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] [AR] _Principia_, i., 26. [AS] _Intellectual System_, ed. Harrison, vol. iii., p. 131. [AT] _Essay_, ii., 17, 7.