Embodied mathematics is what you are describing I think. The idea is that mathematics arises out of ordinary experience extended by metaphor. It charts a pretty satisfying middle ground between Platonism and Fictionalism. Mathematics is a story, but it is &quot;at the bottom&quot; tied into our experience of everyday reality. Do real numbers exist? Probably not, but the the continuum is like a long stick you can make marks on.<p>Can you have a trillion apples, so you know that a trillion + a trillion is two trillion? No, but you can reason about &quot;trillion&quot; as existing metaphorically.