MOTION.

(Arguments of Zeno against the existence of.)

Some objections of Zeno against the existence of motion, are preserved in Aristotle’s works. Read Aristotle’s Physics, In the ninth chapter of the sixth book. ⁹² where you will find four objections made by Zeno examined.

The first is: If an arrow, which tends towards a certain place, should move, it would move and rest at the same time. But that is a contradiction; therefore it doth not move. The consequence of the major is proved thus. The arrow is every moment in a space equal to itself. It is then at rest; for a thing is not in a space when it leaves it: wherefore there is no moment in which it moves; and if it moved in some moments, it would be at once in motion and at rest. To understand this objection the better, we must take notice of two principles which cannot be denied: one is, that a body cannot be in two places at once; the other, that two parts of time cannot exist together. The first of these two principles is so evident, even without making use of any attention, that I need not explain it: but as the other requires a little more reflection, in order to be understood, and comprehends the whole force of the objection, I will render it more obvious by an instance. I say then that what suits Monday and Tuesday with respect to succession, suits every portion of time whatsoever. Since then it is impossible for Monday and Tuesday to exist together, and that of necessity Monday must cease to be before

Tuesday begins to be, there is no paît of time whatsoever, which can co-exist with another; each must exist alone; each must begin to be, when the precedent ceaseth to be; and each must cease to be before the following can begin to exist, whence it follows, that time is not divisible in infinitum, and that the successive duration of things is composed of moments, properly so called, each of which is simple and indivisible, perfectly distinct from time past and future, and contains no more than the present time. Those who deny this consequence, must be given up to their stupidity, or their want of sincerity, or the insurmountable power of their prejudices. But if you once grant that the present time is indivisible, you will be unavoidably obliged to admit Zeno’s objection.. You cannot find an instant when the arrow leaves its place; for if you find one, it will be at the same time in that place, and yet not there. Aristotle contents himself with answering, that Zeno very falsely supposes the indivisibility of moments.

Zeno’s second objection was this: If there be motion, what moves must pass from one place to another; for all motion comprehends two extremities, “terminum à quo,” and “terminum ad quern,” the place from whence it departs, and that to which it comes. But these two extremities are separated by spaces which contain an infinity of parts, since matter is divisible in infinitum; it is therefore impossible for the body that is moved to proceed from one extremity to the other. The intermediate space is composed of an infinity of parts, through which it ought to run successively, one after the other, without ever being able to touch that which is before at the same time that it touches that which is behind; so that to run through one foot of matter, I mean, to reach from the beginning of the first inch to the end of the twelfth inch, an infinite time would be necessary; for the spaces, which it is successively obliged to run

through, betwixt the two extremities, being infinite in number, it is plain that they cannot be run through in less than an infinity of moments, unless it were pretended that the body which moves is in several places at the same time, which is false and impossible. To this Aristotle makes a wretched answer: he saith that a foot of matter being no otherwise than virtually infinite or infinite in power, may very well be run through in a finite time. I set down his answer with the perspicuity which the Conimbrian commentaries have given it. “Aristotle says that he has already answered this objection, having shewn in this book, that a body infinite in division, that is, not actually, but virtually so, may be run over in a finite time. For as time hath a continuity of parts, which are infinite in the same manner as the parts of body are infinite, time and body will answer to one another by the same laws of infinity, and in the same division of their parts. Nor is it against the nature of such infinite that body should be thus run over.”

You have here two particulars: That each part of time is divisible in infinitum; which is invincibly refuted above: That a body is only virtually infinite; which signifies that the infinity of a foot of matter, consists in this, that it may be divided without end into smaller parts, but not in its actually undergoing that division. To urge this, is to impose on the world; for if matter is divisible in infinitum, it actually contains an infinite number of parts, and is not therefore an infinite in power, but an infinite which really and actually exists. The continuity of parts hinders not their actual distinction; consequently their actual infinity depends not on the division; but subsists equally in a close quantity, and in that which is called discrete. But if we should grant this infinity in power, which by the actual division of its parts, would become an actual infinite, we should not lose any ground, for motion hath the same virtue as

division. It touches one part of the space without touching the other, and touches them all one after another; is not this actually to distinguish them? Is not this to do the very same thing which a geometrician performs on a table, when he draws lines which mark out all the half inches? He doth not break the table into half inches, but makes a division which expresses the actual distinction of parts; and I do not believe that Aristotle would have denied, that if an infinity of lines were drawn on an inch of matter, it would introduce a division which should reduce that to an actual infinity, which, according to him, was only virtually so. But what would be done with respect to the eyes, by drawing lines on an inch of matter, is certainly done with respect to the understanding by motion. This may be confirmed by what the geometricians say concerning the production of lines and surfaces. Clavius in Euclid, lib. i, num. 2, and 5. ⁹³ “The mathematicians, in order to give us a clear idea of a line, imagine a point to move from one place to another, for as a point is indivisible, that imaginary motion would leave a certain long trace without any breadth. The mathematicians in order to represent to us a surface, desire us to imagine any line moving across from one place to another, and the trace which that motion leaves, is a surface.” We conceive that a body which moves by successively touching the parts of space, determines them as effectually as the chalk in the hand; and besides, when it may be said that the division of an infinite is ended, is there not then an actual infinite? Do not Aristotle and his followers assert, that an hour contains an infinity of parts? Wherefore when it is past, it must be owned that an infinity of parts have actually existed one after another. Is this a virtual, and not an actual, infinity? Let us then say that this distinction is null, and that Zeno’s objection remains in full force. An hour, a year, or an age, &c. are each a finite time: a foot of matter is an infinite space; and therefore there is no body in motion that can ever reach from the beginning of a foot to the end of it. We shall see in the following remark, whether this objection may be eluded, by supposing that the parts of a foot of matter are not infinite. Let us content ourselves in this place with observing that the subterfuge of the infinity of the parts of time is of no service; for if there were in an hour an infinity of parts, it could never either begin or end. All its parts must exist separately; any two of them never do, nor can exist together: they must then be comprised between a first and last unity, which is incompatible with an infinite number.

