But, the argument continues, since there cannot be two substances with the same attribute, every substance must be infinite; for, to be finite, a thing must be limited by something: and nothing can be limited except by a thing of the same kind (for example, a material thing cannot be limited by a thought). But if a thing be limited by another thing of the same kind, the thing limited and the thing limiting have the same attribute. It follows that they are not two things, but one. The thing in question is not limited but infinite.
In criticizing this, I may call attention, in passing, to the highly disputable and gratuitously assumed premise, that, to be finite, a thing must be limited by _something_. If this be denied, the ground of the reasoning is removed; while, if it be granted, no argument is needed to prove that something is infinite, for one has only said in other words that all limits must be limits within something. The question is begged at once. With this, however, I am not concerned. What interests me is this: The argument assumes a limited thing and a something beyond it, and then asserts that they are one. But two things of the same kind in different places, or marked as different by distinctions of any sort, are readily distinguished as two. To come to the concrete, extension conceived as on this side of a point and extension conceived as beyond the point are not extension simply, but "this" extension and "that" extension. They are the same only in sense fourth, not in sense first. We have here not merely the attribute extension, but the further elements "this" and "that." The conclusion, then, that what we started out with is infinite, is wholly unwarranted. It is not this that is infinite, but this with something else which is to some degree like it, although not wholly so. That is to say, the thing assumed as finite can only be proved to be infinite by confounding two samenesses. The thing proved to be infinite is a new object including it and what it is assumed to presuppose. If it be not permissible to make this distinction between the object assumed as finite, for the sake of the argument, and the object which is proved to be infinite, it is also not permissible to assert that an object to be finite "would have to be limited by another of the same kind." If the two are one, these words are meaningless. If they are not one, one cannot conclude from the argument that every substance is necessarily infinite, but only that something is necessarily infinite, a conclusion already given in the single premise that what is limited must be limited by something of the same kind. As a matter of fact, Spinoza retains in his argument not only the attribute, but the mode, the "this" and the "beyond this;" and then he overlooks the mode and considers merely the attribute, which gives him strict identity. This procedure we have met before in the dispute concerning universals.