the Idea of a hundred; because the Chain that holds the Parts together, is to him wholly unferviceable, nor can he represent to his Mind the feveral interjacent Combinations, without which it is impoffible in this Cafe to arrive at a distinct Perception. The great 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 moft natural View of the Conduct and Procedure of the Understanding, and makes us fenfible of the great Art and Addrefs that is neceflary, in the claffing of our very complex Conceptions. He that can fo put together the component Parts of an Idea, as that they fhall lie obvious to the Notice of the Mind, and prefent themselves when Occafion requires, in a juft and orderly Connection, will not find it very difficult, to obtain clear and accurate Perceptions, in most of thofe 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 unneceflary Fatigue, by entangling and perplexing them with Confiderations remote from the Buffnefs 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 eafe the View of the Mind, by taking them to Pieces, and fetting 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 fhall 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 fome length, the Conduct of the Mind in Numbering; it feeming to me the best Model in this Kind, whether we confider the many Advantages derived from fuch an orderly Difpofition of our Ideas, or the great Art and Skill difplayed in binding thefe Ideas together. This allo 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 Potibility of doubling or increafing our Stock in any Degree, remaining as obvious to the Under standing, Standing, after a great and continued Run of Progreffions, as when we first began the Computation. The Confide ration of Number of great Ufe, in afcertaining our Ideas f Space and Duration. VIII. If we now turn our Thoughts towards: Space and Duration, heré too we fhall find, that we very seldom 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, eafily flide 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 ftated Measures, by which precifely 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 Progrefs of Duration. The leffer Parts, as lying moft open to the Notice of the Understanding, and being more on a Level with its Powers, are retained with tolerable Exactnefs; and the larger Portions, when the Number of Repetitions of which they are made up, is known, are thereby alfo 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 confider it as equal to a certain Number of Yards. If we are ftill for increafing the Standard, we may take the Semidiameter of the Earth, and fuppofing it equal to 8000 Miles, make Ufe of it as a Measure, by which to afcertain the Distance of the Sun or fixed Stars. Juft fo it is in Duration; from Hours we rife 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 to degenerate confu into a gular Heap. fed and irre IX. IT is however to Number alone, that we owe this Diftinctness of Perception, inafinuch as Space, and Time, confidered apart, from the regular and orderly Repetition of Miles or Years, leave no determinate Impreffions in the Mind, by which to know and diftinguifh their feveral Portions. Ideas of either, thus taken in at a Venture, are a confufed 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 thefe 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 Object too mighty for the Survey of the buman Mind. X. AND thus as before in Number, fo 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 eafy Apprehenfion to the Understanding, and by their Subdivifions into still leffer Spaces, exhibit themselves diftinctly in all their Parts. With these variously 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 juft. But when we let loose our Underftandings after a boundless Remainder, and would fathom the Depth of Infinity, we find ourfelves loft amidst the Greatnets of our own Conceptions. Some Notions it is true we have, but fuch as exceeding the Dimenfions of the Mind, lie involved in Darkness and Obfcurity; and being deftitute of Order, Method, and Connection, afford no Foundation, whereon to build any just and accurate Conclufions. Neuer reprefented in its ful Dimen Bons; but by es ane dies and growing Idea. XI. AND this perhaps may be the Reason, why many modern Philofophers, in their Difcourfes concerning Infinity, have run into apparent Contradictions; because encountering with an Object too large for the Survey of the Underftanding, they found themfelves furrounded with inextricable Difficulties, which their fcanty 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 ore, as comprehends and exhaufts its Object, or ex move. hibits hibits it to the Mind, in its full Size and Dimenfions. 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 ftill 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 Eter 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 Immenfity. For when we confider Duration, either as paft, or to come, we find nothing to ftop 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 muft own at last, that we can no more arrive at the End of Duration, than at the End of Number. It is true, the feveral Generations of Men, rife and disappear in very quick Succeffions; Earth itfelf may decay, and thofe bright Luminaries that adorn the Firmament of Heaven, be extinguished. But the Courfe 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 ftill 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 prefent 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 reprefents Eternity in its full Dimenfions. The Idea of Immenfity derived from the Confideration of Space ever growing on all Sides of us. XIII. As in the Confideration of Time, we fix upon the prefent Moment, regarding it as the middle Point, which divides the whole Line of Duration into two equal Parts; fo 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 utmoft Bounds of the Univerfe; at leaft fo far, as it falls within our Notice. But then the Imagination refts not here, it fees immeafurable Spaces beyond, capable of receiving new Worlds, which it can purfue, as rifing one above another, in an endlefs 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 Immenfity; which is in Fact nothing elfe, but the Infinity of Number, applied to certain Portions of Extenfion, as Miles, or Leagues, &c. and thefe conceived, as extended every Way around us, in infinite and innumerable right Lines. Compound Ideas refulting 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 moft fimple and obvious Notices, to the Conception of Infinity itfelf; 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 feveral Ideas of different Kinds together, and voluntarily combines them into one complex Conception. Such for Inftance is our Idea of a Tune, as comprehending a Variety of Notes, with many different Modulations of Sound. And here it is to be obferved, that tho' the complex Idea may be excited in us, by hearing the Air itself ftruck off, upon a proper Inftrument; yet confidered originally, it ftill belongs to this Clafs of Perceptions, which are diftinguished as the arbitrary Collections of the Mind. It was the Musician, or Compofer, that combined the feveral Notes, and determined the Order in which they were to follow one another; nor had that particular Compofition of Sounds, any real Union in Nature, before they were thus brought together in his Mind. Of the fame Nature are moft 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 Diftilling, Carving, Treafon, &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 thefe Combi fet XV. IT is here that the Understanding has the greatest Scope, and finds moft Employment for its active Powers; nor indeed is it poffible to Bounds to the Ideas of this Clafs; the Combinations already made being almost innumerable, and thofe yet in the Power of the Mind affording an endlefs Diverfity. It may not however be amifs to confider, nations. any how |