any responses to my other points against your logical positivism and extreme pragmatism, so I'll assume that, apart from the disagreement over the truth value of mathematical statements, I've convinced you of the rest.