[MacsHeadroom]

Because "Rationalists claim that there are significant ways in which our concepts and knowledge are gained independently of sense experience."

Either there is knowledge absent sense experience or their is not. This is where the philosophies differ and where mutual exclusion arises.

[empath75]

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.

[marksc]

>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.

[paulpauper]

that is what Kant argued regarding the synthetic priori . You cannot know the thing-in-itself.