The Works of George Berkeley Part 40

And first I shall say somewhat of Natural Philosophy. On this subject it is that the sceptics triumph. All that stock of arguments they produce to depreciate our faculties and make mankind appear ignorant and low, are drawn princ.i.p.ally from this head, namely, that we are under an invincible blindness as to the _true_ and _real_ nature of things. This they exaggerate, and love to enlarge on. We are miserably bantered, say they, by our senses, and amused only with the outside and shew of things. The real essence, the internal qualities and const.i.tution of every the meanest object, is hid from our view: something there is in every drop of water, every grain of sand, which it is beyond the power of human understanding to fathom or comprehend(695). But, it is evident from what has been shewn that all this complaint is groundless, and that we are influenced by false principles to that degree as to mistrust our senses, and think we know nothing of those things which we perfectly comprehend.

102. One great inducement to our p.r.o.nouncing ourselves ignorant of the nature of things is, the current opinion that every thing includes _within itself_ the cause of its properties: or that there is in each object an inward essence, which is the source whence its discernible qualities flow, and whereon they depend. Some have pretended to account for appearances by occult qualities; but of late they are mostly resolved into mechanical causes, to wit, the figure, motion, weight, and suchlike qualities, of insensible particles(696): whereas, in truth, there is no other agent or efficient cause than _spirit_, it being evident that motion, as well as all other _ideas_, is perfectly inert. See sect. 25. Hence, to endeavour to explain the production of colours or sounds, by figure, motion, magnitude, and the like, must needs be labour in vain. And accordingly we see the attempts of that kind are not at all satisfactory. Which may be said in general of those instances wherein one idea or quality is a.s.signed for the cause of another. I need not say how many hypotheses and speculations are left out, and how much the study of nature is abridged by this doctrine(697).

103. The great mechanical principle now in vogue is _attraction_. That a stone falls to the earth, or the sea swells towards the moon, may to some appear sufficiently explained thereby. But how are we enlightened by being told this is done by attraction? Is it that that word signifies the manner of the tendency, and that it is by the mutual drawing of bodies instead of their being impelled or protruded towards each other? But nothing is determined of the manner or action, and it may as truly (for aught we know) be termed _impulse_, or _protrusion_, as _attraction_. Again, the parts of steel we see cohere firmly together, and this also is accounted for by attraction; but, in this, as in the other instances, I do not perceive that anything is signified besides the effect itself; for as to the manner of the action whereby it is produced, or the cause which produces it, these are not so much as aimed at.

104. Indeed, if we take a view of the several phenomena, and compare them together, we may observe some likeness and conformity between them. For example, in the falling of a stone to the ground, in the rising of the sea towards the moon, in cohesion and crystallization, there is something alike; namely, an union or mutual approach of bodies. So that any one of these or the like phenomena may not seem strange or surprising to a man who has nicely observed and compared the effects of nature. For that only is thought so which is uncommon, or a thing by itself, and out of the ordinary course of our observation. That bodies should tend towards the centre of the earth is not thought strange, because it is what we perceive every moment of our lives. But that they should have a like gravitation towards the centre of the moon may seem odd and unaccountable to most men, because it is discerned only in the tides. But a philosopher, whose thoughts take in a larger compa.s.s of nature, having observed a certain similitude of appearances, as well in the heavens as the earth, that argue innumerable bodies to have a mutual tendency towards each other, which he denotes by the general name _attraction_, whatever can be reduced to that, he thinks justly accounted for. Thus he explains the tides by the attraction of the terraqueous globe towards the moon; which to him doth not appear odd or anomalous, but only a particular example of a general rule or law of nature.

105. If therefore we consider the difference there is betwixt natural philosophers and other men, with regard to their knowledge of the phenomena, we shall find it consists, not in an exacter knowledge of the efficient cause that produces them-for that can be no other than the _will __ of a spirit_-but only in a greater largeness of comprehension, whereby a.n.a.logies, harmonies, and agreements are discovered in the works of nature, and the particular effects explained, that is, reduced to general rules, see sect. 62: which rules, grounded on the a.n.a.logy and uniformness observed in the production of natural effects, are most agreeable and sought after by the mind; for that they extend our prospect beyond what is present and near to us, and enable us to make very probable conjectures touching things that may have happened at very great distances of time and place, as well as to predict things to come: which sort of endeavour towards Omniscience is much affected by the mind.

106. But we should proceed warily in such things: for we are apt to lay too great a stress on a.n.a.logies, and, to the prejudice of truth, humour that eagerness of the mind, whereby it is carried to extend its knowledge into general theorems. For example, gravitation or mutual attraction, because it appears in many instances, some are straightway for p.r.o.nouncing _universal_; and that to attract and be attracted by every other body is an essential quality inherent in all bodies whatsoever. Whereas it is evident the fixed stars have no such tendency towards each other; and, so far is that gravitation from being _essential_ to bodies that in some instances a quite contrary principle seems to shew itself; as in the perpendicular growth of plants, and the elasticity of the air. There is nothing necessary or essential in the case(698); but it depends entirely on the will of the Governing Spirit(699), who causes certain bodies to cleave together or tend towards each other according to various laws, whilst He keeps others at a fixed distance; and to some He gives a quite contrary tendency to fly asunder, just as He sees convenient.

