:

d

the Idea of a hundred; because the Chain that holds the Parts together, is to him wholly unserviceable, nor can he represent to his Mind the several interjacent Combinations, without which it is impoffible in this Cafe to arrive at a diftinct Perception.

The great
Aduantages
of Address
in claffing our
complex Con-
cepcions.

VII. I HAVE infifted the more largely upon this, not only because it is by Number that we measure all other Things, as Duration, Extenfion, Motion, &c. but alio, because it us lets into the most natural View of the Conduct and Procedure

of the Understanding, and makes us sensible of the great Art and Address that is neceflary, in the classing of our very complex Conceptions. He that can so put together the component Parts of an Idea, as that they shall lie obvious to the Notice of the Mind, and present themselves when Occafion requires, in a just and orderly Connection, will not find it very difficult, to obtain clear and accurate Perceptions, in most of those Subjects, about which our Thoughts are converfant. For the great Art of Knowledge lies, in managing with Skill the Capacity of the Intellect, and contriving fuch Helps, as if they strengthen not its natural Powers, may yet expose them to no unnecessary Fatigue, by entangling and perplexing them with Confiderations remote from the Buffness in Hand. When Ideas become very complex, and by the Multiplicity of their Parts, grow too unweildy to be dealt with in the Lump, we must ease the View of the Mind, by taking them to Pieces, and setting before it the feveral Portions feparately, one after another. By this leisurely Survey, we are enabled to take in the whole, and if we can draw it into fuch an orderly Combination, as will naturally lead the Attention Step by Step, in any fucceeding Confideration of the fame Idea, we shall ever have it at Command, and with a fingle Glance of Thought be able to run over all its Parts. I have therefore explained here at some length, the Conduct of the Mind in Numbering; it feeming to me the best Model in this Kind, whether we confider the inany Advantages derived from fuch an orderly Difpofition of our Ideas, or the great Art and Skill difplayed in binding these Ideas together. This also is farther remarkable, in the Confideration of Number, that from it chiefly we derive the Notion we have of Infinity; it being apparent, that in adding Number to Number, there is no End; the Poffibility of doubling or increasing our Stock in any Degree, remaining as obvious to the Understanding,

standing, after a great and continued Run of Progreflions,
as when we first began the Computation.

ration of Number of great Ufe, in ascertaining our Ideas of Space and Duration.

VIII. If we now turn our Thoughts towards: The ConfideSpace and Duration, here too we shall find, that we very feldom arrive at clear and diftinct Ideas of either, but when we introduce the Confideration of Number. The more obvious and limited Portions, it is true, easily slide into the Mind in the natural Way of Perception; but it was the Neceffity of comparing these together, that put us upon the Contrivance of certain stated Measures, by which precisely to determine the Quantity in each. Thus Inches, Feet, Yards, Miles, &c. afcertain our Ideas of Extenfion; as Minutes, Hours, Days, Years, &c. measure the Progress of Duration. The lefsfer Parts, as lying most open to the Notice of the Understanding, and being more on a Level with its Powers, are retained with tolerable Exactness; and the larger Portions, when the Number of Repetitions of which they are made up, is known, are thereby also reduced into clear and determinate Conceptions. A Foot, and Yard, are Measures easily comprehended by the Mind; nor do we find any Difficulty in conceiving a Mile, when we consider it as equal to a certain Number of Yards. If we are still for increasing the Standard, we may take the Semidiameter of the Earth, and supposing it equal to 8000 Miles, make Ufe of it as a Measure, by which to afcertain the Distance of the Sun or fixed Stars. Just so it is in Duration; from Hours we rise to Days, Months and Years; by these repeated and added together, we measure Time paft, or can run forward at Pleasure into Futurity, and that without any Confufion or Perplexity.

Without it

they are apt

IX. It is however to Number alone, that we owe this Diftinctness of Perception, inasmuch as Space, and Time, confidered apart, from the to degenerate regular and orderly Repetition of Miles or Years, into a confuJed and irreleave no determinate Impreffions in the Mind, by gular Heap. which to know and diftinguish their several Portions. Ideas of either, thus taken in at a Venture, are a confuled and irregular Heap, efpecially where we endeavour to enlarge and magnify our Views, and give full Play to the Powers of the Intellect. Something indeed the Mind conceives, vaft and mighty, but nothing that is precife, accurate, and juft. But when it begins to confider these Ideas as made up of Parts, and fixing upon fuch as are proportioned

to

to its Reach, fets itself to examine how often they are repeated to make up the whole, the Perceptions of the Understanding put on a new Form, and difcover their exact Bounds and Li. mits.

- Infinity an Oljet ton mighty for ibe Suracy of to byman

Mind.

X. AND thus as before in Number, so here in Extenfion and Duration, the Mind begins with fimple and obvious Notices, advancing by Degrees to more enlarged and intricate Conceptions.

A Day, or a Furlong, are of easy Apprehenfion to the Understanding, and by their Subdivisions into still lesser Spaces, exhibit themselves distinctly in all their Parts. With these varioufly repeated, we travel thro' Space and Time, fo that being able to reduce all our Ideas of this Clafs, however mighty and enlarged, to the clear and determinate Perceptions of Number, we can conduct our Thoughts without Perplexity, and never find ourselves puzzled, but when prefuming too much on our own Strength, we launch into Speculations, that stretch beyond the Powers of the human Intellect. Number may be compared to a Line, that setting out from Unity, runs on in a continual Increase of Length, without a Poffibility of ever arriving at its ultimate Period. So far as we purfue it in our Thoughts, and trace its regular Advances, fo far our Ideas are accurate and just. But when we let loose our Understandings after a boundless Remainder, and would fathom the Depth of Infinity, we find ourselves loft amidsf the Greatness of our own Conceptions. Some Notions it is true we have, but such as exceeding the Dimensions of the Mind, lie involved in Darkness and Obscurity; and being deftitute of Order, Method, and Connection, afiord no Foundation, whereon to build any just and accurate Conclufions.

