Refutation of Certain Doctrines of Aristotle 30–51

From the same book: “And place is somewhere, not as in a place, … but as the limit is in the limited. For not [every] being is in place, but the movable body.” If everything in place is somewhere, but not everything somewhere is in place, then “somewhere” is wider than “in place.” How then are “somewhere” and “in place” said to belong to one category, when they differ so much from each other that he says that place is somewhere but not in place? And if the limit of the limited is the place of one limited thing and the limit of another, how is it not necessary that place always be both place and limit? And if place is prior to the things in place, how is the necessity not removed that place always be the place of one thing and the limit of another? And if what in no way is is not in place (for it would be somewhere, as he said), how is “somewhere” not the same as “in place”? And if not every being is in place, how will some beings not be the same as what is not, since not being in place is common to both? And if only the movable body is in place, how is the heaven, being a movable body, not in place?

From the same book, On time: “That it either does not exist at all, or barely and obscurely, one might suspect from the following. Part of it has been and is not, part is going to be and is not yet; and of these both infinite time and time as it is taken at any moment are composed. What is composed of things that are not would seem impossible to share in substance. Further, of every divisible thing, if it exists, it is necessary that, when it exists, either some or all of its parts exist. But of time some parts have been, some are going to be, and none is, though it is divisible. The now is not a part; for a part measures, and the whole must be composed of the parts; but time does not seem to be composed of nows.” If everything that comes to be did not exist before it came to be, then time is not eternal and without beginning; and therefore neither is motion eternal and without beginning, of which time is the number. For if the future part of time is not yet … before it came to be it was future; there was, then, a time when the past part of time was not. And if the infinite must be without beginning, then time is not infinite, since it has as the beginning of its being the change from what is future. And if the past part of time is time in actuality, and the future in potentiality, and actuality and potentiality are among the things that are, then time, composed of the past and the future, is not composed of things that are not. And if time does not share in substance, yet it does share in being attached to substances; so that from this too it is evident that time is among the things that are. And if the past part of time is seen in the past parts of what is divisible, how is no part of time [present], though it is divisible? And if the now is not … what is called the indivisible and the point of time? How is it possible for the change to come about from the future into the now, and from the now into the past, if the now is not a part of time? For all are parts of time: the first, the future, the later, the now, …

From the same fourth book of the same treatise: “That time, then, is neither motion nor without motion, is evident.” But it is evident too that time is generated and not eternal, has a beginning and is not without beginning, is finite and not infinite. And if time is such, so necessarily is motion, of which time is the number.

From the same book: “For as much as the motion is, so much time always seems to have passed.” From the things to which being generated and having come to be belong, being eternal, being without beginning, and being infinite are necessarily absent.

“We say that time has passed when we perceive the before and after in motion. We distinguish them by taking them to be one thing and another, and something between them different from them. For when we think of the extremes as different from the middle, and the soul says that the nows are two, one before and the other after, then we say this … seems to be [time]. For time is the number of motion with respect to before and after. Time, then, is not motion, but that by which motion has number. A sign of this: we judge more and less by number, and more and less motion by time.” He who defines the coming to be of time by the before and after in motion calls neither time nor motion eternal, without beginning, and infinite. For if it has come to be, it is neither eternal nor without beginning; and if it is bounded by its own extremes, it is not infinite.

From the same: “The now measures time as before and after; and motion follows magnitude, and time follows motion.” If the now is not a part of time, as he said in the thirty-third chapter, how does it measure time? Either the now does not measure time, or it must itself be a part of time. And if motion follows magnitude, and time follows motion, then magnitude is generated, like motion and time, which follow it.

“The least number in multitude is two or one, but in magnitude there is no least; for the least in number is one or two, but in magnitude there is none.” If the point in the line and the now in time are not least parts, what else is the point in the line and the now in time? And if it is not a least part but a limit, how is it that the limit cannot be without the limited, but the point can be without the line? And if where there is no least there is no greatest either, in what does the remaining difference of the parts consist, when the difference of greatest and least is abolished?

From the same: “So it is evident that the things that always are, or always are not, are not in time; for they are not contained by time, nor is their being measured by time.” How then have you said that motion is eternal, and time its number? For the things from which time is inseparable cannot fail to be in time.

From the same: “Whatever neither moves nor rests is not in time; for being in time is being measured by time, and time is the measure of motion and rest.” If what is in time moves and rests, and the heaven moves, according to the speaker, and the earth rests, then the heaven and the earth, and their motion and rest, are in time. And if time is generated, necessarily [so are they].

From the fifth book of the same treatise: “So that necessarily, from what has been said, there are three changes … the one from a subject to a non-subject, and the one from a non-subject to a subject. For the change from non-subject to non-subject is not a change, because it is not by opposition; for there are neither contraries nor contradiction. The change from non-subject to subject, by contradiction, is generation; that from subject to non-subject is perishing.” Matter, then, is nowhere — the matter you said above underlies the things that come to be and perish, for the one as that from which, for the other as that into which.

From the same book: “For what is not white or not good can nevertheless be moved accidentally, for the not-white might be a man; but what is simply not a ‘this’ in no way; for it is impossible for what is not to be moved.” If substance cannot come to be from what is not moved, and what is simply not a “this” is in no way moved (for it is impossible for what is not to be moved), how has substance, simply, come to be from matter, which is not a “this”?