107. After what has been premised, I think we may lay down the following conclusions. First, it is plain philosophers amuse themselves in vain, when they enquire for any natural efficient cause, distinct from a _mind_ or _spirit_. Secondly, considering the whole creation is the workmans.h.i.+p of a _wise and good Agent_, it should seem to become philosophers to employ their thoughts (contrary to what some hold(700)) about the final causes of things. [(701) For, besides that this would prove a very pleasing entertainment to the mind, it might be of great advantage, in that it not only discovers to us the attributes of the Creator, but may also direct us in several instances to the proper uses and applications of things.] And I must confess I see no reason why pointing out the various ends to which natural things are adapted, and for which they were originally with unspeakable wisdom contrived, should not be thought one good way of accounting for them, and altogether worthy a philosopher.

Thirdly, from what has been premised, no reason can be drawn why the history of nature should not still be studied, and observations and experiments made; which, that they are of use to mankind, and enable us to draw any general conclusions, is not the result of any immutable habitudes or relations between things themselves, but only of G.o.d's goodness and kindness to men in the administration of the world. See sects. 30 and 31.

Fourthly, by a diligent observation of the phenomena within our view, we may discover the general laws of nature, and from them deduce other phenomena. I do not say _demonstrate_; for all deductions of that kind depend on a supposition that the Author of Nature always operates uniformly, and in a constant observance of those rules _we_ take for principles, which we cannot evidently know(702).

108. It appears from sect. 66, &c. that the steady consistent methods of nature may not unfitly be styled the Language of its Author, whereby He discovers His attributes to our view and directs us how to act for the convenience and felicity of life. Those men who frame(703) general rules from the phenomena, and afterwards derive(704) the phenomena from those rules, seem to consider signs(705) rather than causes. (706)A man may well understand natural signs without knowing their a.n.a.logy, or being able to say by what rule a thing is so or so. And, as it is very possible to write improperly, through too strict an observance of general grammar-rules; so, in arguing from general laws of nature, it is not impossible we may extend(707) the a.n.a.logy too far, and by that means run into mistakes.

109. [(708) To carry on the resemblance.] As in reading other books a wise man will choose to fix his thoughts on the sense and apply it to use, rather than lay them out in grammatical remarks on the language; so, in perusing the volume of nature, methinks it is beneath the dignity of the mind to affect an exactness in reducing each particular phenomenon to general rules, or shewing how it follows from them. We should propose to ourselves n.o.bler views, such as to recreate and exalt the mind with a prospect of the beauty, order, extent, and variety of natural things: hence, by proper inferences, to enlarge our notions of the grandeur, wisdom, and beneficence of the Creator: and lastly, to make the several parts of the creation, so far as in us lies, subservient to the ends they were designed for-G.o.d's glory, and the sustentation and comfort of ourselves and fellow-creatures.

110. [(709) The best key for the aforesaid a.n.a.logy, or natural Science, will be easily acknowledged to be a certain celebrated Treatise of _Mechanics_.] In the entrance of which justly admired treatise, Time, s.p.a.ce, and Motion are distinguished into _absolute_ and _relative_, _true_ and _apparent_, _mathematical_ and _vulgar_: which distinction, as it is at large explained by the author, does suppose those quant.i.ties to have an existence without the mind: and that they are ordinarily conceived with relation to sensible things, to which nevertheless in their own nature they bear no relation at all.

III. As for _Time_, as it is there taken in an absolute or abstracted sense, for the duration or perseverance of the existence of things, I have nothing more to add concerning it after what has been already said on that subject. Sects. 97 and 98. For the rest, this celebrated author holds there is an _absolute s.p.a.ce_, which, being unperceivable to sense, remains in itself similar and immoveable; and relative s.p.a.ce to be the measure thereof, which, being moveable and defined by its situation in respect of sensible bodies, is vulgarly taken for immoveable s.p.a.ce. _Place_ he defines to be that part of s.p.a.ce which is occupied by any body: and according as the s.p.a.ce is absolute or relative so also is the place.