The third objection was the famous argument called Achilles. Zeno of Elea was the inventor of it, if we believe Diogenes Laërtius, who tells us nevertheless that Phavorinus ascribed it to Parmenides, and to several others. This objection hath the same foundation with the second, but it is more adapted to the declamatory stile. It tends to shew that the swiftest body in motion pursuing the slowest, can never reach it. Suppose a tortoise to be twenty paces before Achilles, and limit the swiftness of the hero in proportion to that of the tortoise as one to twenty. Whilst he advances twenty paces, the tortoise advances one: she will then be before him still. Whilst he proceeds to the twenty-first pace, she will gain the twentieth part, she will go through the twentieth part of the twenty-first part, and so on. Aristotle refers us to what he says in answer to the second objection; and we may refer him to our reply. See also what shall be said in the following remark, concerning the difficulty of explaining wherein consists the swiftness of motion.

I proceed to the fourth objection, which shows the contradictions of motion. Suppose a table of four ells, and take also two bodies of the same measure,

one of wood, and the other of stone. Let the table be immoveably fixed, and bear the piece of wood according to the length of two ells westward, and suppose the piece of stone placed to the east, and only to touch the edge of the table. Suppose it to move on the table westward, and that in half an hour it goes the length of two ells; it will become contiguous to the piece of wood. Suppose that they touch one another only by their edges, and in such a manner that the motion of the one towards the west, doth not hinder the motion of the other to the east. At the moment of their contiguity, let the piece of wood begin to tend towards the east, whilst the other continues to tend towards the west; let them move with equal velocity. In half an hour, the piece of stone will finish its course all over the table; and so it will move through a space of four ells, the whole length of the table, in an hour. But the piece of wood will run through the same space of four ells in half an hour, by reason that it touched the whole extent of the piece of stone by the edges: therefore it is true that two bodies, moving with an equal swiftness, go through the same space, one in half an hour, and the other in an hour: and therefore an hour and half an hour are equal times; which is contradictory. Aristotle saith, that this is a sophism, since one of those moving bodies is considered in reference to a space which continues at rest, meaning the table, and the other with respect to a space in motion, meaning the piece of stone. I own he is in the right to observe that difference, but this doth not remove the difficulty; for a thing which seems incomprehensible, remains still to be explained; that is, that a piece of wood should at the same time move four ells on its south-side, and but two on its inferior surface.

But I will illustrate this with a clearer instance. Suppose two books in folio of equal length, as two feet each. Place them on a table, one before the other;

move them at the same time one above the other, one towards the east and the other towards the west, till the eastern edge of the one and the western edge of the other touch one another; and you will find that the edges by which they did touch one another, are now four feet distant from each other; and yet each of the books hath moved but the space of two feet. You may strengthen the objection by supposing whatsoever body you please in motion, in the midst of several others, which are moving several ways, and in various degrees of swiftness; you will find that the same body will in the same time run through several sorts of space, double, triple, &c. to one another; consider well of it, and you will find that this is only explicable by arithmetical calculations, which are only the idea of our mind; but that thing doth not seem practicable in the bodies themselves. The same difficulties may be raised from the small wheels of a coach, running over as much ground as the great ones, in the same number of rotations about their centre. The same thing may be said of a very small wheel and a very large one, fixed to one and the same axis. ⁹⁴ For we ought to remember these three essential properties of motion. 1. It is impossible for a body in motion to touch the same part of a space twice successively. 2. It never can touch two of them at once. 3. It never can touch the third before the second, nor the fourth before the third, &c. He who can physically reconcile these three particulars with the distance of four feet betwixt two bodies, which have run through no more than the space of two feet, must be no ignorant person. Observe, these three properties are as necessarily requisite to a body which goes over spaces, whose motion is contrary to its own, for instance, the two folio books above mentioned, as to one which passes through spaces where it meets with no resistance.

I am apt to think that those who would revive Zeno’s opinion, ought to argue thus.

