discourse and reason pretty well, and have very clear conceptions of several other things, before they can tell twenty. And some, through the default of their memories, who cannot retain the several combinations of numbers, with their names annexed in their distinct orders, and the dependence of so long a train of numeral progressions, and their relation one to another, are not able all their lifetime to reckon or regularly go over any moderate series of numbers. For he that will count twenty, or have any idea of that number, must know that nineteen went before, with the distinct name or sign of every one of them, as they stand marked in their order; for wherever this fails, a gap is made, the chain breaks, and the progress in numbering can go no farther. So that to reckon right it is required, (1) That the mind distinguish carefully two ideas which are different, one from another, only by the addition or subtraction of one unit. (2) That it retain in memory the names or marks of the several combinations from a unit to that number; and that not confusedly, and at random; but in that exact order that the numbers follow one another.

Number measures all measurables.-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 addition 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? For let a man collect into one sum as great a number as he pleases, this multitude, how great soever, lessens not the power of adding to it, nor brings him any nearer the end of the inexhaustible stock of Number, where still there remains as much to be added as if none were taken out. 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.

CHAPTER XVII.

OF INFINITY.

Infinity in its original intention attributed to space, duration, and number.-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, [1.] To what Infinity is, by the mind, more immediately attributed; and then, [2.] How the mind comes to frame it.

Finite and Infinite seem to be looked upon by the 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. It is 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, we do it primarily in respect to His duration and ubiquity; and, I think, more figuratively to His power, wisdom, and goodness, and other attributes which are properly inexhaustible, and incomprehensible, &c. For when we call them infinite, we have no other idea of this Infinity [than] what carries with it some reflection on and intimation of that number or extent of the acts or objects of God's power, wisdom, and goodness; which can never be supposed so great or so many, [that] these attributes will not always surmount and exceed [them], let us multiply them in our thoughts as far as we can, with all the infinity of endless number. I do not pretend to say how these attributes are in God, who is infinitely beyond the reach of our narrow capacities; they do, without doubt, contain in them all possible perfection but this, I say, is our way of conceiving them; and these our ideas of their Infinity.

The idea of finite easily got.-Finite then and Infinite being by the mind looked 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.

How we come by the idea of infinity.—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 feet, and by the addition of a third, three feet, and so on, without ever coming to an end of addition.

space

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Our idea of space boundless.-This, I think, is the way whereby the mind gets the idea of Infinite Space. It is a quite different consideration to examine whether the mind has the idea of such a boundless space actually existing, since our ideas are not always proofs of the existence of things; but yet, I may say that we are apt to think that Space in itself is actually boundless; to which imagination the idea of Space or Expansion of itself naturally leads us. For, it being considered by us either [1.] as the extension of body, or [2.] as existing by itself without any solid matter taking it up, (for of such a void have not only the idea, but I have proved, as I think, from the motion of body, its necessary existence), it is impossible the mind should be ever able to find or suppose any end of it, or be stopped anywhere in its progress in this Space, how far soever it extends its thoughts. Any bounds made with body, even adamantine walls, are so far from putting a stop to the mind in its farther progress in Space and Extension, that it rather facilitates and enlarges it: for so far as that body reaches, so far no one can doubt of Extension; and when we are come to the utmost extremity of body, what is there that can there put a stop, and satisfy the mind that it is at the end of Space, when it perceives it is not; nay, when it is satisfied that body itself can move into it? For if it be necessary for the motion of body that there

should be an empty space, though never so little, here amongst bodies; and it be possible for body to move in or through that empty space-(nay, it is impossible for any particle of matter to move but into an empty space) – the same possibility of a body's moving into a void space beyond the utmost bounds of body, as well as into avoid space interspersed amongst bodies, will always remain clear and evident: the idea of empty, pure Space, whether within or beyond the confines of all bodies, being exactly the same, differing not in nature, though in bulk; and there being nothing to hinder body from moving into it so that wherever the mind places itself by any thought, either amongst, or remote from, all bodies, it can, in this uniform idea of Space, nowhere find any bounds, any end; and so must necessarily conclude it, by the very nature and idea of each part of it, to be actually infinite.

And so of duration.-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 with all the endless addition of number, we come by the idea of Eternity. For we find in ourselves, [that] 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. But here again it is another question, quite different from our having an idea of Eternity, to know whether there were any real being whose duration has been eternal. And as to this, I say, he that considers something now existing must necessarily come to something Eternal. But having spoken of this