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 indeterminable 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 numbers; whereas this is like
the division of an unit into its fractions, wherein the mind also can
proceed in infinitum, as wel 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 POSITIVE 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 progression, 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 stil of adding any combination of units to any
former number, and that as long and as much as one will; the like also
being in the infinity 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 duration 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, repeated 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 actual 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 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 negative, the negation on it is positive. He that considers
that the end is, in body, but the extremity or superficies 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 as they will have the end to be
nothing but the bare negation of existence, I am sure they cannot deny
but the beginning of the first instant of being, and is not by any body
conceived to be a bare negation; and therefore, by their own argument,
the idea of eternal, À PARTE ANTE, or of a duration without a beginning,
is but a negative idea.
15. What is positive, what negative, in our Idea of infinite.
The idea of infinite has, I confess, something of positive in al
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
positive 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 something in the posture of the mind reaching
after a complete 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 confused 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 endeavouring to make it
infinite,--it being always enlarging, always advancing,--the idea is
still imperfect and incomplete. So much space as the mind takes a view
of in its contemplation of greatness, is a clear picture, and positive
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
COMPREHENDED. 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 infinite), that has not a comprehensive idea
of the dimensions 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 al 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 al 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 al 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. 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 wel as I, who wil 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 Space.
He that thinks he has a positive idea of infinite space, will, when
he considers 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 smal ness, which wil always be
less than any one whereof we have the positive idea. Al 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 out 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 1/2, 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 al 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 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 country 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 ile Labitur, et labetur in
omne volubilis aevum.'
20. Some think they have a positive Idea of Eternity, 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 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 space, because
they can have no idea of infinite matter. Which consequence, I conceive,
is very il collected, because the existence of matter is no ways
necessary to the existence of space, 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 wel 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 hol ow 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
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
space, because 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 omnipresence, as wel as infinite duration by his eternal
existence, 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 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 al 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 space, 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 space 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 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 consideration of duration, space, 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 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 wel 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 al 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.
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 al 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. Modes of Sounds.
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. 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 cal ed 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.
4. Modes of Colours.
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.
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, needleworks, &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. Modes of Tastes.
Al 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, and cannot be set down in writing;
and therefore must be left without enumeration to the thoughts and
experience of my reader.
6. Some simple Modes have no Names.
In general it may be observed, that those simple modes which are
considered but as different DEGREES of the same simple idea, though they
are in themselves many of them very distinct ideas, yet have ordinarily
no distinct names, nor are much taken notice of, as distinct ideas,
where the difference is but very small between them. Whether men have
neglected these modes, and given no names to them, as wanting measures
nicely to distinguish them; or because, when they were so distinguished,
that knowledge would not be of general or necessary use, I leave it to
the thoughts of others. It is sufficient to my purpose to show, that al
our simple ideas come to our minds only by sensation and reflection; and
that when the mood has them, it can variously repeat and compound them,
and so make new complex ideas. But, though white, red, or sweet,
&c. have not been modified, or made into complex ideas, by several
combinations, so as to be named, and thereby ranked into species; yet
some others of the simple ideas, viz. those of unity, duration, and
motion, &c., above instanced in, as also power and thinking, have been
thus modified to a great variety of complex ideas, with names belonging
to them.
7. Why some Modes have, and others have not, Names.
The reason whereof, I suppose, has been this,--That the great
concernment of men being with men one amongst another, the knowledge of
men, and their actions, and the signifying of them to one another, was
most necessary; and therefore they made ideas of ACTIONS very nicely
modified, and gave those complex ideas names, that they might the more
easily record and discourse of those things they were daily conversant
in, without long ambages and circumlocutions; and that the things they
were continually to give and receive information about might be the
easier and quicker understood. That this is so, and that men in framing
different complex ideas, and giving them names, have been much governed
by the end of speech in general, (which is a very short and expedite way
of conveying their thoughts one to another), is evident in the names
which in several arts have been found out, and applied to several
complex ideas of modified actions, belonging to their several trades,
for dispatch sake, in their direction or discourses about them. Which
ideas are not generally framed in the minds of men not conversant about
these operations. And thence the words that stand for them, by the
greatest part of men of the same language, are not understood: v. g.
COLTSHIRE, DRILLING, FILTRATION, COHOBATION, are words standing for
certain complex ideas, which being seldom in the minds of any but those
few whose particular employments do at every turn suggest them to their
thoughts, those names of them are not general y understood but by smiths
and chymists; who, having framed the complex ideas which these words
stand for, and having given names to them, or received them from others,
upon hearing of these names in communication, readily conceive those
ideas in their minds;-as by COHOBATION al the simple ideas of
distilling, and the pouring the liquor distilled from anything back upon
the remaining matter, and distilling it again. Thus we see that there
are great varieties of simple ideas, as of tastes and smells, which have
no names; and of modes many more; which either not having been generally
enough observed, or else not being of any great use to be taken notice
of in the affairs and converse of men, they have not had names given to
them, and so pass not for species. This we shall have occasion hereafter
to consider more at large, when we come to speak of WORDS.
CHAPTER XIX.
OF THE MODES OF THINKING.