Neuer reprefented in its ful Dimenfions; but by an er d'ejs and

eurgrowing

Idea.

XI. AND this perhaps may be the Reason, why many modern Philosophers, in their Difcourses concerning Infinity, have run into apparent Contradictions; because encountering with an Object too large for the Survey of the Understanding, they found themselves furrounded

with inextricable Difficulties, which their scanty and defective Ideas were by no means able to diffipate or reThe Truth of it is, finite Ideas alone, are proportioned to a finite Understanding; and altho' we are not wholly without a Notion of the Infinity of Number, yet it is not uch a or e, as comprehends and exhausts its Object, or exhibits hibits it to the Mind, in its full Size and Dimensions. We only fee the Idea, as capable of an endless Increase, but cannot by any Effort of Thought, take in the whole Profpect; and indeed, it is properly that Part of it, which lies beyond the Reach of our Perception, and still remains to be taken into the Account, to which we give the Name of Infinity.

Duration

whether con confidered as paft

or to come

boundless, whence our Idea of Eternity.

XII. THIS Idea of the Infinity of Number, imperfect as it may feem, is nevertheless that, by which the Mind afcends to the Conception of Eternity and Immensity. For when we confider Duration, either as paft, or to come, we find nothing to stop the Progress of our Thoughts, in the Repetition of Years, or Millions of Years : the farther we proceed, the more the Idea grows upon us, and when we have wearied ourselves with vain Efforts, we must own at last, that we can no more arrive at the End of Duration, than at the End of Number. It is true, the several Generations of Men, rise and difappear in very quick Succeffions; Earth itself may decay, and those bright Luminaries that adorn the Firmament of Heaven, be extinguished. But the Course of Time will not be thereby difturbed; that flows uniform and invariable, nor is bounded by the Period of their Existence. This double View of Duration, as having already revolved thro' numberless Ages, and yet still advancing into Futurity in an endless Progreffion, properly conftitutes our Idea of Eternity. We speak indeed of an Eternity past, and an Eternity to come, but both these are bounded at one Extreme; the former terminates in the present Moment, and therefore has an End; the latter fets out from the fame Period, and therefore has a Beginning; but taken together, they form a Line both ways infinitely extended, and which represents Eternity in its full Dimenfions.

The Idea of Immensity derived from the Confideration growing on all Sides of us.

of Space ever

XIII. As in the Confideration of Time, we fix upon the present Moment, regarding it as the middle Point, which divides the whole Line of Duration into two equal Parts; so in the Confideration of Space, that particular Place in which we exift, is looked upon as a kind of Center to the whole Expanfion. From thence we let loose our Thoughts on every Side; above, below, around, and find we can travel on, in the Repetition of Miles, and Millions of Miles, without ever arriving at the End of the Progreffion. It is not difficult indeed, to carry our ConVOL. II. ceptions

D

ceptions to the utmost Bounds of the Universe; at least so far, as it falls within our Notice. But then the Imagination rests not here, it fees immeasurable Spaces beyond, capable of receiving new Worlds, which it can pursue, as rifing one above another, in an endless Succeffion. This Confideration of Space, ever growing on all Sides of us, and yet never to be exhaufted, is that which gives us the Idea of Immensity; which is in Fact nothing else, but the Infinity of Number, applied to certain Portions of Extenfion, as Miles, or Leagues, &c. and these conceived, as extended every Way around us, in infinite and innumerable right Lines.

Compound

Ideas resulting from the Union of Perceptions of different

Kinds.

XIV. HITHERTO we have confidered the Mind, as employed about one and the fame Idea, enlarging and diverfifying it in various Forms. We have feen it rifing from the most simple and obvious Notices, to the Conception of Infini

ty itself; and taken a View of it, in all the different Stages of its Improvement. Let us now proceed to the more complicated Act of Compofition, when the Mind brings several Ideas of different Kinds together, and voluntarily combines them into one complex Conception. Such for Instance is our Idea of a Tune, as comprehending a Variety of Notes, with many different Modulations of Sound. And here it is to be observed, that tho' the complex Idea may be excited in us, by hearing the Air itself struck off, upon a proper Inftrument; yet confidered originally, it still belongs to this Class of Perceptions, which are diftinguished as the arbitrary Collections of the Mind. It was the Musician, or Composer, that combined the several Notes, and determined the Order in which they were to follow one another; nor had that particular Composition of Sounds, any real Union in Nature, before they were thus brought together in his Mind. Of the fame Nature are most of our Ideas of human Actions; for tho' many of them come to our Notice, by feeing the Actions themselves, or hearing them defcrib'd by others; as Distilling, Carving, Treason, &c. yet it is plain, that they must have been projected and contrived in the Mind of Man, before they had a real Existence.

How the Mind
is determined
in making
thefe Combi-
nations,

XV. IT is here that the Understanding has the greatest Scope, and finds most Employment for its active Powers; nor indeed is it poffible to fet any Bounds to the Ideas of this Class; the Combinations already made being almost innumerable, and those yet in the Power of the Mind affording an endless Diversity. It may not however be amiss to confider,

how