Philosiphy

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reckon right, it is required, (1) That the mind distin-

guish 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 an unit to that number; and

that not confusedly, and at random, but in that exact

order that the numbers follow one another. In either of

which, if it trips, the whole business of numbering will

be disturbed, and there will remain only the confused

idea of multitude, but the ideas necessary to distinct

numeration will not be attained to.

8. Number measures all measureables. This further 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 dura-

tion; 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? For such

an inexhaustible stock, number (of all other our ideas)

most clearly furnishes us with, as is obvious to every

one. For let a man collect into one sum as great a num-

ber as he pleases, this multitude, how great soever, less-

ens not one jot the power of adding to it, or brings him

any nearer the end of the inexhaustible stock of num-

ber; 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

1. 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, can-

not do it better than by considering to what infinity is

by the mind more immediately attributed; and then how

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the mind comes to frame it. Finite and infinite seem to

me 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 consid-

ered in the foregoing chapters. It is true, that we can-

not 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 to his duration and ubiq-

uity; and, I think, more figuratively to his power, wis-

dom, and goodness, and other attributes, which are prop-

erly inexhaustible and incomprehensible, &c. For, when

we call them infinite, we have no other idea of this

infinity but what carries with it some reflection on, and

imitation of, that number or extent of the acts or ob-

jects of God’s power, wisdom, and goodness, which can

never be supposed so great, or so many, which these

attributes will not always surmount and exceed, 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 be-

yond the reach of our narrow capacities: they do, with-

out doubt, contain in them all possible perfection: but

this, I say, is our way of conceiving them, and these our

ideas of their infinity.

2. The idea of finite easily got. Finite then, and infi-

nite, being by the mind looked on as modifications of

expansion and duration, the next thing to be consid-

ered, is,—How the mind comes by them. As for the idea

of finite, there is no great difficulty. The obvious por-

tions 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 we con-

verse with come so much short of any approach or pro-

portion to that largeness.

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3. 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 his additions, whether of the same idea of

a foot, or, if he pleases, of doubling it, or any other idea

he has of any length, as a mile, or diameter of the earth,

or of the orbis magnus: for whichever of these he takes,

and how often soever he doubles, or any otherwise

multiplies it, he finds, that, after he has continued his

doubling in his thoughts, and enlarged his idea as much

as he pleases, he has no more reason to stop, nor is one

jot nearer the end of such addition, than he was at first

setting out: the power of enlarging his idea of space by

further additions remaining still the same, he hence takes

the idea of infinite space.

4. 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, since this comes here in

our way, I suppose I may say, that we are apt to think

that space in itself is actually boundless, to which imagi-

nation the idea of space or expansion of itself naturally

leads us. For, it being considered by us, either as the

extension of body, or as existing by itself, without any

solid matter taking it up, (for of such a void space we

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 sup-

pose 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 further

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 that it is not; nay, when

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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 ever so little, here amongst

bodies; and if 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 a

void space interspersed amongst bodies, will always re-

main 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 bod-

ies, 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.

5. 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 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 per-

ceives 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 dura-

tion has been eternal. And as to this, I say, he that

considers something now existing, must necessarily come

to Something eternal. But having spoke of this in an-

other place, I shall say here no more of it, but proceed

on to some other considerations of our idea of infinity.

6. Why other ideas are not capable of infinity. If it be

so, that our idea of infinity be got from the power we

observe in ourselves of repeating, without end, our own

ideas, it may be demanded,—Why we do not attribute

infinity to other ideas, as well as those of space and

duration; since they may be as easily, and as often, re-

peated in our minds as the other: and yet nobody ever

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thinks of infinite sweetness, or infinite whiteness, though

he can repeat the idea of sweet or white, as frequently

as those of a yard or a day? To which I answer,—All the

ideas that are considered as having parts, and are ca-

pable of increase by the addition of any equal or less

parts, afford us, by their repetition, the idea of infinity;