There is no extension, therefore there is no motion. The consequence is good, for what hath no extension, fills no space, and what fills no space cannot possibly pass from one place to another, and consequently move. This is incontestible: the difficulty is then to prove that there is no extension. Zeno might have argued thus: extension cannot be composed either of mathematical points, or of atoms, or of parts divisible in infinitum; therefore its existence is impossible. The consequence seems certain, by reason it is impossible to conceive more than these three modes of composition in extension; wherefore the antecedent remains alone to be proved. A few words shall suffice as to mathematical points, for a man of the meanest capacity may apprehend with the utmost evidence, if he be but a little attentive, that several nothingnesses of extension joined together, will never make an extension. Consult the first body of scholastical philosophy that comes to hand, and you will there find the most convincing reasons, supported by many geometrical demonstrations, against the existence of these points. Wherefore, to say no more on that head, let us take it to be impossible, or at least inconceivable, that matter should be composed of them. Nor is it less impossible or inconceivable that it should be composed of the Epicurean atoms, that is, of extended and indivisible corpuscles; for every extension, how small soever, hath a right and left side, an upper and lower side: therefore it is a conjunction of distinct bodies; and I may deny of the right side what I affirm of the left, for these two sides are not in the same place. A body cannot be in two places at once; and consequently every extension which fills several parts of space contains several bodies. I know besides, and the anatomists do not deny it, that because two atoms are two beings, they are separable from one another; whence I conclude, with the utmost certainty, that since the right side of an atom is not the

same being with the left side, it is separable from the left; and therefore the indivisibility of an atom is merely chimerical. Whence it follows, that if there be an extension, its parts are divisible in infinitum. But, on the other side, if they cannot be divisible in infinitum, we ought to conclude the existence of extension impossible, or at least incomprehensible.

The divisibility in infinitum is an opinion embraced by Aristotle, and almost all the professors of philosophy, in all universities for several ages. Not that they understand it, or can answer the objections it is liable to; but because, having clearly apprehended the impossibility of either mathematical or physical points, they found no other course but this to take. Besides, this opinion affords great conveniencies; for when their distinctions are exhausted, without being able to render this doctrine comprehensible, they shelter themselves in the nature of the subject, and allege, that our understandings being limited, none ought to be surprised that they cannot resolve what relates to infinity, and that it is essential to such a continuity to be liable to such difficulties as are insurmountable by human reason. Observe that those who espouse the hypothesis of atoms, do not do it because they comprehend that an extended body may be simple, but because they believe the two other hypotheses to be impossible. We may say the same thing of those who admit of mathematical points. In general, all those who argue on extension, are determined in their choice of an hypothesis no otherwise than by the following principle: “If there be but three ways of explaining a subject, the truth of the third necessarily results from the falsity of the other two.” Whence they do not believe themselves mistaken in the choice of the third, when they are clearly convinced that the two others are impossible; and accordingly the impenetrable difficulties of the third do not stop them in the least: they comfort

themselves with this consideration, that they may be retorted; or with a persuasion that, after all, this hypothesis is true, because the other two are not so.

A Zenonist might tell those who choose one of these three hypotheses, you do not argue rightly; you make use of the disjunctive syllogism.

Matter is composed either of mathematical points, or physical points, or of parts divible in infinitum.

But it is not composed of. . . nor of. . . For brevity’s sake, I do not express the rejection or the admission: for according to the laws of Logic, one may proceed here from the rejection of any two parts whatsoever to the admission of the third. ⁹⁵

Therefore it is composed of.... The fault of your argumentation lies not in the form, but in the matter; you ought to lay aside your disjunctive syllogism, and make use of this hypothetical one.

If extension existed, it would be composed either of mathematical points, or of physical points, or of parts divisible in infinitum.

But it is not composed either of mathematical points or of physical points, or of parts divisible in infinitum.

Therefore it doth not exist.

There is no fault in the form of this syllogism; the sophism à non sufficienti enumeratione partium is not in the major; the consequence is therefore necessary, provided the minor be true. To be clearly satisfied of the truth of the minor, we need only consider the arguments which those three sects allege one against another, and compare them with their respective answers. When each of those three sects makes the attack, it overthrows, subdues, and triumphs; but when it is on the defensive, it is utterly overthrown and confounded in its turn. To be convinced of their weakness, it is enough to remember that the strongest of them, that which best disputes the ground, is the hypothesis of the divisibility in infinitum. The

school-men have armed it cap-à-pee with all the distinctions which their great leisure would allow them to invent; but all this only serves to afford their scholars matter for talk upon a public disputation, that their relations may not suffer the disgrace of seeing them mute. A father or a brother go away better satisfied, when the scholar distinguishes betwixt a categorematical infinite, and a syncategorematical one, betwixt the parts communicantes, et non communicantes, proportional and aliquot, than if he had answered nothing. It was therefore necessary for the professors to invent some jargon; but all the pains which they have taken, will never be able to obscure this notion which is as clear and evident as the sun; that an infinite number of parts of extension, each of which is extended, and distinct from all others, as well with respect to its entity, as with respect to the space it fills, cannot be contained in a space one hundred thousand millions of times less than the hundred thousandth part of a barley corn.

