This confusion between conceiving a concrete thing and knowing the meaning of abstract terms is as old as Toland’s Christianity not Mysterious, and, indeed, has its germ, though not its development, in the teaching of his assumed master, Locke. Locke taught that all our knowledge is founded on simple ideas, and that a complex idea is merely an accumulation of simple ones. Hence Toland maintained that no object could be mysterious or inconceivable if the terms in which its several attributes are expressed have ideas corresponding to them. But, in point of fact, no simple idea can be conceived as an object by itself, though the word by which it is signified has a perfectly intelligible meaning. I cannot, e.g., conceive whiteness by itself, though I can conceive a white wall, i.e., whiteness in combination with other attributes in a concrete object. To conceive attributes as coexisting, however, we must conceive them as coexisting in a certain manner; for an object of conception is not a mere heap of ideas, but an organized whole, whose constituent ideas exist in a particular combination with and relation to each other. To conceive, therefore, we must not only be able to apprehend each idea separately in the abstract, but also the manner in which they may possibly exist in combination with each other.
“Something infinite,” says Mr. Mill, “is a conception which, like most of our complex ideas, contains a negative element, but which contains positive elements also. Infinite space, for instance; is there nothing positive in that? The negative part of this conception is the absence of bounds. The positive are, the idea of space, and of space greater than any finite space.”—(P. 45.)
This definition of infinite space is exactly that which Descartes gives us of indefinite extension,—“Ita quia non possumus imaginari extensionem tam magnam, quin intelligamus adhuc majorem esse posse, dicemus magnitudinem rerum possibilium esse indefinitam.”[AR] So too, Cudworth,—“There appeareth no sufficient ground for this positive infinity of space; we being certain of no more than this, that be the world or any figurative body never so great, it is not impossible but that it might be still greater and greater without end. Which indefinite increasableness of body and space seems to be mistaken for a positive infinity thereof.”[AS] And Locke, a philosopher for whom Mr. Mill will probably have more respect than for Descartes or Cudworth, writes more plainly: “To have actually in the mind the idea of a space infinite, is to suppose the mind already passed over, and actually to have a view of all those repeated ideas of space, which an endless repetition can never totally represent to it,—which carries in it a plain contradiction.”[AT] Mr. Mill thus unwittingly illustrates, in his own person, the truth of Hamilton’s remark, “If we dream of effecting this [conceiving the infinite in time or space], we only deceive ourselves by substituting the indefinite for the infinite, than which no two notions can be more opposed.” In fact, Mr. Mill does not seem to be aware that what the mathematician calls infinite, the metaphysician calls indefinite, and that arguments drawn from the mathematical use of the term infinite are wholly irrelevant to the metaphysical. How, indeed, could it be otherwise? Can any man suppose that, when the Divine attributes are spoken of as infinite, it is meant that they are indefinitely increasable?[AU]
Principia, i., 26.
Intellectual System, ed. Harrison, vol. iii., p. 131.
Essay, ii., 17, 7.