§ 2. By repeating this Idea in our Minds, and adding the Repetitions together, we come by the complex Ideas of the Modes of it. Thus by adding one to one, we have the complex Idea of a Couple; by putting twelve Unites together, we have the complex Idea of a dozen; and so of a Score, or a Million, or any other Number.
§ 3. The simple modes of Number are of all other the most distinct; every the least Variation, which is an unite, making each Combination, as clearly different from that, which approacheth nearest to it, as the most remote; two being as distinct from one, as Two hundred; and the Idea of Two, as distinct from the Idea of Three, as the Magnitude of the whole Earth, is from that of a Mite. This is not so in other simple Modes, in which it is not so easie, nor, perhaps, possible for us to distinguish betwixt two approaching Ideas, which yet are [218]really different. For who will undertake to find a difference between the white of this Paper, and that of the next degree to it: Or can form distinct Ideas of every the least excess in Extension?
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§8. This farther is observable in Number, That it is that, which the Mind makes use of in measuring all things, that by us are measurable, which principally are Expansion and Duration; and our Idea of Infinity, even when applied to those, seems to be nothing, but the Infinity of Number. For what else are our Ideas of Eternity and Immensity, but the repeated additions of certain Ideas of imagined parts of Duration, and Expansion with the Infinity of Number, in which we can come to no end of Addition? […] And this endless addition or addibility (if any one like the word better) of Numbers, so apparent to the Mind, is that, I think, which gives us the clearest and most distinct Idea of Infinity: of which more in the following Chapter.
Of Infinity
§ 1. HE that would know what kind of Idea it is to which we give the name of Infinity, cannot do it better, than by considering to what Infinity is by the Mind more immediately attributed, and then how the Mind comes to frame it.
Finite, and Infinite, seem to me to be looked upon by the [220]Mind, as the Modes of Quantity, and to be attributed primarily in their first designation only to those things, which have parts, and are capable of increase or diminution, by the addition or subtraction of any the least part: and such are the Ideas of Space, Duration, and Number, which we have considered in the foregoing Chapters. ’Tis true, that we cannot but be assured, that the Great GOD, of whom, and from whom are all things, is incomprehensibly Infinite: but yet, when we apply to that first and supreme Being, our Idea of Infinite, in our weak and narrow Thoughts, we do it primarily in respect of his Duration and Ubiquity; and, I think, more figuratively to his Power, Wisdom, and Goodness, and other Attributes, which are properly inexhaustible and incomprehensible, etc. […]
§ 2. Finite then, and Infinite, being by the Mind look’d on as modifications of Expansion and Duration, the next thing to be considered is, How the Mind comes by them. As for the Idea of Finite, there is no great difficulty. The obvious portions of Extension, that affect our Senses, carry with them into the Mind the Idea of Finite: and the ordinary periods of Succession, whereby we measure Time and Duration, as Hours, Days, and Years, are bounded Lengths. The difficulty is, how we come by those boundless Ideas of Eternity and Immensity, since the Objects, which we converse with, come so much short of any approach or proportion to that Largeness.
§ 3. Every one, that has any Idea of any stated lengths of Space, as a Foot, finds, that he can repeat that Idea; and joining it to the former, make the Idea of two Foot; and by the addition of a third, three Foot; and so on, without ever coming to an end [222]of his additions, […] The power of enlarging his Idea of space by farther additions remaining still the same, he hence takes the Idea of infinite Space.
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§ 5. As, by the power we find in ourselves of repeating, as often as we will, any Idea of Space, we get the Idea of Immensity; so, by being able to repeat the Idea of any length of Duration, we have in our Minds, with all the endless addition of Number, we come by the Idea of Eternity. For we find in ourselves, we can no more come to an end of such repeated Ideas, than we can come to the end of Number, which every one perceives he cannot. […]
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§ 7. Though our Idea of Infinity arise from the contemplation of Quantity, and the endless increase the Mind is able to make in Quantity, by the repeated additions of what Portions thereof it pleases; yet I guess we cause great confusion in our Thoughts, when we join Infinity to any supposed Idea of Quantity the Mind can be thought to have, and so discourse or reason about an infinite quantity, (viz.) an infinite Space, or an infinite Duration: For our Idea of Infinity being, as I think, an endless growing Idea, but the Idea of any Quantity the Mind has, being at that time terminated in that Idea, (for be it as great as it will, it can be no greater than it is,) to join Infinity to it is to adjust a standing measure to a growing bulk; and therefore I think it is not an insignificant subtilty, if I say, that we are [224]carefully to distinguish between the Idea of the Infinity of Space, and the Idea of a Space infinite: The first is nothing but a supposed endless Progression of the Mind, over what repeated Ideas of Space it pleases; but to have actually in the Mind the Idea of a Space infinite, is to suppose the Mind already passed over, and actually to have a view of all those repeated Ideas of Space, which an endless repetition can never totally represent to it, which carries in it a plain contradiction.
§ 8. This, perhaps, will be a little plainer, if we consider it in Numbers. The infinity of Numbers, to the end of whose addition every one perceives there is no approach, easily appears to any one that reflects on it: But how clear soever this Idea of the Infinity of Number be, there is nothing yet more evident, than the absurdity of the actual Idea of an Infinite Number. […] when we would frame in our Minds the Idea of an infinite Space or Duration, that Idea is very obscure, and confused, because it is made up of two Parts, very different, if not inconsistent. For let a Man frame in his mind an Idea of any Space or Number, as great as he will; ’tis plain, the mind rests and terminates in that Idea, which is contrary to the Idea of Infinity, which consists in a supposed endless Progression. And therefore, I think, it is, that we are so easily confounded, when we come to argue, and reason about infinite Space or Duration, etc. Because the parts of such an Idea, not being perceived to be, as they are, inconsistent, the one side or other always perplexes, whatever Consequences we draw from the other […].
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Of other Simple Modes
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§ 2. To slide, roll, tumble, walk, creep, run, dance, leap, skip, and abundance 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. […]
§ 3. The like variety have we in Sounds. Every articulate word is a different modification 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. […]
§ 4. Those of Colours are also very various: Some we take notice of, as the different degrees, or as they were termed, Shades of the same Colour. […]
§ 5. All compounded Tastes and Smells, are also Modes made up of the simple Ideas of those Senses. But they being such, as generally we have no names for, are less taken notice of. […]
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