Here is another difficulty. An extended substance, if it did exist, must necessarily admit of an immediate contact of its parts. According to the hypothesis of a vacuum, several bodies would be separated from all others, but several others must immediately touch. Aristotle, who denied this hypothesis, is obliged to own that there is no part of extension which doth not immediately touch some other parts in all its exterior points. This is incompatible with the divisibility in infinitum; for if there be no body but what contains an infinity of parts, it is evident that each particular part of extension is separated from all others by an infinity of parts, and that the immediate contact of two parts is impossible. But when a thing cannot have whatever is absolutely necessary to its existence, it is certain that its existence is impossible: wherefore the existence of extension necessarily requiring the immediate contact of

its parts, and that immediate contact being impossible in an extension divisible in infinitum, it is evident that the existence of such an extension is impossible, and that this extension barely exists in the mind. What the mathematicians acknowledge with respect to lines and superficies, with which they demonstrate so many excellent things, must be owned to be true with respect to bodies. They honestly own, that length and breadth without depth, are things which cannot exist any where but in our imagination. Let us say the same thing of the three dimensions: they cannot subsist any where but in our minds; they cannot exist any other way than ideally. Our mind is a kind of ground, where a hundred thousand objects of different colours, figures, and situation unite: for from an eminence we may see at once a vast plain covered with houses, trees, and flocks, &c. Whilst it is so far from truth, that all these things can possibly be ranged in this plain, that there are not two which can find room there; each would require ’an infinite space, since it contains an infinity of extended bodies. There should be infinite intervals left round each one, by reason that there is an infinity of bodies betwixt each part, and every other part. Let it not be said that God can do every thing; for if the most religious divines venture to say, that in a right line of twelve inches, he cannot render the first and third inches immediately contiguous, I may very well say that he cannot make two parts of extension immediately touch one another, when an infinity of other parts separate them from one another. Let us therefore say that the contact of the parts of matter is only ideal; and that the extremities of several bodies no where unite but in our mind.

I shall now make a quite contrary objection. The penetration of dimension is impossible, and yet it would be inevitable, if extension should exist; therefore the existence of extension is impossible. Put a

cannon bullet upon a table, a bullet, I say, covered over with some liquid colour, make it roll upon the table, and it will trace out a line by its motion: you will then have two strong proofs of the immediate contact of the bullet and table. The weight of the bullet will shew you that it immediately touches the table; for if it did not touch it in this manner, it would remain suspended in the air, and your eyes will, besides, convince you of this contact by the track which the bullet hath left. Now I maintain that this contact is a penetration of dimensions properly so called. That part of the bullet which touches the table is a determinate body, and really distinct from the other parts of the bullet which do not touch the table. I affirm the same thing of that part of the table touched by the bullet. These two parts touched, are each of them infinitely divisible in length, breadth, and profundity; they must therefore mutually touch one another according to their profundity, and consequently they penetrate one another: This is every day objected to the peripatetics in their public disputes: they defend themselves by a jargon of distinctions, proper for no other use than preventing the displeasure of a scholar’s relations, if they should see him silenced; and as for the farther use of these distinctions they have never served to any other purpose than to make it appear that the objection is unanswerable. Here is therefore a very singular thing; if extension existed, it would not be possible for its parts to touch one another, and it would be impossible that they should not penetrate one another. Are not these most evident contradictions in the existence of extension?

Add to this, that all the ways of suspension which destroy the reality of corporeal qualities, overthrow the reality of extension. Since the same bodies are sweet to some men, and bitter to others, it may reasonably be inferred that they are neither sweet nor

bitter in their own nature, and absolutely speaking. The modern philosophers, though they are no sceptics, have so well apprehended the foundation of the epoch with relation to sounds, odours, heat, and cold, hardness, and softness, ponderosity, and lightness, savours, and colours, &c. that they teach that all these qualities are perceptions of our mind, and do not exist in the objects of our senses. Why should we not say the same thing of extension? If a being, void of colour, yet appears to us under a colour determined as to its species, figure, and situation, why cannot a being, without any extension, be visible to us, under an appearance of determinate extension, shaped, and situate in a certain manner? Observe also, that the same body appears to us little or great, round or square, according to the place whence we view it; and certainly, a body which seems to us very little, appears very great to a fly. It is not therefore by their proper, real, or absolute extension that objects present themselves to our mind: whence we may conclude, that in themselves they are not extended. Would you at this day argue thus: since certain bodies appear sweet to one man, sour to another, and bitter to another, &c. I affirm, that in general they are savoury, though I do not know the savour proper to them, absolutely, and in themselves? All the modern philosophers would explode you. Why then would you venture to say, since certain bodies appear great to this animal, middle sized to that, and very little to a third, I affirm, that in general they are extended, though I do not know their absolute extension? Let us see what a celebrated Dogmatist acknowledges: Nicolle, Art de penser, Part. iv. ch. i. pag. m. 387, 388. See also Rohault, Traité de Physique, Part. i. chap, xxvii. ⁹⁶ “It is clearly discernible by the senses, that such a body is larger than another; but we cannot certainly know what is the true and natural size of each body; to comprehend which we need only consider, that if all mankind had never seen external objects any otherwise than through magnifying glasses, it is certain that they would not have formed any other idea of bodies, and all the measures of body, than according to the size in which they had appeared to them through those glasses. But our eyes themselves are optic glasses, and we do not know exactly whether they diminish or increase the objects which we see, and whether those artificial glasses, which, as we believe, diminish or increase them, do not on the contrary restore them to their true magnitude; wherefore we do not certainly know the absolute and natural magnitude of each body. Neither do we know whether they appear of the same size in our eyes as in those of other men; for though two persons measure them, and agree that a certain body, for instance, is but five feet; yet what the one conceives to be a foot, differs perhaps from what the other takes to be so; for the one conceives what his eyes report to him, as doth the other also; but perhaps the eyes of the one do not report the same thing which the eyes of the other represent, because the optic glasses are differently made.” Father Malebranche, Malebranche, Recherche de la Vérité, livr. i. ch. vi. et seq. ⁹⁷ and Father Lami, Lami, Connoissance de soi-même, tom. ii. pag. 112, et seq. ⁹⁸ a Benedictine monk, will give you an excellent account of all these particulars, and one is capable of carrying my objection to a very great degree of strength.

