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?