But though Hamilton himself distinguishes between the _unconditioned_ and the _absolute_, using the former term generally, for that which is out of all relation, and the latter specially, for that which is out of all relation as complete and finished, his opponent Cousin uses the latter term in a wider sense, as synonymous with the former, and the _infinite_ as coextensive with both. This, however, does not affect the validity of Hamilton's argument. For if it can be shown that the absolute and the infinite (in Hamilton's sense) are both inconceivable, the unconditioned (or absolute in Cousin's sense), which must be conceived as one or the other, is inconceivable also. Or, conversely, if it can be shown that the unconditioned, the unrelated in general, is inconceivable, it follows that the absolute and the infinite, as both involving the unrelated, are inconceivable also. We may now proceed with Mr. Mill's criticism. He says:-- "Absolute, in the sense in which, it stands related to Infinite, means (conformably to its etymology) that which is finished or completed. There are some things of which the utmost ideal amount is a limited quantity, though a quantity never actually reached.... We may speak of absolutely, but not of infinitely, pure water. The purity of water is not a fact of which, whatever degree we suppose attained, there remains a greater beyond. It has an absolute limit: it is capable of being finished or complete, in thought, if not in reality."--(P. 34.) This criticism is either incorrect or _nihil ad rem_. If meant as a statement of Hamilton's use of the term, it is incorrect: _absolute_, in Hamilton's philosophy, does not mean simply "completed," but "out of relation as completed;" _i.e._, self-existent in its completeness, and not implying the existence of anything else. If meant in any other sense than Hamilton's, it is irrelevant. Can Mr. Mill really have believed that Schelling thought it necessary to invent an intellectual intuition out of time and out of consciousness, in order to contemplate "an ideal limited quantity," such as the complete purity of water? Mr. Mill continues:--