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plied to an eternal being, and to a finite: fince 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 yefterday. If, to avoid fucceffion in external existence, they return to the punctum ftans of the schools, I fuppofe they will thereby very little mend the matter, or help us to a more clear and pofitive idea of infinite duration, there being nothing more, inconceivable to me than duration without fucceffion. Befides, that punctum ftans, if it fignify any thing, being not quantum, finite or infinite cannot belong to it. But if our weak apprehenfions cannot separate fucceffion from any duration whatsoever, our idea of eternity can be nothing but of infinite fucceffion of moments of duration, wherein any thing does exift; and whether any one has or can have a pofitive idea of an actual infinite number, I leave him to confider, till his infinite number be fo great that he himself 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 fcanty for pofitive infinity.

§. 17. I think it unavoidable for every confidering rational creature, that will but examine his own or any other exiftence, to have the notion of an eternal wife Being, who had no beginning: and fuch an idea of infinite duration I am fure I have. But this nega tion of a beginning being but the negation of á pofitive thing, fcarce gives me a pofitive idea of infinity; which whenever I endeavoured to extend my thoughts to, I confefs myself at a lofs, and I find I cannot attain any clear comprehenfion of it.

No pofitive

idea of infinite fpage.

§. 18. He that thinks he has a pofitive idea of infinite space, will, when he confiders it, find that he can no more have a pofitive idea of the greateft, than he has of the leaft space. For in this latter, which feems the easier of the two, and more within our comprehension, we are capable only of a comparative idea of smallness,

which will always be lefs than any one whereof we have the pofitive idea. All our pofitive 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 pofitive idea which we have, lies in obfcurity; and we have no other idea of it, but of the power of enlarging the one, and diminifhing the other, without ceafing. A pestle and mortar will as foon bring any particle of matter to indivifibility, as the acuteft thought of a mathematician; and a furveyor may as foon with his chain measure our infinite fpace, as a philofopher by the quickest flight of mind reach it, or by thinking comprehend it; which is to have a pofitive idea of it. He that thinks on a cube of an inch diameter, has a clear and pofitive idea of it in his mind, and fo can frame one of,,, and fo on till he has the idea in his thoughts of fomething very little; but yet reaches not the idea of that incomprehenfible littlenefs which divifion can produce. What remains of smallnefs, is as far from his thoughts as when he first began; and therefore he never comes at all to have a clear and pofitive idea of that smallness, which is confequent to infinite divifibility.

What is pofitive, what negative, in our idea of infinite.

J. 19. Every one that looks towards infinity does, as I have faid, at first glance make fome very large idea of that which he applies it to, let it be fpace or duration; and poffibly he wearies his thoughts, by multiplying in his mind that firft large idea but yet by that he comes no nearer to the having a pofitive clear idea of what remains to make up a pofitive infinite, than the country-fellow had of the water, which was yet to come and pass the channel of the river where he flood:

Rufticus expectat dum tranfeat amnis, at ille
Labitur, & labetur in omne volubilis ævum.

§. 20.

Some thinkthey have a pofitive idea and not of inof eternity, finite space.

S. 20. There are fome I have met with, that put fo much difference between infinite duration and infinite fpace that they perfuade themselves that they have a pofitive idea of eternity; but that they have not, nor can have any idea of infinite fpace. The reafon of which mistake I fuppofe to be this, that finding by a due contemplation of caufes and effects, that it is neceffary to admit fome eternal being, and fo to confider the real exiftence of that being, as taken up and commenfurate to their idea of eternity; but on the other fide, not finding it neceffary, but on the contrary apparently abfurd, that body fhould be infinite; they forwardly conclude, that they have no idea of infinite fpace, because they can have no idea of infinite matter. Which confequence, I conceive, is very ill collected; because the existence of matter is no ways neceffary to the existence of space, no more than the existence of motion, or the fun, is neceffary to duration, though duration ufes to be meatured by it: and I doubt not but that a man may have the idea of ten thousand miles fquare, without any body fo big, as well as the idea of ten thousand years, without any body fo old. It seems as eafy to me to have the idea of fpace empty of body, as to think of the capacity of a bufhel without corn, or the hollow of a nut-fhell without a kernel in it it being no more neceffary that there should be exifting a folid body infinitely extended, becaufe we have an idea of the infinity of space, than it is neceffary that the world fhould be eternal, because we have an idea of infinite duration. And why fhould 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 paft? Though, I fuppofe nobody thinks it conceivable, that any thing does, or has existed in that future duration. Nor is it poffible to join our idea of future duration with prefent or paft exiftence, any more than it is poffible to make the ideas of yesterday, to-day, and to-morrow, to be the fame; or bring ages paft and future together, and make them

contem

1

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 fpace; yet thofe philofophers who are of opinion, that infinite fpace is poffeffed by God's infinite omniprefence, as well as infinite duration by his external exiftence, must be allowed to have as clear an idea of infinite fpace as of infinite duration; though neither of them, I think, has any pofitive idea of infinity in either cafe. For whatfoever pofitive idea a man has in his mind of any quantity, he can repeat it, and add it to the former as eafy as he can add together the ideas of two days, or two paces, which are pofitive ideas of lengths he has in his mind, and fo 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: abfurdities too grofs to be confuted.

Suppofed pofitive ideas of infinity,

takes;

§. 21. But yet after all this, there being men who perfuade themselves that they have clear pofitive comprehenfive ideas of caufe of mif infinity, it is fit they enjoy their privilege: and I should be very glad (with fome others that I know, who acknowledge they have none fuch) 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 dif courfes concerning infinity, whether of fpace, duration, or divifibility, have been the certain marks of a defect in our ideas of infinity, and the difproportion the nature thereof has to the comprehenfion of our narrowcapacities. For whilft men talk and difpute of infinite fpace or duration, as if they had as complete and pofitive ideas of them, as they have of the names they ufe for them, or as they have of a yard, or an hour, or any other determinate quantity; it is no wonder if the incomprehenfible nature of the thing they difcourfe of, or reafon about, leads them into perplexities and contradictions: and their minds be overlaid by an ob

All these

ideas from

fenfation and

reflection.

ject too large and mighty to be surveyed and managed by them. §. 22. If I have dwelt pretty long on the confideration of duration, fpace, and number, and what arifes from the contemplation of them, infinity; it is poffibly no more than the matter requires, there being few fimple ideas, whofe modes give more exercife to the thoughts of men than thefe do. I pretend not to treat of them in their full latitude; it fuffices to my defign, to fhow how the mind receives them, fuch as they are, from fenfation and reflection; and how even the idea we have of infinity, how remote foever it may feem to be from any object of fenfe, or operation of our mind, has nevertheless, as all our other ideas, its original there. Some mathematicians perhaps of advanced fpeculations, may have other ways to introduce into their minds ideas of infinity; but this hinders not, but that they themselves, as well as all other men, got the firft ideas which they. had of infinity, from fenfation and reflection, in the method we have here fet down.

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§. 1. Ting chapters town, how from motion.

HOUGH I have in the forego- Modes of

fimple ideas, taken in by fenfation, the mind comes to extend itself even to infinity; which however it may, of all others, feem most remote from any fenfible perception, yet at laft hath nothing in it but what is made out of fimple ideas, received into the mind by the fenfes, and afterwards there put together by the faculty the mind has to repeat its own ideas: though, I fay, these might be inftances enough of fimple modes of the fimple ideas of fenfation, and fuffice to fhow how the mind comes by them; yet I fhall for method's fake, VOL. I. though

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