My last difficulty shall be grounded on the geometrical demonstrations so subtly displayed, to prove that matter is divisible in infinitum. I maintain they serve for no other use than to make it appear that extension exists no where but in our minds.

In the first place I observe that some of these demonstrations are employed against those who affirm that matter is composed of mathematical points. It is objected to them that the sides of a square would be equal to the diagonal, and that amongst concentrical circles, the least would be equal to the largest. This consequence is proved by making it appear that the right lines which may be drawn from one of the sides of a square to another, will fill the diagonal, and that all the right lines which may be drawn from the circumference of the largest circle, will find room in the smallest circumference. These objections are not stronger against bodies being composed of points, than against their being divisible in infinitum; for if the parts of a certain extension are not more numerous in the diagonal line than in the sides, nor in the circumference of the largest circle than in that of the smallest concentric circle; it is clear that the sides of the square equal the diagonal, and that the smallest concentric circle equals the greatest. But all the right lines which can be drawn from one side of a square to another, and from the circumference of the largest circle to the centre, are equal to each other, they ought then to be considered as aliquot parts; that is, as parts of a certain magnitude, and of the same denomination. Now it is certain that two extensions, whereof the aliquot parts and of the same denomination, as inch, foot, pace, are in equal number, do not exceed one another, it is therefore certain that the sides of the square would be as large as the diagonal line, if the diagonal line cannot be intersected by more right lines than the sides. The same thing may be said of two concentric circles. In the second place I affirm, that it being very true that if circles did exist, as many right lines might be drawn from the circumference to the centre, as there are parts in the circumference, it follows that the existence of a circle is impossible. I am persuaded it will be allowed me that every being which cannot exist, without containing properties which cannot exist, is impossible; but a round extension cannot exist without having a centre in which there meet as many right lines as there are parts in the circumference, and it is certain that such a centre cannot exist; it must then be owned that the existence of this round extension is impossible; but that such a centre cannot exist, I shall clearly prove. Let us suppose a round extension whose circumference is four feet, it then contains forty-eight inches, each of which contains twelve lines; the circumference will then contain five hundred and seventy-six lines, which is the number of the right lines that may be drawn from the circumference to the centre. Let us trace a circle very near the centre; it may be so small that it will not contain above fifty lines; it cannot then give passage to five hundred and seventy-six right lines, therefore it will be impossible for these five hundred and seventy-six right lines begun to be drawn from the circumference of this round extension, to reach the centre; and yet if this extension exist, these five hundred and seventy-six lines must of necessity reach the centre. What remains then to be said, but only that this extension cannot exist, and that accordingly, all the properties of circles and squares, &c. are founded on lines without breadth, which cannot exist otherwise than ideally? Observe, that our reason and our eyes are equally deceived in this case. Our reason clearly conceives, first, that the concentric circle nearest the centre is less than the circle which encompasses it; and secondly, that the diagonal of a square is larger than the side. Our eyes see this without compasses, and more clearly with compasses; and yet the mathematicians teach us, that as many right lines may be drawn from the circumference to the centre as there are points in the circumference, and that from one side of a square to the other, as many right lines may be drawn as there are points in the side: and besides, our eyes shew us that there is not in the circumference of the small concentrical circle, any one point which is not a part of a right line drawn from the circumference of the great circle, and that the diagonal of the square contains no one point that is not a part of a right line drawn from one of the sides of the square to another. Whence then can it proceed that this diagonal is greater than the sides?

This is what relates to the first proof which I suppose Zeno might have made use of to refute the existence of motion. It is founded on the impossibility of the existence of extension. I am willing to believe that what he might have said in the last place, by making use of geometrical demonstrations, is easy to be refuted by the same means, but I am strongly convinced that the arguments taken from the mathematics to prove the divisibility in infinitum, prove too much: for either they prove nothing, or they prove an infinity of aliquot parts.

Zeno’s second objection might have been this: granting that there is an extension which is not merely ideal, but really exists, yet I say that it is immovable; motion is not essential to it, nor contained in the idea of it, and several bodies are sometimes in a state of rest. Motion is therefore an accident; but is it distinct from matter? If it be distinct, of what must it be produced? Doubtless of nothing; and when it ceases it will be reduced to nothing; but do not you know that nothing is made out of nothing, and that nothing returns to nothing: besides, must not motion necessarily be diffused on and through the body that is moved? The former will therefore be as much extended as the latter, and of the same figure; there will therefore be two equal extensions in the same space, and consequently a penetration of dimensions. But when three

or four causes move one body, must not each of them produce its motion? Must not these three or four motions be penetrated together, both with the body and amongst themselves? How then can each produce its effect? A vessel moved by the winds, tide, and rowers, describes a line which partakes more or less of these three actions, according as one of them is stronger than the others. Will you venture to affirm that insensible entities penetrated amongst themselves and with the whole vessel, will have such a regard for one another as not to thwart themselves? If you say that motion is a mode which is not distinct from matter, you must then allow that whatever produces it, creates matter; for without producing matter, it is impossible to produce a being which is the same thing with matter; but would it not be absurd to assert that the wind which moves the vessel, produces a vessel? It appears therefore that these objections cannot be otherwise answered than by supposing with the Cartesians, that God is the sole and immediate cause of motion.

