Volume I Part 20 (1/2)
16. We have no positive Idea of an infinite Duration.
I ask those who say they have a positive idea of eternity, whether their idea of duration includes in it succession, or not? If it does not, they ought to show the difference of their notion of duration, when applied 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 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 more inconceivable to me than duration without succession. Besides, that punctum stans, if it signify anything, 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 nothing but of INFINITE SUCCESSION OF MOMENTS OF DURATION WHEREIN ANYTHING 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 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 scanty for positive infinity.
17. No complete Idea of Eternal Being.
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 endeavour to extend my thoughts to, I confess myself at a loss, and I find I cannot attain any clear comprehension of it.
18. No positive Idea of infinite s.p.a.ce.
He that thinks he has a positive idea of infinite s.p.a.ce, will, when he considers it, find that he can no more have a positive idea of the greatest, than he has of the least s.p.a.ce. For in this latter, which seems the easier of the two, and more within our comprehension, we are capable only of a comparative idea of smallness, which will always be less than any one whereof we have the positive idea. All our POSITIVE ideas of any quant.i.ty, 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 diminis.h.i.+ng the other, WITHOUT CEASING.
A pestle and mortar will as soon bring any particle of matter to indivisibility, as the acutest thought of a mathematician; and a surveyor may as soon with his chain measure out infinite s.p.a.ce, as a philosopher by the quickest flight of mind reach it or by thinking comprehend it; which is to have a positive idea of it. He that thinks on a cube of an inch diameter, has a clear and positive idea of it in his mind, and so can frame one of 1/2, 1/4, 1/8, 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 infinite divisibility.
19. What is positive, what negative, in our Idea of Infinite.
Every one that looks towards infinity does, as I have said, at first glance make some very large idea of that which he applies it to, let it be s.p.a.ce or duration; and possibly he wearies his thoughts, by multiplying in his mind 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 had of the water which was yet to come, and pa.s.s the channel of the river where he stood:
'Rusticus expectat dum defluat amnis, at ille Labitur, et labetur in omne volubilis aevum.'
20. Some think they have a positive Idea of Eternity, and not of infinite s.p.a.ce.
There are some I have met that put so much difference between infinite duration and infinite s.p.a.ce, that they persuade themselves that they have a positive idea of eternity, but that they have not, nor can have any idea of infinite s.p.a.ce. 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 can have no idea of infinite s.p.a.ce, because they can have no idea of infinite matter. Which consequence, I conceive, is very ill collected, because the existence of matter is no ways necessary to the existence of s.p.a.ce, 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 miles 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 s.p.a.ce empty of body, as to think of the capacity of a bushel without corn, or the hollow of a nut-sh.e.l.l 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 s.p.a.ce, 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 s.p.a.ce 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 n.o.body thinks it conceivable that anything does or has existed 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 future together, and make them contemporary. But if these men are of the mind, that they have clearer ideas of infinite duration than of infinite s.p.a.ce, because it is past doubt that G.o.d has existed from all eternity, but there is no real matter co-extended with infinite s.p.a.ce; yet those philosophers who are of opinion that infinite s.p.a.ce is possessed by G.o.d's infinite omnipresence, as well as infinite duration by his eternal existence, must be allowed to have as clear an idea of infinite s.p.a.ce as of infinite duration; though neither of them, I think, has any positive idea of infinity in either case. For whatsoever positive ideas a man has in his mind of any quant.i.ty, 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 s.p.a.ce, he could add two infinites together; nay, make one infinite infinitely bigger than another--absurdities too gross to be confuted.
21. Supposed positive Ideas of Infinity, cause of Mistakes.
But yet if after all this, there be men who persuade themselves that they have clear positive comprehensive ideas of infinity, it is fit they enjoy their privilege: 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 s.p.a.ce, duration, or divisibility, have been the certain marks of a defect 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 s.p.a.ce 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 quant.i.ty; 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 object too large and mighty to be surveyed and managed by them. 22. All these are modes of Ideas got from Sensation and Reflection.
If I have dwelt pretty long on the consideration of duration, s.p.a.ce, and number, and what arises from the contemplation of them,--Infinity, it is possibly no more than the matter requires; there being few simple ideas whose MODES give more exercise to the thoughts of men than those do. I pretend not to treat of them in their full lat.i.tude. It suffices to my design to show how the mind receives them, such as they are, from sensation and reflection; and how even the idea we have of infinity, how remote soever it may seem to be from any object of sense, or operation of our mind, has, nevertheless, as all our other ideas, its original there. Some mathematicians perhaps, of advanced speculations, 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 first ideas which they had of infinity from sensation and reflection, in the method we have here set down.
CHAPTER XVIII.
OTHER SIMPLE MODES.
1. Other simple Modes of simple Ideas of sensation.
Though I have, in the foregoing chapters, shown how from simple ideas taken in by sensation, the mind comes to extend itself even to infinity; which, however it may of all others seem most remote from any sensible perception, yet at last hath nothing in it but what is made out of simple ideas: received into the mind by the senses, and afterwards there put together, by the faculty the mind has to repeat its own ideas; --Though, I say, these might be instances enough of simple modes of the simple ideas of sensation, and suffice to show how the mind comes by them, yet I shall, for method's sake, though briefly, give an account of some few more, and then proceed to more complex ideas.
2. Simple modes of motion.