We can draw crude circles and lines on a chalkboard; we can add two apples to three apples, even if these apples are not identical, and end with five apples. By abstracting from such experience of ordinary perceptible things, we arrive at basic mathematical intuitions. And logical deduction does the rest.
This is the Aristotelian view of mathematics, and it pretty much accords with common sense. But there is one putative mathematical object that it can’t handle: infinity. We have no experience of the infinite. We have no experience of anything like it. -Jim Holt, When Einstein Walked with Gödel: Excursions to the Edge of Thought
When I hold the viewfinder of my camera up to my eye, every perspective, every landscape, offers me new glimpses of a vast expanse that has no end and no beginning. Inside the viewfinder you see infinity shimmer about. Breath in, breath out - Zeno’s paradox is in your lungs. Cantor’s set theory appears every time you take a step. I humbly disagree with you Jim.