because, with this endless repetition, there is continued

an enlargement of which there can be no end. But in

other ideas it is not so. For to the largest idea of exten-

sion or duration that I at present have, the addition of

any the least part makes an increase; but to the perfectest

idea I have of the whitest whiteness, if I add another of

a less or equal whiteness, (and of a whiter than I have,

I cannot add the idea), it makes no increase, and en-

larges not my idea at all; and therefore the different

ideas of whiteness, &c. are called degrees. For those ideas

that consist of parts are capable of being augmented by

every addition of the least part; but if you take the idea

of white, which one parcel of snow yielded yesterday to

our sight, and another idea of white from another par-

cel of snow you see to-day, and put them together in

your mind, they embody, as it were, and run into one,

and the idea of whiteness is not at all increased; and if

we add a less degree of whiteness to a greater, we are so

far from increasing, that we diminish it. Those ideas

that consist not of parts cannot be augmented to what

proportion men please, or be stretched beyond what

they have received by their senses; but space, duration,

and number, being capable of increase by repetition,

leave in the mind an idea of endless room for more; nor

can we conceive anywhere a stop to a further addition

or progression: and so those ideas alone lead our minds

towards the thought of infinity.

7. Difference between infinity of space, and space infi-

nite. Though our idea of infinity arise from the contem-

plation 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, as an infinite space, or an infinite duration.

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For, as 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 insig-

nificant subtilty, if I say, that we are carefully to distin-

guish between the idea of the infinity of space, and the

idea of a space infinite. The first is nothing but a sup-

posed endless progression of the mind, over what re-

peated 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 rep-

etition can never totally represent to it; which carries

in it a plain contradiction.

8. We have no idea of infinite space. 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. Whatsoever positive ideas we have in

our minds of any space, duration, or number, let them

be ever so great, they are still finite; but when we sup-

pose an inexhaustible remainder, from which we remove

all bounds, and wherein we allow the mind an endless

progression of thought, without ever completing the

idea, there we have our idea of infinity: which, though

it seems to be pretty clear when we consider nothing

else in it but the negation of an end, yet, 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; it is plain the

mind rests and terminates in that idea, which is con-

trary to the idea of infinity, which consists in a sup-

posed 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, &c.

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Because the parts of such an idea not being perceived to

be, as they are, inconsistent, the one side or other al-

ways perplexes, whatever consequences we draw from

the other; as an idea of motion not passing on would

perplex any one who should argue from such an idea,

which is not better than an idea of motion at rest. And

such another seems to me to be the idea of a space, or

(which is the same thing) a number infinite, i.e. of a

space or number which the mind actually has, and so

views and terminates in; and of a space or number, which,

in a constant and endless enlarging and progression, it

can in thought never attain to. For, how large soever an

idea of space I have in my mind, it is no larger than it is

that instant that I have it, though I be capable the next

instant to double it, and so on in infinitum; for that

alone is infinite which has no bounds; and that the idea

of infinity, in which our thoughts can find none.

9. Number affords us the clearest idea of infinity. But

of all other ideas, it is number, as I have said, which I

think furnishes us with the clearest and most distinct

idea of infinity we are capable of. For, even in space and

duration, when the mind pursues the idea of infinity, it

there makes use of the ideas and repetitions of numbers,

as of millions and millions of miles, or years, which are

so many distinct ideas,—kept best by number from run-

ning into a confused heap, wherein the mind loses it-

self; and when it has added together as many millions,

&c., as it pleases, of known lengths of space or dura-

tion, the clearest idea it can get of infinity, is the con-

fused incomprehensible remainder of endless addible

numbers, which affords no prospect of stop or bound-

ary.

10. Our different conceptions of the infinity of number

contrasted with those of duration and expansion. It will,

perhaps, give us a little further light into the idea we

have of infinity, and discover to us, that it is nothing

but the infinity of number applied to determinate parts,

of which we have in our minds the distinct ideas, if we

consider that number is not generally thought by us

infinite, whereas duration and extension are apt to be

so; which arises from hence,—that in number we are at

one end, as it were: for there being in number nothing

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less than an unit, we there stop, and are at an end; but

in addition, or increase of number, we can set no bounds:

and so it is like a line, whereof one end terminating

with us, the other is extended still forwards, beyond all

that we can conceive. But in space and duration it is

otherwise. For in duration we consider it as if this line

of number were extended both ways—to an

unconceivable, undeterminate, and infinite length; which

is evident to any one that will but reflect on what con-

sideration he hath of Eternity; which, I suppose, will

find to be nothing else but the turning this infinity of

number both ways, a parte ante, and a parte post, as

they speak. For, when we would consider eternity, a

parte ante, what do we but, beginning from ourselves

and the present time we are in, repeat in our minds the

ideas of years, or ages, or any other assignable portion

of duration past, with a prospect of proceeding in such

addition with all the infinity of number: and when we

would consider eternity, a parte post, we just after the

same rate begin from ourselves, and reckon by multi-

plied periods yet to come, still extending that line of

number as before. And these two being put together,

are that infinite duration we call Eternity: which, as we

turn our view either way, forwards or backwards, ap-

pears infinite, because we still turn that way the infi-

nite end of number, i.e. the power still of adding more.

