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8. 13. Though it be hard, I think, to No positive
find any one so absurd as to say, he has the idea of infi. nity.
positive idea of an actual infinite nuinber ;
the infinity whereof lies only in a power still of adding any combination of units to any former number, and that as long and as much as one will; the like also being in the infinity of space and duration, which power leaves always to the mind room for endless additions; yet there be those who imagine they have positive ideas of infinite duration and space. It would, I think, be enough to destroy any such positive idea of infinite, to ask him that has it, whether he could add to it or no; which would easily show the mistake of such a positive idea. We can, I think, have no positive idea of any space or duration which is not made up, and commensurate to repeated numbers of feet or yards, or days and years, which are the common mea. sures, whereof we have the ideas in our minds, and whereby we judge of the greatness of this sort of quantities. And therefore, since an infinite idea of space or duration must needs be made up of infinite parts, it can have no other infinity than that of number, capable still of farther addition ; but not au actual positivo idea of a number infinite. For, I think, it is evident that the addition of finite things together (as are all lengths, whereof we have the positive ideas) can never otherwise produce the idea of infinite, than as number does; which consisting of additions of finite units onc to another, suggests the idea of infinite, only by a power we find we have of still increasing the sum, and adding more of the same kind, without coming one jot pearer the end of such progression.
§. 14. They who would prove their idea of infinite to be positive, seem to me to do it by a pleasant argument, taken from the negation of an end; which being negative, the negation of it is positive. He that considers that the end is, in body, but the extremity or superficies of that body, will not perhaps be forward to grant that the end is a bare negative: and he that per. ceives the end of his pen is black or white, will be apt so think that the end is something more than a pure
think, negation. Nor is it, when applied to duration, the bare se has to negation of existence, but inore properly the last mo. Dune ment of it. But it they will have the end to be nothing a por? but the bare negation of existence, I am sure they canpy for not deny but the beginning is the first instant of being, wij u and is not by any body conceived to be a bare negation; daralis and therefore by their own argument, the idea of eterur entita nal, à parte ante, or of a duration without a beginning, Cher it is but a negative idea. It wodi $. 15. The idea of infinite has, I con- Wh
What is pofi. ce identi fess, something of positive in all those tive, what Foulds things we apply to it. When we would negative, in nisteke: think of infinite space or duration, we at our idea of
por first step usually inake some very large idea, made as perhaps of millions of ages, or miles, which posde psibly we double and multiply several times. All that ION we thus anass together in our thoughts is positive, and Ends et the assemblage of a great number of positive ideas of of great space or duration. But what still remains beyond this, of die we have no more a positive distinct notion of, than a uite para mariner has of the depth of the sea ; where having let er, cap down a large portion of his sounding-line, he reaches They no bottom: whcreby he knows the depth to be so many
enito fathoins, and more ; but how much the more is, he es are hath no distinct notion at all: And could he always -22 Defter supply new line, and find the plummet always sink,
pulse without ever stopping, he would be something in the initi i posture of the mind reaching after a complete and posi-anak tive idea of infmity. In which case let this line be i allir ten, or one thousand fathoms long, it equally disco. potravers what is beyond it; and gives only this confused
and comparative idea, that this is not all, but one may not yet go farther. So much as the mind comprehends in alio of any space, it has a positive idea of; but in endea. En vouring to make it infinite, it being always enlarging het is always advancing, the idea is still imperfect and inconi
ti plete. So much space as the mind takes a view of in cruallä its contemplation of greatness, is a clear picture, and chat pel positive in the understanding! but infinite is still I be greater 1. Then the idea of so much is positive and clear. %. The idea of greater is also clear, but it is
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 comprehensive idea of the dimensions of it; and such no-body, I think, pretends 'to in what is infinite. For to say a Hů 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 hie bas, or can have a positive idea; which is all the idea, I think, we have of infinite. So that what lies beyond our posia tive 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 coniprehend 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 big. ger: 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 greatir, 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 no g. 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 or duration, when ap:
plied to an eternal being, and to a finite: since per haps, 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 punctum 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 inore inconceivable to me than duration without succession. Besides, that punctum stans, if 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 bé !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.
1. 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 Being, who had no beginning: and such an idea of infinite duration I am sure I have. But this negation 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. ...' $. 18. He that thinks he has a positive
No positive idea of infinite space, will, when he con- .
to idea of infin siders it, find that he can no more have a nite space. positive idea of the greatest, than he has of the least space. For in this latter, which seems the
easier of the two, and inore within our comprehension, · We are capable only of a comparative idea of smallness, which 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 alwars 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 diminishing the other, without ceasing. A pestle and niortar will as soon bring any particle of inatter to indivi. sibility, as the acutest thought of a nathematician; and a surveyor may as soon with his chain measure our infinice space, as a pilosopher or 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 diaineter, has a clear and positive idea of it in his mind, and any cas: frame one of 1, 4, , and so on till he has the idea in his thoughts of something very little; but yet reache's 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 infinite divisibility.
sem $. 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 he wearies his thoughts, by
and Bossililo be 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