_Absolute Motion_ is said to be the translation of a body from absolute place to absolute place, as relative motion is from one relative place to another. And because the parts of absolute s.p.a.ce do not fall under our senses, instead of them we are obliged to use their sensible measures; and so define both place and motion with respect to bodies which we regard as immoveable. But it is said, in philosophical matters we must abstract from our senses; since it may be that none of those bodies which seem to be quiescent are truly so; and the same thing which is moved relatively may be really at rest. As likewise one and the same body may be in relative rest and motion, or even moved with contrary relative motions at the same time, according as its place is variously defined. All which ambiguity is to be found in the apparent motions; but not at all in the true or absolute, which should therefore be alone regarded in philosophy. And the true we are told are distinguished from apparent or relative motions by the following properties. First, in true or absolute motion, all parts which preserve the same position with respect of the whole, partake of the motions of the whole. Secondly, the place being moved, that which is placed therein is also moved: so that a body moving in a place which is in motion doth partic.i.p.ate the motion of its place. Thirdly, true motion is never generated or changed otherwise than by force impressed on the body itself. Fourthly, true motion is always changed by force impressed on the body moved. Fifthly, in circular motion, barely relative, there is no centrifugal force, which nevertheless, in that which is true or absolute, is proportional to the quant.i.ty of motion.

112. But, notwithstanding what hath been said, I must confess it does not appear to me that there can be any motion other than _relative_(710): so that to conceive motion there must be conceived at least two bodies; whereof the distance or position in regard to each other is varied. Hence, if there was one only body in being it could not possibly be moved. This seems evident, in that the idea I have of motion doth necessarily include relation.-[(711)Whether others can conceive it otherwise, a little attention may satisfy them.]

113. But, though in every motion it be necessary to conceive more bodies than one, yet it may be that one only is moved, namely, that on which the force causing the change in the distance or situation of the bodies is impressed. For, however some may define relative motion, so as to term that body _moved_ which changes its distance from some other body, whether the force [(712)or action] causing that change were impressed on it or no, yet, as relative motion is that which is perceived by sense, and regarded in the ordinary affairs of life, it follows that every man of common sense knows what it is as well as the best philosopher. Now, I ask any one whether, in his sense of motion as he walks along the streets, the stones he pa.s.ses over may be said to _move_, because they change distance with his feet? To me it appears that though motion includes a relation of one thing to another, yet it is not necessary that each term of the relation be denominated from it. As a man may think of somewhat which does not think, so a body may be moved to or from another body which is not therefore itself in motion, [(713) I mean relative motion, for other I am not able to conceive.]

114. As the place happens to be variously defined, the motion which is related to it varies(714). A man in a s.h.i.+p may be said to be quiescent with relation to the sides of the vessel, and yet move with relation to the land. Or he may move eastward in respect of the one, and westward in respect of the other. In the common affairs of life, men never go beyond the Earth to define the place of any body; and what is quiescent in respect of _that_ is accounted _absolutely_ to be so. But philosophers, who have a greater extent of thought, and juster notions of the system of things, discover even the Earth itself to be moved. In order therefore to fix their notions, they seem to conceive the Corporeal World as finite, and the utmost unmoved walls or sh.e.l.l thereof to be the place whereby they estimate true motions. If we sound our own conceptions, I believe we may find all the absolute motion we can frame an idea of to be at bottom no other than relative motion thus defined. For, as has been already observed, absolute motion, exclusive of _all_ external relation, is incomprehensible: and to this kind of relative motion all the above-mentioned properties, causes, and effects ascribed to absolute motion will, if I mistake not, be found to agree. As to what is said of the centrifugal force, that it does not at all belong to circular relative motion, I do not see how this follows from the experiment which is brought to prove it. See Newton's _Philosophiae Naturalis Principia Mathematica, in Schol. Def. VIII_. For the water in the vessel, at that time wherein it is said to have the greatest relative circular motion, hath, I think, no motion at all: as is plain from the foregoing section.

115. For, to denominate a body _moved_, it is requisite, first, that it change its distance or situation with regard to some other body: and secondly, that the force occasioning that change be applied to(715) it. If either of these be wanting, I do not think that, agreeably to the sense of mankind, or the propriety of language, a body can be said to be in motion.

I grant indeed that it is possible for us to think a body, which we see change its distance from some other, to be moved, though it have no force applied to(716) it (in which sense there may be apparent motion); but then it is because the force causing the change(717) of distance is imagined by us to be [(718)applied or] impressed on that body thought to move. Which indeed shews we are capable of mistaking a thing to be in motion which is not, and that is all. [(719)But it does not prove that, in the common acceptation of motion, a body is moved merely because it changes distance from another; since as soon as we are undeceived, and find that the moving force was not communicated to it, we no longer hold it to be moved. So, on the other hand, when one only body (the parts whereof preserve a given position between themselves) is imagined to exist, some there are who think that it can be moved all manner of ways, though without any change of distance or situation to any other bodies; which we should not deny, if they meant only that it might have an impressed force, which, upon the bare creation of other bodies, would produce a motion of some certain quant.i.ty and determination. But that an actual motion (distinct from the impressed force, or power, productive of change of place in case there were bodies present whereby to define it) can exist in such a single body, I must confess I am not able to comprehend.]

