[BA] The sense in which Sir W. Hamilton himself uses the word _conception_ is explained in a note to _Reid's Works_, p. 377--namely, the combination of two or more attributes in a _unity of representation_. The second sense which Mr. Mill imagines is simply a mistake of his own. When Hamilton speaks of being "unable to conceive as possible," he does not mean, as Mr. Mill supposes, physically possible under the law of gravitation or some other law of matter, but mentally possible as a representation or image; and thus the supposed second sense is identical with the first. The third sense may also be reduced to the first; for to conceive two attributes as combined in one representation is to form a notion subordinate to those of each attribute separately. We do not say that Sir W. Hamilton has been uniformly accurate in his application of the test of conceivability; but we say that his inaccuracies, such as they are, do not affect the theory of the conditioned, and that in all the long extracts which Mr. Mill quotes, with footnotes, indicating "first sense," "second sense," "third sense," the author's meaning may be more accurately explained in the first sense only. It is marvellous that it should not have occurred to Mr. Mill, while he was writing this passage, "How comes this large number to be a 'whole' at all; and how comes it that 'this whole,' with all its units, can be written down by means of six digits?" Simply because of a conventional arrangement, by which a single digit, according to its position, can express, by one mark, tens, hundreds, thousands, &c., of units; and thus can exhaust the sum by dealing with its items in large masses. But how can such a process exhaust the infinite? We should like to know how long Mr. Mill thinks it would take to work out the following problem:--"If two figures can represent ten, three a hundred, four a thousand, five ten thousand, &c., find the number of figures required to represent infinity."[BB] [BB] Precisely the same misconception of Hamilton's position occurs in Professor De Morgan's paper in the _Cambridge Transactions_, to which we have previously referred. He speaks (p. 13) of the "notion, which runs through many writers, from Descartes to Hamilton, that the mind must be big enough to _hold_ all it can conceive." This notion is certainly not maintained by Hamilton, nor yet by Descartes in the paragraph quoted by Mr. De Morgan; nor, as far as we are aware, in any other part of his works. Infinite divisibility stands or falls with infinite extension. In both cases Mr. Mill confounds infinity with indefiniteness. But with regard to an absolute minimum of space, Mr. Mill's argument requires a separate notice.