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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 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 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 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 consider.
$ 16. I ask those who say they have a We have no positive idea of eternity, whether their positive idea idea of duration includes in it succession,
of an infinite
duration. 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
of infatter, oppose
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 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 nothing 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 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.
S 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 endeavour to extend my thoughts 'to, I confess myself at a loss, and I find I cannot attain any clear comprehension of it. No positive S 18. He that thinks he has a positive idea of in- idea of infinite space, will, when he confinite space. siders 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 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 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 diminishing 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 our infinite space 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, 1, 1, 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.
S 19. Every one that looks towards infinity does, as I have said, at first glance sitive, what make some very large idea of that which negative, in he applies it to, let it be space or dura- our idea of tion; and possibly he wearies his thoughts, in 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 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 in
they have a
positive idea finite duration and infinite space, that
of eternity, they persuade themselves that they have and not of ina positive idea of eternity; but that they finite space.
their minds be overlaid by an object too large and mighty to be surveyed and managed by them. All these $ 22. If I have dwelt pretty long on ideas from the consideration of duration, space, and sensation and reflec
number, and what arises from the con
templation 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 these do. I pretend not to treat of them in their full latitude; 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.
Of other Simple Modes. Modes of $ 1. THOUGH I have in the foregoing motion. 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.
S 2. To slide, roll, tumble, walk, creep, run, dance, leap, skip, and abundance of others that might be named, are words which are no sooner heard but every one, who understands English, has presently in his mind distinct ideas, which are all but the different modifications of motion. Modes of motion answer those of extension : swift and slow are two different ideas of motion, the measures whereof are made of the distances of time and space put together; so they. are complex ideas comprehending time and space with motion.
§ 3. The like variety have we in sounds. Modes of Every articulate word is a different modi. sounds. fication of sound : by which we see, that from the sense of hearing, by such modifications, the mind may be furnished with distinct ideas to almost an infinite number. Sounds also, besides the distinct cries of birds and beasts, are modified by diversity of notes of different length put together, which make that complex idea called a tune, which a musician may have in his mind when he hears or makes no sound at all, by reflecting on the ideas of those sounds so put together silently in his own fancy.
S 4. Those of colours are also very vari. Modes of ous: some we take notice of as the different colours. degrees, or, as they are termed, shades of the same colour. But since we very seldom make assemblages of colours either for use or delight, but figure is taken in also and has its part in it, as in painting, weaving, needle-works, &c. those which are taken notice of do most commonly belong to mixed modes, as being made up of ideas of divers kinds, viz. figure and colour, such as beauty, rainbow, &c.
$ 5. All compounded tastes and smells Modes of are also modes made up of the simple ideas taste. of those senses. But they being such as generally we