116. From what has been said, it follows that the philosophic consideration of motion doth not imply the being of an _absolute s.p.a.ce_, distinct from that which is perceived by sense, and related to bodies: which that it cannot exist without the mind is clear upon the same principles that demonstrate the like of all other objects of sense. And perhaps, if we inquire narrowly, we shall find we cannot even frame an idea of _pure s.p.a.ce exclusive of all body_. This I must confess seems impossible(720), as being a most abstract idea. When I excite a motion in some part of my body, if it be free or without resistance, I say there is _s.p.a.ce_. But if I find a resistance, then I say there is _Body_: and in proportion as the resistance to motion is lesser or greater, I say the s.p.a.ce is more or less _pure_. So that when I speak of pure or empty s.p.a.ce, it is not to be supposed that the word _s.p.a.ce_ stands for an idea distinct from, or conceivable without, body and motion. Though indeed we are apt to think every noun substantive stands for a distinct idea that may be separated from all others; which hath occasioned infinite mistakes. When, therefore, supposing all the world to be annihilated besides my own body, I say there still remains _pure s.p.a.ce_; thereby nothing else is meant but only that I conceive it possible for the limbs of my body to be moved on all sides without the least resistance: but if that too were annihilated then there could be no motion, and consequently no s.p.a.ce(721). Some, perhaps, may think the sense of seeing doth furnish them with the idea of pure s.p.a.ce; but it is plain from what we have elsewhere shewn, that the ideas of s.p.a.ce and distance are not obtained by that sense. See the _Essay concerning Vision_.

117. What is here laid down seems to put an end to all those disputes and difficulties that have sprung up amongst the learned concerning the nature of _pure s.p.a.ce_. But the chief advantage arising from it is that we are freed from that dangerous dilemma, to which several who have employed their thoughts on that subject imagine themselves reduced, viz. of thinking either that Real s.p.a.ce is G.o.d, or else that there is something beside G.o.d which is eternal, uncreated, infinite, indivisible, immutable.

Both which may justly be thought pernicious and absurd notions. It is certain that not a few divines, as well as philosophers of great note, have, from the difficulty they found in conceiving either limits or annihilation of s.p.a.ce, concluded it must be _divine_. And some of late have set themselves particularly to shew that the incommunicable attributes of G.o.d agree to it. Which doctrine, how unworthy soever it may seem of the Divine Nature, yet I must confess I do not see how we can get clear of it, so long as we adhere to the received opinions(722).

118. Hitherto of Natural Philosophy. We come now to make some inquiry concerning that other great branch of speculative knowledge, to wit, Mathematics(723). These, how celebrated soever they may be for their clearness and certainty of demonstration, which is hardly anywhere else to be found, cannot nevertheless be supposed altogether free from mistakes, if in their principles there lurks some secret error which is common to the professors of those sciences with the rest of mankind. Mathematicians, though they deduce their theorems from a great height of evidence, yet their first principles are limited by the consideration of Quant.i.ty. And they do not ascend into any inquiry concerning those transcendental maxims which influence all the particular sciences; each part whereof, Mathematics not excepted, doth consequently partic.i.p.ate of the errors involved in them. That the principles laid down by mathematicians are true, and their way of deduction from those principles clear and incontestible, we do not deny. But we hold there may be certain erroneous maxims of greater extent than the object of Mathematics, and for that reason not expressly mentioned, though tacitly supposed, throughout the whole progress of that science; and that the ill effects of those secret unexamined errors are diffused through all the branches thereof. To be plain, we suspect the mathematicians are no less deeply concerned than other men in the errors arising from the doctrine of abstract general ideas, and the existence of objects without the mind.

119. Arithmetic hath been thought to have for its object abstract ideas of _number_. Of which to understand the properties and mutual habitudes, is supposed no mean part of speculative knowledge. The opinion of the pure and intellectual nature of numbers in abstract has made them in esteem with those philosophers who seem to have affected an uncommon fineness and elevation of thought. It hath set a price on the most trifling numerical speculations, which in practice are of no use, but serve only for amus.e.m.e.nt; and hath heretofore so far infected the minds of some, that they have dreamed of mighty _mysteries_ involved in numbers, and attempted the explication of natural things by them. But, if we narrowly inquire into our own thoughts, and consider what has been premised, we may perhaps entertain a low opinion of those high flights and abstractions, and look on all inquiries about numbers only as so many _difficiles nugae_, so far as they are not subservient to practice, and promote the benefit of life.

120. Unity in abstract we have before considered in sect. 13; from which, and what has been said in the Introduction, it plainly follows there is not any such idea. But, number being defined a _collection of units_, we may conclude that, if there be no such thing as unity, or unit in abstract, there are no _ideas_ of number in abstract, denoted by the numeral names and figures. The theories therefore in Arithmetic, if they are abstracted from the names and figures, as likewise from all use and practice, as well as from the particular things numbered, can be supposed to have nothing at all for their object. Hence we may see how entirely the science of numbers is subordinate to practice, and how jejune and trifling it becomes when considered as a matter of mere speculation(724).