Here is another objection. It is impossible to affirm what motion is, for if you say that it is to pass from one place to another, you explain one obscurity by a greater,—obscurium per obscurius. I immediately ask what you mean by the word place? Do you mean a space distinct from bodies? If so, you will involve yourself in a labyrinth from which you will never be able to get out. Do you mean by it the situation of a body among some others that surround it? but in this case you will define motion in such a manner, that it will a thousand and a thousand times suit with bodies that are at rest. It is certain that hitherto the true definition of motion hath not been found; that of Aristotle is absurd, and that of Des Cartes wretched. Mr Rohault, after much pains in endeavouring to find one which might rectify the notion of Des Cartes, produces a description which

may agree with bodies of which we conceive very distinctly they do not move at all, wherefore Mr Regis thought himself obliged to reject it; but that which he hath given is not capable of distinguishing motion from rest. God, the only mover according to the Cartesians, must do with respect to a house, the same thing as with respect to the air which flies from it in a high wind: he must create the air every moment with new local relations with respect to that house, and he must also every moment create that house with new local relations with respect to that air. And certainly according to the principles of these gentlemen, no body is at rest if an inch of matter is in motion: all then that they say centers in explaining apparent motion, that is, explaining those circumstances which make us judge that one body moves and another doth not; but all this is useless labour; every one is capable of judging of appearances. The question is, to explain the very nature of things which exist independently of our minds; and since in that respect motion is inexplicable, we may as well say that it exists only in our minds.

I shall now offer an objection much stronger than the foregoing. If motion can never begin, it doth not exist, but it is impossible for it ever to begin; therefore, &c. I prove the minor thus. It is impossible for a body to be in two places at once, but it could never begin to move without being in an infinity of places at once; for though it advance ever so slowly, it would touch a part divisible in infinitum, and which consequently corresponds with infinite parts of space; therefore, &c. Besides, it is certain that an infinite number of parts doth not contain any which is first; and yet a body in motion can never touch the second before the first; for motion is a being essentially successive, of which two parts cannot exist together, wherefore motion can never begin if matter is divisible in infinitum, as doubtless it is if

it exist. The same reason demonstrates that a body in motion, rolling on a sloping table, could never fall off the said table, for before it falls it must of necessity touch the last part of the table; and how will it touch that, since all those parts which you will pretend to be the last, contain an infinity of parts, and an infinite number hath no part which can be last? This objection obliged some scholastic philosophers to suppose that nature hath intermixed mathematical points with the parts divisible in infinitum, to the end that they may. serve to connect them, and compose the extremities of bodies. They thought by that means to answer also the objection of the penetrative contact of two surfaces; but this evasion is so absurd, that it doth not deserve to be refuted.

I shall not much insist on the impossibility of circular motion, though that would supply me with a strong objection. I say only in one word, that if there were a circular motion, there would be a whole diameter at rest, whilst all the remainder of the globe moved very swiftly. But conceive this if you can in matter. The Chevalier de Meré did not forget this objection in his letter to Mr Pascal on the futility of the mathematics.

Lastly, I say that if motion existed, it would be equal in all bodies; there would be no Achilles’s nor tortoises; the hound would never reach the hare. Zeno objected this; but it seems he went only upon the divisibility of matter in infinitum; and perhaps, some will say, he would set aside that objection, if he had dealt with adversaries who admitted either mathematical points or atoms. I answer, that this objection equally strikes at all the three systems: for suppose a road composed of indivisible particles; place the tortoise in it one hundred points before Achilles, and if she go on, he will never reach her: Achilles will go but one point every moment, since if he went two he would be in two places at the same

time. The tortoise will also advance one point each moment; which is the least she can do, nothing being less than a point. The true reason of the swiftness of motion is inexplicable: the most happy thought on this head is, that no motion is continued, and that all those bodies which seem to us to move, stop by intervals. That which moves ten times faster than another, rests ten times to the other’s hundred; but however well contrived this subterfuge appears, it is of no use; it is confuted by several solid reasons which you may see in all the bodies of philosophy. I content myself with that which is drawn from the motion of a wheel: you may make a wheel of so large a diameter that the part of the spokes the farthest distant from the center will move one hundred times swifter than the part fixed in the nave. And yet the spokes remain always straight: an evident proof that the lower part doth not rest, whilst the upper moves. The divisibility in infinitum of the particles of time, rejected above as visibly false and contradictory, is of no force against this sixth argument. You will find some other very subtle objections in Sextus Empiricus.

