 The argument for (3) is everything here. If it can be established, then so can (6), because (3) trivially entails (4), (5) is beyond doubt, and (4) and (5) trivially entail (6). Now, (1) and (2) do not strictly entail (3), and so there is room for platonists to maneuver here — and as we'll see, this is precisely how most platonists have responded. However, it is important to notice that (1) and (2) provide a strong prima facie motivation for (3), because they seem to imply that mathematical objects (if there are such things) are totally inaccessible to us, i.e., that information cannot pass from mathematical objects to human beings. But this gives rise to a prima facie worry (which may or may not be answerable) about whether human beings could acquire knowledge of mathematical objects. Thus, we should think of this argument not as refuting platonism but as issuing a challenge to platonists. The challenge is simply to explain how human beings could acquire knowledge of abstract mathematical objects.