121. However, since there may be some who, deluded by the specious show of discovering abstracted verities, waste their time in arithmetical theorems and problems which have not any use, it will not be amiss if we more fully consider and expose the vanity of that pretence. And this will plainly appear by taking a view of Arithmetic in its infancy, and observing what it was that originally put men on the study of that science, and to what scope they directed it. It is natural to think that at first, men, for ease of memory and help of computation, made use of counters, or in writing of single strokes, points, or the like, each whereof was made to signify an unit, i.e. some one thing of whatever kind they had occasion to reckon. Afterwards they found out the more compendious ways of making one character stand in place of several strokes or points. And, lastly, the notation of the Arabians or Indians came into use; wherein, by the repet.i.tion of a few characters or figures, and varying the signification of each figure according to the place it obtains, all numbers may be most aptly expressed. Which seems to have been done in imitation of language, so that an exact a.n.a.logy is observed betwixt the notation by figures and names, the nine simple figures answering the nine first numeral names and places in the former, corresponding to denominations in the latter. And agreeably to those conditions of the simple and local value of figures, were contrived methods of finding, from the given figures or marks of the parts, what figures and how placed are proper to denote the whole, or _vice versa_. And having found the sought figures, the same rule or a.n.a.logy being observed throughout, it is easy to read them into words; and so the number becomes perfectly known. For then the number of any particular things is said to be known, when we know the name or figures (with their due arrangement) that according to the standing a.n.a.logy belong to them. For, these signs being known, we can by the operations of arithmetic know the signs of any part of the particular sums signified by them; and thus computing in signs, (because of the connexion established betwixt them and the distinct mult.i.tudes of things, whereof one is taken for an unit), we may be able rightly to sum up, divide, and proportion the things themselves that we intend to number.

122. In Arithmetic, therefore, we regard not the _things_ but the _signs_; which nevertheless are not regarded for their own sake, but because they direct us how to act with relation to things, and dispose rightly of them.

Now, agreeably to what we have before observed of Words in general (sect.

19, Introd.), it happens here likewise, that abstract ideas are thought to be signified by numeral names or characters, while they do not suggest ideas of particular things to our minds. I shall not at present enter into a more particular dissertation on this subject; but only observe that it is evident from what has been said, those things which pa.s.s for abstract truths and theorems concerning numbers, are in reality conversant about no object distinct from particular numerable things; except only names and characters, which originally came to be considered on no other account but their being _signs_, or capable to represent aptly whatever particular things men had need to compute. Whence it follows that to study them for their own sake would be just as wise, and to as good purpose, as if a man, neglecting the true use or original intention and subserviency of language, should spend his time in impertinent criticisms upon words, or reasonings and controversies purely verbal(725).

123. From numbers we proceed to speak of _extension_(726), which, considered as relative, is the object of Geometry. The _infinite_ divisibility of _finite_ extension, though it is not expressly laid down either as an axiom or theorem in the elements of that science, yet is throughout the same everywhere supposed, and thought to have so inseparable and essential a connexion with the principles and demonstrations in Geometry that mathematicians never admit it into doubt, or make the least question of it. And as this notion is the source from whence do spring all those amusing geometrical paradoxes which have such a direct repugnancy to the plain common sense of mankind, and are admitted with so much reluctance into a mind not yet debauched by learning; so is it the princ.i.p.al occasion of all that nice and extreme subtilty, which renders the study of Mathematics so very difficult and tedious. Hence, if we can make it appear that no _finite_ extension contains innumerable parts, or is infinitely divisible, it follows that we shall at once clear the science of Geometry from a great number of difficulties and contradictions which have ever been esteemed a reproach to human reason, and withal make the attainment thereof a business of much less time and pains than it hitherto hath been.

124. Every particular finite extension which may possibly be the object of our thought is an _idea_ existing only in the mind; and consequently each part thereof must be perceived. If, therefore, I cannot _perceive_ innumerable parts in any finite extension that I consider, it is certain they are not contained in it. But it is evident that I cannot distinguish innumerable parts in any particular line, surface, or solid, which I either perceive by sense, or figure to myself in my mind. Wherefore I conclude they are not contained in it. Nothing can be plainer to me than that the extensions I have in view are no other than my own ideas; and it is no less plain that I cannot resolve any one of my ideas into an infinite number of other ideas; that is, that they are not infinitely divisible(727). If by _finite extension_ be meant something distinct from a finite idea, I declare I do not know what that is, and so cannot affirm or deny anything of it. But if the terms _extension_, _parts_, and the like, are taken in any sense conceivable-that is, for _ideas_,-then to say a finite quant.i.ty or extension consists of parts infinite in number is so manifest and glaring a contradiction, that every one at first sight acknowledges it to be so. And it is impossible it should ever gain the a.s.sent of any reasonable creature who is not brought to it by gentle and slow degrees, as a converted Gentile(728) to the belief of transubstantiation. Ancient and rooted prejudices do often pa.s.s into principles. And those propositions which once obtain the force and credit of a _principle_, are not only themselves, but likewise whatever is deducible from them, thought privileged from all examination. And there is no absurdity so gross, which, by this means, the mind of man may not be prepared to swallow(729).