It is not likely that Zeno forgot the objections which may be grounded on the distinction of a plenum and a vacuum. Melissus, who studied under the same master with him, denied motion, and made use of this proof: If motion exist, there must of necessity be a vacuum, but there is no vacuum, therefore, &c. This shews that in Zeno’s time there was a great philosopher, who did not believe motion and a plenum to be consistent together. Wherefore since Zeno denied a vacuum, I cannot persuade myself that he did not make use of the same proof with Melissus, against those who admitted motion. He made it his business to oppose them, and used several arguments for that purpose. Would he have forgotten the argument which the asserters of a vacuum have so often

employed? He might have turned it otherwise than they, but not less speciously. If there were no vacuum, said they, there would be no motion; but motion exists, therefore there is a vacuum. He would have argued on the contrary foot, agreeing with them in this principle, that motion cannot exist in a full space; for, from this position, common to them and himself, he might have drawn a consequence diametrically opposite to theirs. His syllogism ought to have run thus: if there were any motion, there would be a vacuum; but there is no vacuum, therefore there is no motion. Observe, that when I say his manner of arguing would not have been less specious than theirs; I mean this only with respect to philosophers capable of comprehending the reasons against a vacuum; for I know very well that to common minds it is almost as strange a paradox to deny a vacuum, as to deny motion. Anaxagoras found the vulgar so possessed with the existence of a vacuum, that he had recourse to some trivial experiments to destroy this false prejudice. Aristotle, in the chapter where he mentions this, alleges some of the arguments which were made use of to prove a vacuum: they are not of any force, and he refutes them pretty well in the following chapter. Gassendus hath given all possible force to the experiments and arguments which favour the hypothesis of Epicurus concerning a vacuum; but he hath said nothing really convincing, and the weakness of it is fully exposed in the Art of Thinking. However, I believe that Zeno rendered himself formidable on this topic: such a subtle and vehement logician as he, could very dexterously perplex this subject, and it is not probable that he neglected it.

But if he had known what several excellent mathematicians say in this age, he might have made vast ravages, and given himself airs of triumph. They assert that a vacuum is absolutely necessary, and that without it the motion of the planets, and the

consequences thereof are things inexplicable and impossible. I have heard a great mathematician (who hath reaped great advantages from the works and conversation of Sir Isaac Newton) say, that it is no longer a problem “whether motion be possible, supposing a plenum that the falsity and impossibility of that proposition hath been not only proved, but mathematically demonstrated, and that henceforth to deny a vacuum will be to deny a point supported by the utmost evidence. He maintained that vacuity takes up incomparably more room than matter in the most ponderous bodies; so that in the air, for instance, there are not more corpuscles than there are great cities on earth. Thus we are doubtless highly obliged to the mathematics: they demonstrate the existence of what is contrary to the most evident notions of our intellect; for if there be any nature with whose essential properties we are clearly acquainted, it is extension: we have a clear and distinct idea of it, which informs us that the essence of extension consists in the three dimensions, and that its inseparable attributes and properties are divisibility, mobility, and impenetrability. If these ideas be false, deceitful, chimerical, and illusory, is there a notion in our mind which we ought not to take for a vain phantom, or matter of distrust? Can the demonstrations which prove a vacuum remove our distrust? Are they more evident than the idea which shews us that a foot of extension may change its place, and cannot be in the same place with another foot of extension? Let us search as much as we please into all the recesses of our mind, we shall never find there any idea of an immovable, indivisible, and penetrable extension. And yet if there be a vacuum, there must exist an extension, essentially endued with these three attributes. It is no small difficulty, to be forced to admit the existence of a nature of which we have no idea, and is besides repugnant to the clearest ideas of our mind.

But there are a great many other difficulties, —is this vacuum, or immovable, indivisible, and penetrable extension, a substance, or a mode? It must be one of the two, for the adequate division of being, comprehends only these two members. If it be a mode, they must then define its substance; but that is what they can never do. If it be a substance, I ask whether it be created or uncreated? If created, it may perish, while the matter, from which it is really distinct, may not cease to be. But it is absurd, and contradictory, that a vacuum, or a space distinct from bodies, should be destroyed, and yet that bodies should remain distant from each other, after the destruction of the vacuum. If this space distinct from bodies is an uncreated substance, it will follow either that it is God, or that God is not the only substance which necessarily exists. Which part soever you take of this alternative, you will find yourself confounded: the last is a formal, and the other at least a material impiety; for all extension is composed of distinct parts, and consequently separable from each other; whence it results, that if God were extended, he would not be a simple, immutable, and properly infinite being, but a collection of beings, “ens per aggregationem,” each of which would be finite, though all of them together would be unlimited. He would be like the material world, which, in the Cartesian hypothesis, is an infinite extension. And as to those who should pretend that God may be extended without being material or corporeal, and allege, as an argument, his simplicity, you will find them solidly refuted in one of Mr Arnauld’s books: I shall cite only these words from it: “So far is the simplicity of God from allowing us room to think that he may be extended, that all divines have acknowledged after St Thomas, that it is a necessary consequence of the simplicity of God not to be capable of being extended.” Will they say with the

