 The contentious premises in this argument are premises  5  and  2.  One might offer the following sort of counterexample to  premise 5.  Let’s say that in the past, I’ve added together many pairs of even numbers; and in each of those cases, I’ve known/justifiably believed (a priori) that the sum of the two numbers was also even. Then someone asks me: is it always the case that the sum of two even numbers is itself even? Assume that, for whatever reason, I’m genuinely uncertain of the answer—I don’t see the answer intuitively, or perhaps I doubt my more general mathematical intuitions. Nevertheless, I realize that in the past, whenever I’ve added two even numbers the sum has itself been even. Thus, I inductively infer that the hypothesis is correct: the sum of two even numbers is always itself even.