But of course there’s such a thing as an a priori statement! Running a computation forwards without any uncertainty in it yields a result: this is “a priori” in the sense that, since it operates only on abstract mental data with no reference to empirical reality, it requires no experience to “get right” (rather, experience is required to locate a useful computation, out of all possible computations). 2+2 really does equal 4, every time, all the time, because any computation isomorphic to 2+2 must always yield an answer isomorphic to 4.
But of course there’s such a thing as an a priori statement! Running a computation forwards without any uncertainty in it yields a result: this is “a priori” in the sense that, since it operates only on abstract mental data with no reference to empirical reality, it requires no experience to “get right” (rather, experience is required to locate a useful computation, out of all possible computations). 2+2 really does equal 4, every time, all the time, because any computation isomorphic to 2+2 must always yield an answer isomorphic to 4.