> particles still trace out world lines Of course they do. That is perfectly consistent mathematically with there being two time dimensions. Two time dimension

> particles still trace out world lines Of course they do. That is perfectly consistent mathematically with there being two time dimensions. Two time dimensions is a property of the spacetime geometry, not of individual worldlines. > whether you would want particles to trace out world surfaces That would be a different mathematical structure, where "particles" would have something like "two time evolutions" instead of one. What that would imply about the spacetime geometry and its dimensions is a different question. > I could just say let us deny ∀x(x=x) and run with it How would you even do that? How would you even make a consistent mathematical structure with that as an axiom? And if you can't, doesn't that mean you can't deny that proposition? > I could postulate this but I can not really make sense of a thing not being equal to itself. You're contradicting yourself. If you can't make sense of it, you can't postulate it. "Postulate" doesn't mean "throw some words together". It means "take as an axiom and develop a consistent mathematical structure based on it". If you can't make sense of it, you can't develop a consistent mathematical structure based on it. > Did we arbitrarily pick the axioms of logic or did we pick them because they make sense in our universe? If we can't develop a consistent mathematical structure based on any other set of axioms, what choice do we have?