125. He whose understanding is prepossessed with the doctrine of abstract general ideas may be persuaded that (whatever be thought of the ideas of sense) _extension in abstract_ is infinitely divisible. And one who thinks the objects of sense exist without the mind will perhaps, in virtue thereof, be brought to admit(730) that a line but an inch long may contain innumerable parts really existing, though too small to be discerned. These errors are grafted as well in the minds of geometricians as of other men, and have a like influence on their reasonings; and it were no difficult thing to shew how the arguments from Geometry made use of to support the infinite divisibility of extension are bottomed on them. [(731) But this, if it be thought necessary, we may hereafter find a proper place to treat of in a particular manner.] At present we shall only observe in general whence it is the mathematicians are all so fond and tenacious of that doctrine.

126. It has been observed in another place that the theorems and demonstrations in Geometry are conversant about universal ideas (sect. 15, Introd.): where it is explained in what sense this ought to be understood, to wit, the particular lines and figures included in the diagram are supposed to stand for innumerable others of different sizes; or, in other words, the geometer considers them abstracting from their magnitude: which doth not imply that he forms an abstract idea, but only that he cares not what the particular magnitude is, whether great or small, but looks on that as a thing indifferent to the demonstration. Hence it follows that a line in the scheme but an inch long must be spoken of as though it contained ten thousand parts, since it is regarded not in itself, but as it is universal; and it is universal only in its signification, whereby it _represents_ innumerable lines greater than itself, in which may be distinguished ten thousand parts or more, though there may not be above an inch in _it_. After this manner, the properties of the lines signified are (by a very usual figure) transferred to the sign; and thence, through mistake, thought to appertain to it considered in its own nature.

127. Because there is no number of parts so great but it is possible there may be a line containing more, the inch-line is said to contain parts more than any a.s.signable number; which is true, not of the inch taken absolutely, but only for the things signified by it. But men, not retaining that distinction in their thoughts, slide into a belief that the small particular line described on paper contains in itself parts innumerable. There is no such thing as the ten thousandth part of an inch; but there is of a mile or diameter of the earth, which may be signified by that inch. When therefore I delineate a triangle on paper, and take one side, not above an inch for example in length, to be the radius, this I consider as divided into 10,000 or 100,000 parts, or more. For, though the ten thousandth part of that line considered in itself, is nothing at all, and consequently may be neglected without any error or inconveniency, yet these described lines, being only marks standing for greater quant.i.ties, whereof it may be the ten thousandth part is very considerable, it follows that, to prevent notable errors in practice, the radius must be taken of 10,000 parts, or more.

128. From what has been said the reason is plain why, to the end any theorem may become universal in its use, it is necessary we speak of the lines described on paper as though they contained parts which really they do not. In doing of which, if we examine the matter throughly, we shall perhaps discover that we cannot conceive an inch itself as consisting of, or being divisible into, a thousand parts, but only some other line which is far greater than an inch, and represented by it; and that when we say a line is _infinitely divisible_, we must mean(732) _a line which is infinitely great_. What we have here observed seems to be the chief cause, why to suppose the _infinite_ divisibility of _finite extension_ has been thought necessary in geometry.

129. The several absurdities and contradictions which flowed from this false principle might, one would think, have been esteemed so many demonstrations against it. But, by I know not what logic, it is held that proofs _a posteriori_ are not to be admitted against propositions relating to Infinity. As though it were not impossible even for an Infinite Mind to reconcile contradictions; or as if anything absurd and repugnant could have a necessary connexion with truth, or flow from it. But whoever considers the weakness of this pretence, will think it was contrived on purpose to humour the laziness of the mind, which had rather acquiesce in an indolent scepticism than be at the pains to go through with a severe examination of those principles it has ever embraced for true.

130. Of late the speculations about Infinites have run so high, and grown to such strange notions, as have occasioned no small scruples and disputes among the geometers of the present age. Some there are of great note who, not content with holding that finite lines may be divided into an infinite number of parts, do yet farther maintain, that each of those Infinitesimals is itself subdivisible into an infinity of other parts, or Infinitesimals of a second order, and so on _ad infinitum_. These, I say, a.s.sert there are Infinitesimals of Infinitesimals of Infinitesimals, without ever coming to an end. So that according to them an inch does not barely contain an infinite number of parts, but an infinity of an infinity of an infinity _ad infinitum_ of parts. Others there be who hold all orders of Infinitesimals below the first to be nothing at all; thinking it with good reason absurd to imagine there is any positive quant.i.ty or part of extension which, though multiplied infinitely, can ever equal the smallest given extension. And yet on the other hand it seems no less absurd to think the square, cube, or other power of a positive real root, should itself be nothing at all; which they who hold Infinitesimals of the first order, denying all of the subsequent orders, are obliged to maintain.

