https://plato.stanford.edu/entries/goedel/goedel-phenomenolo...

Also, that definition of a circle as an ellipse via locus points (which you mentioned) still requires defining ellipses by an imaginary, ideal circle--even if transcendental (and I've mentioned elsewhere, the circle never appears). The circle that appears is always already an ellipse, empirically, so in pure mathematical terms as I've said the ellipse is actually absolutely different from the circle, which always exceeds it. In order for the circle and ellipse to be set in relation one must be forced to be analytically composed under the other.

Edit: Its clear that phenomenology was the most important philosophical influence on the modern theory of computation, but its curious to me that those that study pure math and physics haven't, for the most part, realized that yet, even as they employ computers to do so much of their work.