doubles the increase as often as he will:  the remaining abyss being still as far beyond the end of all these progressions as it is from the length of a day or an hour.  For nothing finite bears any proportion to infinite; and therefore our ideas, which are all finite, cannot bear any.  Thus it is also in our idea of extension, when we increase it by addition, as well as when we diminish it by division, and would enlarge our thoughts to infinite space.  After a few doublings of those ideas of extension, which are the largest we are accustomed to have, we lose the clear distinct idea of that space:  it becomes a confusedly great one, with a surplus of still greater; about which, when we would argue or reason, we shall always find ourselves at a loss; confused ideas, in our arguings and deductions from that part of them which is confused, always leading us into confusion.

CHAPTER XXX.

Of real and fantastical ideas.

1.  Ideas considered in reference to their Archetypes.

Besides what we have already mentioned concerning ideas, other considerations belong to them, in reference to things from whence they are taken, or which they may be supposed to represent; and thus, I think, they may come under a threefold distinction, and are:—­First, either real or fantastical; Secondly, adequate or inadequate; Thirdly, true or false.

First, by real ideas, I mean such as have a foundation in nature; such as have a conformity with the real being and existence of things, or with their archetypes.  Fantastical or chimerical, I call such as have no foundation in nature, nor have any conformity with that reality of being to which they are tacitly referred, as to their archetypes.  If we examine the several sorts of ideas before mentioned, we shall find that,

2.  Simple Ideas are all real appearances of things.

First, Our simple ideas are all real, all agree to the reality of things:  not that they are all of them the images or representations of what does exist; the contrary whereof, in all but the primary qualities of bodies, hath been already shown.  But, though whiteness and coldness are no more in snow than pain is; yet those ideas of whiteness and coldness, pain, &c., being in us the effects of powers in things without us, ordained by our Maker to produce in us such sensations; they are real ideas in us, whereby we distinguish the qualities that are really in things themselves.  For, these several appearances being designed to be the mark whereby we are to know and distinguish things which we have to do with, our ideas do as well serve us to that purpose, and are as real distinguishing characters, whether they be only constant effects, or else exact resemblances of something in the things themselves: