15. What is positive, what negative, in our idea of infinite.
The idea of infinite has, I confess, something of
positive in all those things we apply to it. When we would think of infinite space or duration, we at first step
usually make some very large idea, as perhaps of millions of ages, or miles, which possibly we double and
multiply several times. All that we thus amass together in our thoughts is positive, and the assemblage of a great
number of positive ideas of space or duration. But what still remains beyond this we have no more a positive
distinct notion of than a mariner has of the depth of the sea; where, having let down a large portion of his
sounding-line, he reaches no bottom. Whereby he knows the depth to be so many fathoms, and more; but how
much the more is, he hath no distinct notion at all: and could he always supply new line, and find the plummet
always sink, without ever stopping, he would be something in the posture of the mind reaching after a complete
and positive idea of infinity. In which case, let this line be ten, or ten thousand fathoms long, it equally discovers
what is beyond it, and gives only this confused and comparative idea, that this is not all, but one may yet go
farther. So much as the mind comprehends of any space, it has a positive idea of: but in endeavouring to make it
infinite,--it being always enlarging, always advancing,--the idea is still imperfect and incomplete. So much
space as the mind takes a view of in its contemplation of greatness, is a clear picture, and positive in the
understanding: but infinite is still greater. 1. Then the idea of so much is positive and clear. 2. The idea of greater
is also clear; but it is but a comparative idea, the idea of so much greater as cannot be comprehended. 3. And this
is plainly negative: not positive. For he has no positive clear idea of the largeness of any extension, (which is that
sought for in the idea of infinite), that has not a comprehensive idea of the dimensions of it: and such, nobody, I
think, pretends to in what is infinite. For to say a man has a positive clear idea of any quantity, without knowing
how great it is, is as reasonable as to say, he has the positive clear idea of the number of the sands on the
sea-shore, who knows not how many there be, but only that they are more than twenty. For just such a perfect and
positive idea has he of an infinite space or duration, who says it is larger than the extent or duration of ten, one
hundred, one thousand, or any other number of miles, or years, whereof he has or can have a positive idea; which
is all the idea, I think, we have of infinite. So that what lies beyond our positive idea towards infinity, lies in
obscurity, and has the indeterminate confusion of a negative idea, wherein I know I neither do nor can
comprehend all I would, it being too large for a finite and narrow capacity. And that cannot but be very far from a
positive complete idea, wherein the greatest part of what I would comprehend is left out, under the undeterminate
intimation of being still greater. For to say, that, having in any quantity measured so much, or gone so far, you are
not yet at the end, is only to say that that quantity is greater. So that the negation of an end in any quantity is, in
other words, only to say that it is bigger; and a total negation of an end is but carrying this bigger still with you, in
all the progressions of your thoughts shall make in quantity; and adding this idea of still greater to all the ideas
you have, or can be supposed to have, of quantity. Now, whether such an idea as that be positive, I leave any one
to consider.