Mr. Gillespie has not defined infinity, and it is possible therefore his argument may be misapprehended in this paper. Infinite signifies nothing more than indefinite. When a person speaks of infinite extension he can only mean to refer to the extension of something to which he has been unable to set limits. The mind can not conceive extension _per se_, either absolute or finite. It can only conceive something extended. It might be impossible mentally to define the extension of some substance. In such a case its extension would be indefinite; or, as Mr. Gillespie uses the word, infinite. No one can therefore possibly have any idea of infinity of extension. Yet it is upon the existence of such an idea, and on the impossibility of getting rid of it, that Mr. Gillespie grounds his first proposition. If the idea does not exist, the argument is destroyed at the first step.
Mr. Gillespie argues that it is utterly beyond the power of the human mind to conceive infinity of extension non-existent. He would have been more correct in asserting that it is utterly beyond the power of the human mind to conceive infinity of extension at all, either existent or non-existent. Extension can only be conceived as quality of substance. It is possible to conceive substance extended. It is impossible in thought to limit the possible extension of substance. Mr. Gillespie having asserted that we can not but believe that infinity of extension exists, proceeds to declare that it exists necessarily. For, he says, everything the existence of which we can not but believe, exists necessarily. It is not necessary at present to examine what Mr. Gillespie means by existing necessarily; it is sufficient to have shown that we do not believe in the existence of infinity of extension, although we may and do believe in the existence of substance, to the extension of which we may be unable to set limits. But, says Mr. Gillespie, "everything the existence of which we can not but believe is necessarily existing." Then as we can not but believe in the existence of the universe (or, to adopt Mr. Gillespie's phrase, the material universe), the material universe exists necessarily. If by "anything necessarily existing," he means anything the essence of which involves existence, or the nature of which can only be considered as existent, then Mr. Gillespie, by demonstrating the necessary existence of the universe, refutes his own later argument, that God is its creator. Mr. Gillespie's argument, as before remarked, is open to misconception, because he has left us without any definition of some of the most important words he uses. To avoid the same objection, it is necessary to state that by substance or existence I mean that which is in itself and is conceived per se--that is, the conception of which does not involve the conception of anything else as antecedent to it. By quality, that by which I cognize any mode of existence. By mode, each cognized condition of existence. Regarding extension as quality of mode of substance, and not as substance itself, it appears absurd to argue that the quality exists otherwise than as quality of mode.