The whole of the propositions following the first are so built upon it, that if it fails they are baseless. The second proposition is, that infinity of extension is necessarily indivisible. In dealing with this proposition, Mr. Gillespie talks of the _parts_ of infinity of extension, and winds up by saying that he means parts in the sense of partial consideration only. Now not only is it denied that you can have any idea of infinity of extension, but it is also denied that infinity can be the subject of partial consideration. Mr. Gillespie's whole proof of this proposition is intended to affirm that the parts of infinity of extension are necessarily indivisible from each other.
I have already denied the possibility of conceiving infinity in parts; and, indeed, if it were possible to conceive infinity in parts, then that infinity could not be indivisible, for Mr. Gillespie says that, by indivisible, he means indivisible, either really or mentally. Now each part of anything conceived is, in the act of conceiving, mentally separated from, either other parts of, or from the remainder of, the whole of which it is part. It is clearly impossible to have a partial consideration of infinity, because the part considered must be mentally distinguished from the unconsidered remainder, and, in that case, you have, in thought, the part considered finite, and the residue certainly limited, at least, by the extent of the part under consideration.
If any of the foregoing objections are well-founded, they are fatal to Mr. Gillespie's argument.
The argument in favor of the corollary to the second proposition is that the parts of infinity of extension are necessarily immovable among themselves; but if there be no such thing as infinity of extension--that is, if extension be only a quality and not necessarily infinite; if infinite mean only indefiniteness or illimitability, and if infinity can not have parts--this argument goes for very little. The acceptance of the argument that the parts of infinity of extension are immovable is rendered difficult when the reader considers Mr. Gillespie's sub-proposition (4) that the parts of the material universe are movable and divisible from each other. He urges that a part of the infinity of extension or of its substratum must penetrate the material universe and every atom of it. But if infinity can have no parts, no part of it can penetrate the material universe. If infinity have parts (which is absurd), and if some part penetrate every atom of the material universe, and if the part so penetrating be immovable, how can the material universe be considered as movable, and yet as penetrated in every atom by immovability? If penetrated be a proper phrase, then, at the moment when the part of infinity was penetrating the material universe, the part of infinity so penetrating must have been in motion. Mr. Gillespie's logic is faulty. Use his own language, and there is either no penetration, or there is no immovability.