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but a comparative idea, viz. the idea of so much greater as cannot be comprehended; 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 comprebensive 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 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 bas, 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 your thoughts shall make in quantity; and adding this idea of still greator, 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. . We have 10
6. 16. I ask those who say they have a positive idea positive idea of eternity, whether their idea of an infinite of duration includes in it succession, or duration.
not? if it does not, they ought to show the difference of their notion of duration, when apo
plied to an eternal being, and to a finite : since perhaps, there may be others, as well as I, who will own to them their weakness of understanding in this point; and acknowledge, that the notion they have of duration forces them to conceive, that whatever has duration, is of a longer continuance“ to-day than it was yesterday. If, to avoid succession in 'external existence, they return to the punctumí stans of the schools, I suppose they will thereby very little mend the matter, or help us to a more clear and positive idea of infinite duration, there being nothing more inconceivable to me than duration without succession. Besides, that punctum stans, it it signify any thing, being not quantum, finite or infinite cannot belong to it. But if our weak apprehensions cannot separate succession from any duration whatsoever, our idea of eternity can be 10thing but of infinite succession of moments of duration, wherein any thing does exist; and whether any one has or can have a positive idea of an actual infinite number, I leave him to consider, till his infinite number be so great that he bimself can add no more to it; and as long as he can increase it, I doubt he himself will think the idea he hath of it a little too scanty for positive infinity.
6. 17. I think it unavoidable for every considering rational creature, that will but examine his own or any other existence, to have the notion of an eternal wise Peing, who had no beginning : and such an idea of infinite duration I am sure I have. tion of a beginning being but the negation of a positive thing, scarce gives me a positive idea of infinity; which whenever I endeavoured to extend my thoughts to, I confess myself at a loss, and I find I cannot attain any clear comprehension of it. Ş. 18. He that thinks he has a positive
No positive idea of infinite space, will, when he con
idea of infisiders it, find that he can no more have a positive idea of the greatest, than he has of the least space. For in this latter, which seems the easier of the two, and more within our coinprehension, we are capable only of a comparative idea of smallness,
But this negawhich will always be less than any one whereof we bave the positive idea. All our positive ideas of any quantity, whether great or little have always bounds; though our comparative idea, whereby we can always add to the one, and take from the other, hath no bounds : for that which remains either great or little, not being comprehended in that positive idea which we have, lies in obscurity; and we have no other idea of it, but of the power of enlarging the one, and dimninishing the other, without ceasing. A pestle and niortar will as soon bring any particle of inatter to indivisibility, as the acutest thought of a mathematician; and a surveyor may as soon with his chain measure our infinice space, as a piilosopher Üy the quickest fight of mind reach it, or by thinking comprehend it; which is to have a positive idea of it. Ile that thinks on a cube of an inch diameter, bas a clear and positive idea of it in his mind, and ) can frame one of ], 1, s, and so on till he has the idea in his thoughts of something very little; but yet reaches not the idea of that incomprehensible littleness which division can produce. What remains of smallness, is as far from his thoughts as when he first began ; and therefore he never comes at all to have a clear and positive idea of that smallness, which is consequent to intinite divisibility. What is po.
$. 19. Every one that looks towards insitive, what finity does, as I have said, at first glance negative, in make some very large idea of that which our idea of
he applies it to. let it be space or duration ; Infinite,
and possibly be wearies his thoughts, by multiplying in his inind that first large idea : but yet by that he comes no nearer to the having a positive clear idea of what remains to make up a positive infinite, than the country-fellow liad of the water, which was yet to come and pass the channel of the river where he stood :
Rusticus expectat dum transeat amnis, at ille
$. 20. There are some I have met with, Some think that put so much difference between infinite they have a duration and infinite space that they per- positive idea suade theinselves that they have a positive of eternity,
and not of in idea of eternity; but that they bave not, nor can have any idea of infinite space. The reason of which mistake I suppose to be this, that finding by a due contemplation of causes and effects, that it is necessary to admit some eternal being, and so to consider the real existence of that being, as taken up and commensurate to their idea of eternity ; but on the other side, not finding it necessary, but on the contrary apparently absurd, that body should be infinite ; they forwardly conclude, that they have no idea of infinite space, because they can have no idea of infinite matter. Which consequence, I conceive, is very ill collected; because the existence of matter is not ways necessary to the existence of space, no more than the existence of motion, or the sun, is necessary to duration, though duration uses to be measured by it: and I doubt not but that a man may have the idea of ten thousand iniles square, without any body so big, as well as the idea of ten thousand years, without any body so old. It seems as easy to me to have the idea of space empty of body, as to think of the capacity of a bushel without corn, or the hollow of a nut-shell without a kernel in it: it being no more necessary that there should be existing a solid body infinitely extended, because we have an idea of the infinity of space, than it is necessary that the world should be eternal, because we have an idea of infinite duration. And why should we think our idea of infinite space requires the real existence of matter to support it, when we find that we have as clear an idea of an infinite duration to come, as we have of infinite duration past? Though, I suppose nobody thinks it conceivable, that any thing does, or has exa isted in that future duration. Nor is it possible to join our idea of future duration with present or past existence, any more than it is possible to make the ideas of yesterday, to-day, and to-morrow, to be the same; or. bring ages past and futurc together, and make them
contemporary. But if these men are of the mind, that they have clearer ideas of infinite duration than of infinite space, because it is past doubt that God has existed from all eternity, but there is no real matter co-extended with infinite space; yet those philosophers who are of opinion, that intinite space is possessed by God's infinite omnipresence, as well as infinite duration by his eternal existence, must be allowed to have as clear an idea of infinite space as of infinite duration ; though peither of them, I think, has any positive idea of intinity in either case. For whatsoever positive idea a man has in his mind of any quantity, he can repeat it, and add it to the former as easy as he can add together the ideas of two days, or two paces, which are positive ideas of lengths he has in his mind, and so on as long as he pleases: whereby if a man had a positive idea of infinite, either duration or space, he could add two infinites together ; nay, make one infinite infinitely bigger than another : absurdities too gross to be contuted. Supposed po.
§. 21. But yet after all this, there being sitive ideas men who persuade themselves that they of infinity, have clear positive comprehensive ideas of cause of inis. infinity, it is fit they enjoy their privilege: takes.
and I should be very glad (with some others that I know, who acknowledge.they have none such) to be better informed by their communication. For I have been hitherto apt to think that the great and inextricable difficulties which perpetually involve all discourses concerning infinity, whether of space, duration, or divisibility, have been the certain marks of a detect in our ideas of infinity, and the disproportion the nature thereof has to the comprehension of our narrow capacities. For whilst men talk and dispute of infinite space or duration, as if they had as complete and positive ideas of them, as they have of the names they use - for them, or as they have of a yard, or an hour, or any other determinate quantity; it is no wonder if the incomprehensible nature of the thing they discourse of, or reason about, leads them into perplexities and contradictions: and their minds be overlaid by an ob