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What is positive, what negative in our Idea of Infinite.       §15. 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
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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 that 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
compleat and positive Idea of Infinity. In which case, let this Line
be 10, or 10000 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 compre-
hends 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 incompleat. 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. 3. The Idea of so much greater, as
cannot be comprehended, and this is plain 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 compre-
hensive Idea of the Dimensions of it: And such, no body, 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 reason-
able as to say, He has the positive clear Idea of the number of the
Sands on the Sea-shore, who knows not how many they 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 10, 100, 1000, 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 compleat Idea, wherein the greatest part, of
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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 Nega-
tion 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 the carrying this
Bigger still with you, in all the Progressions 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 con-
sider.
Locke Hum II, 17, §15, pp. 217-218-219