Update to Ray 2.0: The examples about the Italian school/Frege/Cauchy are all supposed to be examples of us formalizing intuitive processes (algebraic geometry, set theory, analysis) in the “wrong way”. Reply to Ray 2.1: I think you mostly understand my post but just to clarify, I don't even get into ZFC. PA itself could be … Continue reading Ray 2.2 : update and reply →

I read Asvin's post. I generally agree with it. I am a bit shaky on some examples - I think there is room for a balance. It is certainly disturbing to imagine that certain empirical predictions will fail. What Asvin seems to be saying is that it is at least conceptually possible that the following … Continue reading Ray 2.1 : Balancing p.o.v →

There is a common sentiment that mathematical truths are distinct in nature from truths of other kind (in the sciences or otherwise) in that mathematical truth is eternal and unchanging. I would like to pose an alternative view to this considers mathematical truth as essentially being on the same footing as other kinds of truth. To … Continue reading Ray 2.0 : Mathematical investigations as parallel to other sciences →