the Philosophy of the Conditioned is entirely founded on a mistake, inasmuch as infinite space on the one hand, and, on the other, both an absolute minimum and an infinite divisibility of space, are perfectly conceivable. With regard to the former of these two assertions, Mr. Mill's whole argument is

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.

vitiated, as we have already shown, by his confusion between infinite and indefinite; but it is worth while to quote one of his special instances in this chapter, as a specimen of the kind of reasoning which an eminent writer on logic can sometimes employ. In reference to Sir W. Hamilton's assertion, that infinite space would require infinite time to conceive it, he says, "Let us try the doctrine upon a complex whole, short of infinite, such as the number 695,788. Sir W. Hamilton would not, I suppose, have maintained that this number is inconceivable. How long did he think it would take to go over every separate unit of this whole, so as to obtain a perfect knowledge of the exact sum, as different from all other sums, either greater or less?"

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."*

* Precisely the same misconception of Hamilton's position occurs

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.

"It is not denied," he says, "that there is a portion of extension which to the naked eye appears an indivisible point; it has been called by philosophers the minimum visibile. This minimum we can indefinitely magnify by means of optical instruments, making visible the still smaller parts which compose it. In each successive experiment there is still a minimum visibile, anything less than which cannot be discovered with that instrument, but can with one of a higher power. Suppose, now, that

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.

as we increase the magnifying power of our instruments, and before we have reached the limit of possible increase, we arrive at a stage at which that which seemed the smallest visible space under a given microscope, does not. appear larger under one which, by its mechanical construction, is adapted to magnify more, but still remains apparently indivisible. I say, that if this happened, we should believe in a minimum of extension; or if some à priori metaphysical prejudice prevented us from believing it, we should at least be enabled to conceive it."—(P. 84.)

The natural conclusion of most men under such circumstances would be, that there was some fault in the microscope. But even if this conclusion were rejected, we presume Mr. Mill would allow that, under the supposed circumstances, the exact magnitude of the minimum of extension would be calculable. We have only to measure the minimum visibile, and know what is the magnifying power of our microscope, to determine the