11. How we conceive the infinity of space. The same

happens also in space, wherein, conceiving ourselves to

be, as it were, in the centre, we do on all sides pursue

those indeterminable lines of number; and reckoning

any way from ourselves, a yard, mile, diameter of the

earth, or orbis magnus,—by the infinity of number, we

add others to them, as often as we will. And having no

more reason to set bounds to those repeated ideas than

we have to set bounds to number, we have that indeter-

minable idea of immensity.

12. Infinite divisibility. And since in any bulk of matter

our thoughts can never arrive at the utmost divisibility,

therefore there is an apparent infinity to us also in that,

which has the infinity also of number; but with this

difference,—that, in the former considerations of the

infinity of space and duration, we only use addition of

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numbers; whereas this is like the division of an unit

into its fractions, wherein the mind also can proceed in

infinitum, as well as in the former additions; it being

indeed but the addition still of new numbers: though in

the addition of the one, we can have no more the posi-

tive idea of a space infinitely great, than, in the division

of the other, we can have the [positive] idea of a body

infinitely little;—our idea of infinity being, as I may

say, a growing or fugitive idea, still in a boundless pro-

gression, that can stop nowhere.

13. No positive idea of infinity. Though it be hard, I

think, to find anyone so absurd as to say he has the

positive idea of an actual infinite number;—the infinity

whereof lies only in a power still of adding any combina-

tion of units to any former number, and that as long

and as much as one will; the like also being in the infin-

ity of space and duration, which power leaves always to

the mind room for endless additions;—yet there be those

who imagine they have positive ideas of infinite dura-

tion and space. It would, I think, be enough to destroy

any such positive idea of infinite, to ask him that has

it,—whether he could add to it or no; which would

easily show the mistake of such a positive idea. We can,

I think, have no positive idea of any space or duration

which is not made up of, and commensurate to, re-

peated numbers of feet or yards, or days and years; which

are the common measures, whereof we have the ideas in

our minds, and whereby we judge of the greatness of

this sort of quantities. And therefore, since an infinite

idea of space or duration must needs be made up of

infinite parts, it can have no other infinity than that of

number capable still of further addition; but not an ac-

tual positive idea of a number infinite. For, I think it is

evident, that the addition of finite things together (as

are all lengths whereof we have the positive ideas) can

never otherwise produce the idea of infinite than as

number does; which, consisting of additions of finite

units one to another, suggests the idea of infinite, only

by a power we find we have of still increasing the sum,

and adding more of the same kind; without coming one

jot nearer the end of such progression.

14. How we cannot have a positive idea of infinity in

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quantity. They who would prove their idea of infinite to

be positive, seem to me to do it by a pleasant argument,

taken from the negation of an end; which being nega-

tive, the negation of it is positive. He that considers

that the end is, in body, but the extremity or superfi-

cies of that body, will not perhaps be forward to grant

that the end is a bare negative: and he that perceives

the end of his pen is black or white, will be apt to think

that the end is something more than a pure negation.

Nor is it, when applied to duration, the bare negation of

existence, but more properly the last moment of it. But

if they will have the end to be nothing but the bare

negation of existence, I am sure they cannot deny but

the beginning is the first instant of being, and is not by

any body conceived to be a bare negation; and there-

fore, by their own argument, the idea of eternal, a parte

ante, or of a duration without a beginning, is but a

negative idea.