131. Have we not therefore reason to conclude they are _both_ in the wrong, and that there is in effect no such thing as parts infinitely small, or an infinite number of parts contained in any finite quant.i.ty?

But you will say that if this doctrine obtains it will follow the very foundations of Geometry are destroyed, and those great men who have raised that science to so astonis.h.i.+ng a height, have been all the while building a castle in the air. To this it may be replied, that whatever is useful in geometry, and promotes the benefit of human life, does still remain firm and unshaken on our Principles; that science considered as practical will rather receive advantage than any prejudice from what has been said. But to set this in a due light,[(733) and shew how lines and figures may be measured, and their properties investigated, without supposing finite extension to be infinitely divisible,] may be the proper business of another place(734). For the rest, though it should follow that some of the more intricate and subtle parts of Speculative Mathematics may be pared off without any prejudice to truth, yet I do not see what damage will be thence derived to mankind. On the contrary, I think it were highly to be wished that men of great abilities and obstinate application(735) would draw off their thoughts from those amus.e.m.e.nts, and employ them in the study of such things as lie nearer the concerns of life, or have a more direct influence on the manners.

132. If it be said that several theorems, undoubtedly true, are discovered by methods in which Infinitesimals are made use of, which could never have been if their existence included a contradiction in it:-I answer, that upon a thorough examination it will not be found that in any instance it is necessary to make use of or conceive _infinitesimal_ parts of _finite_ lines, or even quant.i.ties less than the _minimum sensibile_: nay, it will be evident this is never done, it being impossible. [(736) And whatever mathematicians may think of Fluxions, or the Differential Calculus, and the like, a little reflexion will shew them that, in working by those methods, they do not conceive or imagine lines or surfaces less than what are perceivable to sense. They may indeed call those little and almost insensible quant.i.ties Infinitesimals, or Infinitesimals of Infinitesimals, if they please. But at bottom this is all, they being in truth finite; nor does the solution of problems require the supposing any other. But this will be more clearly made out hereafter.]

133. By what we have hitherto said, it is plain that very numerous and important errors have taken their rise from those false Principles which were impugned in the foregoing parts of this Treatise; and the opposites of those erroneous tenets at the same time appear to be most fruitful Principles, from whence do flow innumerable consequences, highly advantageous to true philosophy as well as to religion. Particularly _Matter_, or _the absolute_(737)_ existence of corporeal objects_, hath been shewn to be that wherein the most avowed and pernicious enemies of all knowledge, whether human or divine, have ever placed their chief strength and confidence. And surely if by distinguis.h.i.+ng the real existence of unthinking things from their being perceived, and allowing them a subsistence of their own, out of the minds of spirits, no one thing is explained in nature, but on the contrary a great many inexplicable difficulties arise; if the supposition of Matter(738) is barely precarious, as not being grounded on so much as one single reason; if its consequences cannot endure the light of examination and free inquiry, but screen themselves under the dark and general pretence of _infinites being incomprehensible_; if withal the removal of _this_ Matter be not attended with the least evil consequence; if it be not even missed in the world, but everything as well, nay much easier conceived without it; if, lastly, both Sceptics and Atheists are for ever silenced upon supposing only spirits and ideas, and this scheme of things is perfectly agreeable both to Reason and Religion: methinks we may expect it should be admitted and firmly embraced, though it were proposed only as an _hypothesis_, and the existence of Matter had been allowed possible; which yet I think we have evidently demonstrated that it is not.

134. True it is that, in consequence of the foregoing Principles, several disputes and speculations which are esteemed no mean parts of learning are rejected as useless [(739) and in effect conversant about nothing at all].

But how great a prejudice soever against our notions this may give to those who have already been deeply engaged, and made large advances in studies of that nature, yet by others we hope it will not be thought any just ground of dislike to the principles and tenets herein laid down, that they abridge the labour of study, and make human sciences more clear, compendious, and attainable than they were before.

135. Having despatched what we intended to say concerning the knowledge of _ideas_, the method we proposed leads us in the next place to treat of _spirits_(740): with regard to which, perhaps, human knowledge is not so deficient as is vulgarly imagined. The great reason that is a.s.signed for our being thought ignorant of the nature of Spirits is our not having an _idea_ of it. But, surely it ought not to be looked on as a defect in a human understanding that it does not perceive the idea of Spirit, if it is manifestly impossible there should be any such idea. And this if I mistake not has been demonstrated in section 27. To which I shall here add that a Spirit has been shewn to be the only substance or support wherein unthinking beings or ideas can exist: but that this _substance_ which supports or perceives ideas should itself be an idea, or like an idea, is evidently absurd.

