Er, I am still confused about the prior point you made, and now I am also confused by your “can’t discard…” argument. There *is* a mathematical description of particles, which involves the sum of their *paths*. Yet, an axiom is *not* the mathematical description of a particle. An example of an axiom: “Parallel lines meet at the infinite horizon.” A mathematical system which includes *that axiom* is non-Euclidean. That axiom is not a particle, *nor* is it the mathematical description of a particle. The axiom is a relationship which is assumed to be true for that mathematical system. You can pick different assumptions, different axioms, to form different mathematical systems. Have I explained this well enough?