Why does mathematics manage to represent a function of reality? My question concerns how your logic and its structure (like topology, or the very fields of advanced logic in mathematics) manage to represent reality?
In Penrose words:
Plato made it clear that the mathematical propositions—the things that could be regarded as unassailably true—referred not to actual physical objects (like the approximate squares, triangles, circles, spheres, and cubes that might be constructed from marks in the sand, or from wood or stone) but to certain idealized entities. He envisaged that these ideal entities inhabited a different world, distinct from the physical world. Today, we might refer to this world as the Platonic world of mathematical forms. Physical structures, such as squares, circles, or triangles cut from papyrus, or marked on a flat surface, or perhaps cubes, tetrahedra, or spheres carved from marble, might conform to these ideals very closely, but only approximately. The actual mathematical squares, cubes, circles, spheres, triangles, etc.,
Particularly, I think this is possible because all statements in mathematics are ultimately conditional statements on chosen axioms. It does not tell us which assumptions are true, but it tells us what follows if certain assumptions are true (and also, if certain assumptions cannot be supported). For mathematical realists (radical Platonism), theorems have physically real consequences and our world is only one among the infinite ocean of mathematically possible universes.
But I don't understand why this abstract logic manages to "tangential" reality... why does this happen? I accept any suggestion for reading, or an explanation that might shed some light on this tunnel.