136. It will perhaps be said that we want a _sense_ (as some have imagined(741)) proper to know substances withal; which, if we had, we might know our own soul as we do a triangle. To this I answer, that in case we had a new sense bestowed upon us, we could only receive thereby some new _sensations_ or _ideas of sense_. But I believe n.o.body will say that what he means by the terms _soul_ and _substance_ is only some particular sort of idea or sensation. We may therefore infer that, all things duly considered, it is not more reasonable to think our faculties defective, in that they do not furnish us with an _idea_ of Spirit, or active thinking substance, than it would be if we should blame them for not being able to comprehend a _round square_(742).

137. From the opinion that Spirits are to be known after the manner of an idea or sensation have risen many absurd and heterodox tenets, and much scepticism about the nature of the soul. It is even probable that this opinion may have produced a doubt in some whether they had any soul at all distinct from their body; since upon inquiry they could not find they had an idea of it. That an _idea_, which is inactive, and the existence whereof consists in being perceived, should be the image or likeness of an agent subsisting by itself, seems to need no other refutation than barely attending to what is meant by those words. But perhaps you will say that though an idea cannot resemble a Spirit in its thinking, acting, or subsisting by itself, yet it may in some other respects; and it is not necessary that an idea or image be in all respects like the original.

138. I answer, If it does not in those mentioned, it is impossible it should represent it in any other thing. Do but leave out the power of willing, thinking, and perceiving ideas, and there remains nothing else wherein the idea can be like a spirit. For, by the word _spirit_ we mean only that which thinks, wills, and perceives; this, and this alone, const.i.tutes the signification of that term. If therefore it is impossible that any degree of those powers should be represented in an idea [(743)or notion], it is evident there can be no idea [or notion] of a Spirit.

139. But it will be objected that, if there is no _idea_ signified by the terms _soul_, _spirit_, and _substance_, they are wholly insignificant, or have no meaning in them. I answer, those words do mean or signify a real thing; which is neither an idea nor like an idea, but that which perceives ideas, and wills, and reasons about them. What I am _myself_, that which I denote by the term _I_, is the same with what is meant by _soul_, or _spiritual substance_. [(744)But if I should say that _I_ was nothing, or that _I_ was an _idea_ or _notion_, nothing could be more evidently absurd than either of these propositions.] If it be said that this is only quarrelling at a word, and that, since the immediate significations of other names are by common consent called _ideas_, no reason can be a.s.signed why that which is signified by the name _spirit_ or _soul_ may not partake in the same appellation. I answer, all the unthinking objects of the mind agree in that they are entirely pa.s.sive, and their existence consists only in being perceived: whereas a _soul_ or _spirit_ is an active being, whose existence consists, not in being perceived, but in perceiving ideas and thinking(745). It is therefore necessary, in order to prevent equivocation and confounding natures perfectly disagreeing and unlike, that we distinguish between _spirit_ and _idea_. See sect. 27.

140. In a large sense indeed, we may be said to have an idea [(746)or rather a notion] of _spirit_. That is, we understand the meaning of the word, otherwise we could not affirm or deny anything of it. Moreover, as we conceive the ideas that are in the minds of other spirits by means of our own, which we suppose to be resemblances of them, so we know other spirits by means of our own soul: which in that sense is the image or idea of them; it having a like respect to other spirits that blueness or heat by me perceived has to those ideas perceived by another(747).

141. [(748)The natural immortality of the soul is a necessary consequence of the foregoing doctrine. But before we attempt to prove this, it is fit that we explain the meaning of that tenet.] It must not be supposed that they who a.s.sert the natural immortality of the soul(749) are of opinion that it is absolutely incapable of annihilation even by the infinite power of the Creator who first gave it being, but only that it is not liable to be broken or dissolved by the ordinary laws of nature or motion They indeed who hold the soul of man to be only a thin vital flame, or system of animal spirits, make it peris.h.i.+ng and corruptible as the body; since there is nothing more easily dissipated than such a being, which it is naturally impossible should survive the ruin of the tabernacle wherein it is inclosed. And this notion hath been greedily embraced and cherished by the worst part of mankind, as the most effectual antidote against all impressions of virtue and religion. But it hath been made evident that bodies, of what frame or texture soever, are barely pa.s.sive ideas in the mind, which is more distant and heterogeneous from them than light is from darkness(750). We have shewn that the soul is indivisible, incorporeal, unextended; and it is consequently incorruptible. Nothing can be plainer than that the motions, changes, decays, and dissolutions which we hourly see befal natural bodies (and which is what we mean by the _course of nature_) cannot possibly affect an active, simple, uncompounded substance: such a being therefore is indissoluble by the force of nature; that is to say, _the soul of man_ is _naturally immortal_(751).