15. What is positive, what negative, in our idea of infi-

nite. The idea of infinite has, I confess, something of

positive in all those things we apply to it. When we

would think of infinite space or duration, we at first

step usually make some very large idea, as perhaps of

millions of ages, or miles, which possibly we double and

multiply several times. All that we thus amass together

in our thoughts is positive, and the assemblage of a

great number of positive ideas of space or duration. But

what still remains beyond this we have no more a posi-

tive distinct notion of than a mariner has of the depth

of the sea; where, having let down a large portion of his

sounding-line, he reaches no bottom. Whereby he knows

the depth to be so many fathoms, and more; but how

much the more is, he hath no distinct notion at all: and

could he always supply new line, and find the plummet

always sink, without ever stopping, he would be some-

thing in the posture of the mind reaching after a com-

plete and positive idea of infinity. In which case, let this

line be ten, or ten thousand fathoms long, it equally

discovers what is beyond it, and gives only this con-

fused and comparative idea, that this is not all, but one

may yet go farther. So much as the mind comprehends

of any space, it has a positive idea of: but in endeavour-

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ing to make it infinite,—it being always enlarging, al-

ways advancing,—the idea is still imperfect and incom-

plete. So much space as the mind takes a view of in its

contemplation of greatness, is a clear picture, and posi-

tive in the understanding: but infinite is still greater. 1.

Then the idea of so much is positive and clear. 2. The

idea of greater is also clear; but it is but a comparative

idea, the idea of so much greater as cannot be compre-

hended. 3. And this is plainly negative: not positive. For

he has no positive clear idea of the largeness of any

extension, (which is that sought for in the idea of infi-

nite), that has not a comprehensive idea of the dimen-

sions of it: and such, nobody, I think, pretends to in

what is infinite. For to say a man has a positive clear

idea of any quantity, without knowing how great it is,

is as reasonable as to say, he has the positive clear idea

of 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 obscu-

rity, 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 posi-

tive 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 quan-

tity 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 of 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.

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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 oth-

ers 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 incon-

ceivable to me than duration without succession. Be-

sides, 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 un-

avoidable 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 posi-

tive 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 space. He that thinks he

has a positive idea of infinite space, will, when he con-

siders it, find that he can no more have a positive idea

of the greatest, than he has of the least space. For in

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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 mat-

ter to indivisibility, as the acutest thought of a math-

ematician; and a surveyor may as soon with his chain

measure out infinite space, as a philosopher by the quick-

est 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 pro-

duce. 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 infi-

nite. 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 space 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 coun-

try fellow had of the water which was yet to come, and

pass the channel of the river where he stood:

Rusticus expectat dum defluat amnis, at ille

Labitur, et labetur in omne volubilis oevum.

20. Some think they have a positive idea of eternity,

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and not of infinite space. There are some I have met

that put so much difference between infinite duration

and infinite space, that they persuade themselves that

they have a positive idea of eternity, but that they have

not, nor can have any idea of infinite space. 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 con-

sider 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 con-

trary, apparently absurd, that body should be infinite,

they forwardly conclude that they can have no idea of

infinite space, because they can have no idea of infinite

matter. Which consequence, I conceive, is very ill col-

lected, because the existence of matter is no ways nec-

essary to the existence of space, no more than the exist-

ence of motion, or the sun, is necessary to duration,

though duration used 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 space empty of

body, as to think of the capacity of a bushel without

corn, or the hollow of a nut-shell 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 space, 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 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 past? Though I suppose nobody thinks it con-

ceivable that anything does or has existed in that fu-

ture duration. Nor is it possible to join our idea of fu-

ture 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 space, because

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it is past doubt that God has existed from all eternity,

but there is no real matter co-extended with infinite

space; yet those philosophers who are of opinion that

infinite space is possessed by God’s infinite omnipres-

ence, as well as infinite duration by his eternal exist-

ence, must be allowed to have as clear an idea of infinite

space 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 quantity, 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

space, he could add two infinities together; nay, make

one infinite infinitely bigger than another—absurdities

too gross to be confuted.

21. Supposed positive ideas of infinity, cause of mis-

takes. But yet if after all this, there be men who per-

suade themselves that they have clear positive compre-

hensive ideas of infinity, it is fit they enjoy their privi-

lege: 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 con-

cerning infinity,—whether of space, duration, or divis-

ibility, 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 space or dura-

tion, 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 determi-

nate quantity; 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 consider-

ation of duration, space, and number, and what arises

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from the contemplation of them,—Infinity, it is possi-

bly 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 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 them-

selves, 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 per-

ception, 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. 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 pres-

ently in his mind distinct ideas, which are all but the

different modifications of motion. Modes of motion an-

swer those of extension; swift and slow are two differ-

ent ideas of motion, the measures whereof are made of