His argument for subconclusion 1 appeals to premise 2. It is that if one denies subconclusion 1, one must also deny premise 1. [text] But one cannot deny premise 1, so, by reductio ad absurdum, subconclusion 1 must be true. After all, if the shade next to the red-208 (in premise 2) is not different from red-208, then it is the same. And if the one next to that is not different, then it is the same as the shade next to it and so (by transitivity of sameness) is the same as red-208. But then by continuing to argue in this fashion (and appealing to premise 2) we can conclude that red-208 is the same as green-436, which is clearly false and which contradicts premise 1. Thus subconclusion 1 must be true.

But this is not yet the conclusion we need. Premises 3 and 4 state that Blake would be able to generate an idea of blue-227 without ever having experienced blue-227. This, by subconclusion 1, is an idea that is different from any of the ideas that Blake received through impressions. But if the thesis is correct, this idea must be derived from impressions. But by premise 5 -- and this is a key premise -- this is a simple idea, not a compound one. Therefore, it is not derived from other ideas (such as from other shades of blue). It must then be directly copied from an impression. But Blake has no impression from which it could be directly copied (by premise 3). This contradiction shows the thesis to be false (by reductio ad absurdum).

(The conclusion of this argument is first stated by Hume as "it is not absolutely impossible for ideas to arise, independent of their correspondent >impressions." [text] Later he states the conclusion as "the simple ideas are not always, in every instance, derived from the correspondent impressions . . ." [text])