We cannot construe to the imagination a polygon with an infinite number of sides (i.e. with a number of sides greater than any given number), but neither can we construe to the imagination a polygon with a million of sides; nevertheless, we understand what is meant by the first description as well as by the second, and can reason upon both.  There is, indeed, this difference between the two:  That the terms used in describing the first, proclaim at once in their direct meaning that we should in vain attempt to construe it to the imagination; whereas the terms used in describing the second do not intimate that fact.  We know the fact only by trial, or by an estimate of our own mental force which is the result of many past trials.  If the difference here noted were all which Sir W. Hamilton has in view when he declares the Infinite to be unknowable and incogitable, we should accede to his opinion; but we apprehend that he means much more, and he certainly requires more to justify the marked antithesis in which he places himself against M. Cousin and Hegel.  Indeed, the facility with which he declares matters to be incogitable, which these two and other philosophers not only cogitate but maintain as truth, is to us truly surprising.  The only question which appears to us important is, whether we can understand and reason upon the meaning of the terms and propositions addressed to us.  If we can, the subjects propounded must be cogitable and conceivable, whether we admit the propositions affirmed concerning them or not; if we cannot, then these subjects are indeed incogitable by ourselves in the present state of our knowledge, but they may not be so to our opponent who employs the terms.

In criticising the arguments of Sir W. Hamilton against M. Cousin, Mr Mill insists much on a distinction between (1) the Infinite, and (2) the Infinite in any one or more positive attributes, such as infinite wisdom, goodness, redness, hardness, &c.[4] He thinks that Sir W. Hamilton has made out his case against the first, but not against the last; that the first is really ‘an unmeaning and senseless abstraction,’ a fasciculus of negations, unknowable and inconceivable, but not the last.  We think that Mr Mill makes more of this distinction than the case warrants; that the first is not unmeaning, but an intelligible abstraction, only a higher reach of abstraction than the last; that it is knowable inadequately, in the same way as the last—­though more inadequately, because of its higher abstraction.

As the finite is intelligible, so also is its negation—­the Infinite:  we do not say (with M. Cousin) that the two are conjointly given in consciousness—­but the two are understood and partially apprehended by the mind conjointly and in contrast.  Though the Infinite is doubtless negative as to a degree, it is not wholly or exclusively negative, since it includes a necessary reference to some positive attribute, to which the degree belongs; the positive element is