> Mathematical knowledge can be justified by pure logic without reference to any sensory experience.
No, I don't think it can. I challenge you to give me an example of mathematical knowledge that you can justify without reference to any sensory experience, keeping in mind that reading and hearing people talk are both sensory experiences.
It doesn't even have to be math. I'll bet you can't even define the distinction between "true" and "false" without reference to sensory experience.