must, in both cases, conceive of the general notion of something great in magnitude that can be pointed to, and regard the observed and unobserved instances as sharing that notion. But saying, “It cannot be conceived,” is stronger than saying, “We do not know of it,” or, “We have not observed it.” For saying, “We do not know of it,” or, “We have not observed it,” negates it only with respect to what one has already known and observed, not what one has yet to know and observe. Saying, “It cannot be conceived,” however, denies that it could ever be conceivable.

If something great in magnitude that can be pointed to cannot be conceived in any other way, then the syllogistic demonstration rests solely on what the person employing it has conceived and understood by the notion of something great in magnitude that can be pointed to. For when he posits a point within that great thing that can be pointed to and says, “It is either identical with the other or it is not,” he posits and supposes this only within what he has understood and known, and which has taken shape in his mind. This is what he understands by the notion of something great in magnitude that can be pointed to. Thus, if it is permissible to affirm the unobserved in a manner