schoolmen, that space is, at most, no more than a privation of body; that it hath no reality, and that properly speaking, a vacuum is nothing? This is so unreasonable an assertion, that all the modern philosophers who declare for a vacuum, have laid it aside, however convenient it was in other respects. Gassendus carefully avoided having recourse to so absurd an hypothesis, and chose rather to plunge himself into the most hideous abyss of conjecturing, that all beings are not either substances or accidents, and that all substances are not either spirits or bodies; and of placing the extension of space amongst the beings which are neither corporeal nor spiritual, neither substances nor accidents. Mr Locke, believing that he could not define what a vacuum is, hath yet given us clearly to understand that he took it for a positive being. He was too knowing not to discern that nothingness cannot be extended in length, breadth, and thickness. Mr Hartsoeker hath very well apprehended this truth. “There is no vacuum in nature saith he, “this ought to be admitted without any difficulty, because it is utterly contradictory to conceive a mere nothingness, with all the properties which can only agree to a real being.” But if it be contradictory that nothingness should be endued with extension, or any other quality, it is not less contradictory, that extension should be a simple being, since it contains some things, of which we may truly deny what we may truly affirm of some others which it includes. The space filled up by the sun is not the same space taken up by the moon; for if the sun and the moon filled the same space, those two luminaries would be in the same place, and penetrated with one another, since two things cannot be penetrated with a third, without being penetrated among themselves. It is most evident that the sun and moon are not in the same place. It may then be truly said of the space of the sun, that it is penetrated with the suit, which may as truly be denied of the space penetrated with the moon: here are then two portions of space really distinct from one another, since they receive two contradictory denominations, of being penetrated, and not being penetrated with the sun. This fully confutes those who venture to assert, that space is nothing but the immensity of God; and it is certain that the divine immensity could not be the place of bodies, without giving room to conclude that it is composed of as many parts really distinct, as there are bodies in the world. It will be in vain for you to allege that infinity hath no parts; this must necessarily be false in all infinite numbers, since a number essentially includes several unities: nor will you have more reason to tell us, that incorporeal extension is wholly contained in its space, and also wholly contained in each part of its space; for not only we have no idea of it, and it thwarts all our ideas of extension, but besides it will prove that all bodies take up the same place, since each could not take up its own, if the Divine extension were entirely penetrated with each body, numerically the same with the sun, and with the earth. You will find in Mr Arnauld a solid refutation of those who say that God is diffused throughout infinite space.

By this specimen of the difficulties which may be raised against a vacuum, my readers may easily apprehend, that our Zeno would, at this present time, be much more formidable than he was in his own age. It is no longer to be doubted, would he say, that if all is full, motion is impossible. This impossibility hath been mathematically proved. He would be far from disputing against those demonstrations, but admit them as incontestable; he would solely apply himself to prove the impossibility of a vacuum, and would reduce his adversaries to an absurdity. He would confute them on whatsoever side they turned; he would plunge them into perplexities by his dilemmas; he would make them lose ground wherever

they retired; and if he did not silence them, he would at least force them to confess, that they neither understand nor comprehend what they say. “If any one ask me (they are Mr Locke’s words), what this space I speak of, is? I will tell him when he tells me what his extension is. They ask whether this space be body or spirit? To which I answer by another question, Who told you that there can be only bodies and minds? If it be asked, (as usually it is) whether this space, void of body, be substance or accident, I shall readily answer, I know not: nor shall I be ashamed to own my ignorance, till they who ask that question, shew me a clear, distinct idea of substance.” Since so great a metaphysician as Mr Locke, after having so well studied this subject, is not able to answer the questions of the Cartesians, otherwise than by asking other questions which he thinks yet more obscure and perplexed than theirs, we may judge that the objections which Zeno might propose, could not be answered; and we may certainly conjecture that he would speak thus to his adversaries: You shelter yourselves in the hypothesis of a vacuum when you are driven from that of motion and a plenum; but you cannot hold out in this hypothesis, as the impossibility of it is demonstrated. Learn some better way to come off; for by that which you have already chosen you avoid one precipice, and throw yourselves into another. Follow me, I will shew you a better way: do not conclude, from the impossibility of motion in a plenum, that there is a vacuum, but rather conclude, from the impossibility of a vacuum, that there is no motion, I mean real motion, but at most an appearance of motion, or an ideal and intellectual motion.

Thus, or in a manner very like it, we may suppose our Zeno of Elea to have argued against motion. I will not affirm that his reasons persuaded him that nothing moved; he might be of another opinion, though he believed that none could refute them, nor

elude their force. If I should judge of him by myself, I should affirm that he as well as other men believed the motion of matter; for though I find myself very incapable of solving all the difficulties which we have just now seen, and though the philosophical answers which may be made to them do not seem to me very solid, yet that does not hinder me from following the common opinion. Nay, I am persuaded that the proposing of these arguments may be of great use with respect to religion; and I say here with regard to the difficulties of motion, what M. Nicolle said of those of the divisibility in infinitum. “The advantage which may be drawn from these speculations is not merely to acquire this sort of knowledge, which in itself is very barren; but to learn to know the limits of our understanding, and to force it however unwilling to own that some things exist, though it is not capable of comprehending them: for which reason it is proper to fatigue the intellect with these subtilties, in order to subdue its presumption, and deprive it of the assurance of ever opposing its faint light to the truths which the church proposes, under pretext that it cannot comprehend them: for since all the force of human understanding cannot comprehend the smallest atom of matter, and is obliged to own that it clearly sees that such an atom is infinitely divisible, without being able to conceive how that can be, is it not plain that the man acts against reason, who refuses to believe the wonderful effects of God’s omnipotence, which is of itself incomprehensible, because our minds cannot comprehend these effects.”—Art. Zeno. The above conclusion from Nicolle is one of the peace offerings which it is usual for Bayle to present to authority when he has been doing his best to undermine it. These arguments against the existence of motion, have been selected in order to afford a curious example of the intellectual subtilty which Harris of Salisbury, and others, would have us restore, as the only genuine philosophy.—Ed. ⁹⁹