Part 32

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, assert 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 quantity 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 quantity? 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 astonishing 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 amusements, 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 quantities 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 quantities 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 distinguishing 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 assigned 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 nobody 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, constitutes 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 assigned 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 passive, 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 assert 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 perishing 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 passive 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).

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

142. After what has been said, it is, I suppose, plain that our souls are not to be known in the same manner as senseless, inactive objects, or by way of _idea_. _Spirits_ and _ideas_ are things so wholly different, that when we say “they exist,” “they are known,” or the like, these words must not be thought to signify anything common to both natures(752). There is nothing alike or common in them; and to expect that by any multiplication or enlargement of our faculties, we may be enabled to know a spirit as we do a triangle, seems as absurd as if we should hope to _see a sound_. This is inculcated because I imagine it may be of moment towards clearing several important questions, and preventing some very dangerous errors concerning the nature of the soul.

[(753)We may not, I think, strictly be said to have an _idea_ of an active being, or of an action; although we may be said to have a _notion_ of them. I have some knowledge or notion of _my mind_, and its acts about ideas; inasmuch as I know or understand what is meant by these words. What I know, that I have some notion of. I will not say that the terms _idea_ and _notion_ may not be used convertibly, if the world will have it so. But yet it conduceth to clearness and propriety, that we distinguish things very different by different names. It is also to be remarked that, all _relations_ including an act of the mind(754), we cannot so properly be said to have an idea, but rather a notion, of the relations and habitudes between things. But if, in the modern way(755), the word _idea_ is extended to _spirits_, and _relations_, and _acts_, this is, after all, an affair of verbal concern.]

143. It will not be amiss to add, that the doctrine of _abstract ideas_ has had no small share in rendering those sciences intricate and obscure which are particularly conversant about spiritual things. Men have imagined they could frame abstract notions of the _powers_ and _acts_ of the mind, and consider them prescinded as well from the mind or spirit itself, as from their respective objects and effects. Hence a great number of dark and ambiguous terms, presumed to stand for abstract notions, have been introduced into metaphysics and morality; and from these have grown infinite distractions and disputes amongst the learned(756).

144. But, nothing seems more to have contributed towards engaging men in controversies and mistakes with regard to the nature and operations of the mind, than the being used to speak of those things in terms borrowed from sensible ideas. For example, the will is termed the _motion_ of the soul: this infuses a belief that the mind of man is as a ball in motion, impelled and determined by the objects of sense, as necessarily as that is by the stroke of a racket. Hence arise endless scruples and errors of dangerous consequence in morality. All which, I doubt not, may be cleared, and truth appear plain, uniform, and consistent, could but philosophers be prevailed on to [(757)depart from some received prejudices and modes of speech, and] retire into themselves, and attentively consider their own meaning. [(758)But the difficulties arising on this head demand a more particular disquisition than suits with the design of this treatise.]

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

145. From what hath been said, it is plain that we cannot know the existence of _other spirits_ otherwise than by their operations, or the ideas by them, excited in us. I perceive several motions, changes, and combinations of ideas, that inform me there are certain particular agents, like myself, which accompany them, and concur in their production. Hence, the knowledge I have of other spirits is not immediate, as is the knowledge of my ideas; but depending on the intervention of ideas, by me referred to agents or spirits distinct from myself, as effects or concomitant signs(759).

146. But, though there be some things which convince us human agents are concerned in producing them, yet it is evident to every one that those things which are called the Works of Nature, that is, the far greater part of the ideas or sensations perceived by us, are _not_ produced by, or dependent on, the wills of _men_. There is therefore some other Spirit that causes them; since it is repugnant(760) that they should subsist by themselves. See sect. 29. But, if we attentively consider the constant regularity, order, and concatenation of natural things, the surprising magnificence, beauty and perfection of the larger, and the exquisite contrivance of the smaller parts of the creation, together with the exact harmony and correspondence of the whole, but above all the never-enough-admired laws of pain and pleasure, and the instincts or natural inclinations, appetites, and passions of animals;—I say if we consider all these things, and at the same time attend to the meaning and import of the attributes One, Eternal, Infinitely Wise, Good, and Perfect, we shall clearly perceive that they belong to the aforesaid Spirit, “who works all in all” and “by whom all things consist.”

147. Hence, it is evident that God is known as certainly and immediately as any other mind or spirit whatsoever, distinct from ourselves. We may even assert that the existence of God is far more evidently perceived than the existence of men; because the effects of Nature are infinitely more numerous and considerable than those ascribed to human agents. There is not any one mark that denotes a man, or effect produced by him, which does not more strongly evince the being of that Spirit who is the Author of Nature(761). For it is evident that, in affecting other persons, the will of man hath no other object than barely the motion of the limbs of his body; but that such a motion should be attended by, or excite any idea in the mind of another, depends wholly on the will of the Creator. He alone it is who, “upholding all things by the word of His power,” maintains that intercourse between spirits whereby they are able to perceive the existence of each other(762). And yet this pure and clear Light which enlightens everyone is itself invisible [(763)to the greatest part of mankind].

148. It seems to be a general pretence of the unthinking herd that they cannot _see_ God. Could we but see Him, say they, as we see a man, we should believe that He is, and believing obey His commands. But alas, we need only open our eyes to see the Sovereign Lord of all things, with a _more_ full and clear view than we do any one of our fellow-creatures. Not that I imagine we see God (as some will have it) by a direct and immediate view; or see corporeal things, not by themselves, but by seeing that which represents them in the essence of God; which doctrine is, I must confess, to me incomprehensible(764). But I shall explain my meaning. A human spirit or person is not perceived by sense, as not being an idea. When therefore we see the colour, size, figure, and motions of a man, we perceive only certain sensations or ideas excited in our own minds; and these being exhibited to our view in sundry distinct collections, serve to mark out unto us the existence of finite and created spirits like ourselves. Hence it is plain we do not see a man, if by _man_ is meant, that which lives, moves, perceives, and thinks as we do: but only such a certain collection of ideas, as directs us to think there is a distinct principle of thought and motion, like to ourselves, accompanying and represented by it. And after the same manner we see God: all the difference is that, whereas some one finite and narrow assemblage of ideas denotes a particular human mind, whithersoever we direct our view we do at all times and in all places perceive manifest tokens of the Divinity: everything we see, hear, feel, or anywise perceive by sense, being a sign or effect of the power of God; as is our perception of those very motions which are produced by men(765).

149. It is therefore plain that nothing can be more evident to any one that is capable of the least reflexion than the existence of God, or a Spirit who is intimately present to our minds, producing in them all that variety of ideas or sensations which continually affect us, on whom we have an absolute and entire dependence, in short “in whom we live, and move, and have our being.” That the discovery of this great truth, which lies so near and obvious to the mind, should be attained to by the reason of so very few, is a sad instance of the stupidity and inattention of men, who, though they are surrounded with such clear manifestations of the Deity, are yet so little affected by them that they seem, as it were, blinded with excess of light(766).