The workings of the physical world can be modeled by math, often of extremely sophisticated sort, beyond even calculus. How can Ayer then assert that math, being the foundation of natural sciences, gives us no information about the external reality?
It is an arbitrary, though convenient, rule of language that words that stand for temporal relations are to be used transitively; but, given this rule, the proposition that, if A is earlier than B and B is earlier than C, A is earlier than C becomes a necessary truth. (186-7)
It’s not a “rule of language”; it’s how Mr. Time works! (Perhaps even in all possible worlds.)
In philosophy, all “radical” systems, including Ayer’s “radical empiricism” or logical positivism, are uniformly false, because philosophy is complicated and hard.