I'm not sure why you're excluding the possibility of both. Math is largely based on reason, and I think most empiricists believe that mathematicians have knowledge not based on sense experience.
>most empiricists believe that mathematicians have knowledge not based on sense experience.
Even the knowledge that 1+1=2 comes from sensing objects in the world. If you'd never seen more than 1 thing ever you would have no sense experience to base your conceptual framework of addition on.
All knowledge -mathematical or otherwise- can be traced back to sense experience. Your ability to reason mathematically comes from your experience of the world and from your experience of your own thoughts. Intuition is fundamentally a sensory experience.
Re:Rationalism vs. Empiricism
by paulpauper on Sunday July 16, 2017 @02:07PM
(#14783299)
that is what Kant argued regarding the synthetic priori . You cannot know the thing-in-itself.
Either there is knowledge absent sense experience or their is not. This is where the philosophies differ and where mutual exclusion arises.