From the ninth book of the same treatise: “If it is impossible for time to be or to be thought without the now, and the now is a kind of middle, having both a beginning and an end, a beginning of time to come and an end of time past, then there must always be time. For the extremity of the last time taken is a now; for there is nothing to take in time besides the now; so that, since it is a beginning and an end, there must be time on both sides of it. But if there is time, there must also be motion, since time is an affection of motion.” In these words Aristotle builds his case that the heaven is eternal. For if [the now] is a kind of middle, and a beginning and an end, and always has time on either side, once this is posited it necessarily follows that time is eternal; and if time is eternal, the motion of which time is the number is necessarily eternal; and if motion is eternal, the moved body too is necessarily eternal. He posited this co-eternity absurdly, and it will be refuted as follows. As the time that is to come will come to be, so the past time too came to be. But the time that is to come, as it has the [now] that is going to come to be, so it also has its beginning; and as nothing of the past is in the future, so nothing of the future is in the present. But if the now is, and is present, and the future is not yet, neither being nor present, then the present now is not the beginning of the time to come; rather, the now that is going to be, that is the beginning of the future, which is neither a kind of middle having time on both sides, but only on one side, nor beginning and end, the same now, of one time and another (that is, beginning of the future and end of the past); but one now is the beginning, and another the end, of the same time. Again, if it is impossible for the now to be now unless it was first future and not being, then it is impossible for the now to be co-eternal. For if everything that first is not, but later is, is generated, and the now is such, then the now is generated. And if the now, then necessarily also the whole of time, whose beginning and end is the now; and if time, then necessarily motion too, of which time is the number; and if motion, then necessarily the moved body too is generated.

From the same: “In general, to think that this is a sufficient principle, that something always is or comes to be so, is not a right supposition. To this Democritus reduces the causes of nature, that it came to be so before as well; but he does not think it right to seek a principle of the ‘always,’ speaking rightly in some cases, but not rightly in that he says it of all. For the triangle always has its angles equal to two right angles; yet there is some other, eternal cause of this eternity; but of the principles there is no other cause, since they are eternal.” If, then, as things come to be now, so they came to be before, it is not right to suppose that there is a principle of the things that always come to be according to nature; it is necessarily right, then, to suppose that the principle of the things that come to be according to nature is what did not come to be as things come to be now, but otherwise; and therefore it is right to seek the principle of what always comes to be too. Animal comes to be from animal in one way, and animal came to be from what was not animal in another. And animal from non-animal neither came to be according to nature nor always comes to be; but animal from animal comes to be always and according to nature, from the time when what was not from an animal received the beginning of coming to be from animal. And this holds for all things that always come to be according to nature, not for some only; for it is impossible for what comes from generated principles to have the same generation that the principles had. Eternity in generated things cannot be without beginning. For the triangle always has its three angles equal to two right angles, having as its principle a generated thing, the straight line, whose definition is a line evenly extended. For this is the cause of the triangle's having its three angles equal to two right angles; and if this does not exist, a triangle cannot exist; but if a triangle does not exist, a straight line can exist. The principles of the things that always come to be according to nature cannot be eternal. For the nature they have, they impart to the things that come from them; but this is generated; generated, then, is the nature of the principles too, even if the mode of their generation is changed and differs from that of the things that come from the principles. There is some eternity …

From the same: “There must be something that is and is eternal, the first mover; for it has been shown that there must always be motion; and if always, it must also be continuous; for what always is is continuous, but what is successive is not continuous. And the continuous is one; and it is one if it is by one mover and of one moved. For if one thing and another move it, the whole motion is not continuous but successive.” If the first mover [moves] the motion of locomotion, and the motion of locomotion belongs to the heaven, and the heaven is a natural body, and a natural body has in itself, naturally, the principle of its natural motion, then the heaven is superfluously moved by the first mover with the motion of locomotion; for even if the first mover did not move it, it would be moved by itself, because it is a fifth element, having neither heaviness that moves it downward nor lightness that moves it upward, but another, nameless power that moves it around the center. If the first mover moves the heaven with the motion of locomotion neither according to nature (for to move it so is superfluous) nor contrary to nature (for motion contrary to nature is secondary to motion according to nature), then nothing moves the heaven. If every motion came to be before as it comes to be now, and it comes to be now by the change of what is going to be, and what is going to be did not yet exist before it came to be, and everything that first is not but later is is generated, and the generated cannot be without beginning and eternal, then motion is not eternal and without beginning.

From the same book: “It is evident that locomotion is first; for ‘first,’ as in other things, may be said in many ways in the case of motion too. That is called prior without which the others will not be, but which is without the others; and what is prior in time, and in substance. … that locomotion must be first. For it is not necessary that what is moved locally should grow or alter, nor indeed come to be or perish; but none of these is possible if the continuous motion, which the first mover moves, does not exist. Further, it is first in time; for to eternal things alone is it possible to be moved with this motion; but in any one body … locomotion must be the last of motions. For after coming to be come first growth and alteration; locomotion is the motion of things already perfected. But there must be something else moved by locomotion before, which will also be the cause of generation for the things that come to be, not itself coming to be, as the begetter of the begotten; since generation might seem to be the first of motions for this reason, that the thing must first come to be. In the case of any one of the things that come to be this is so; but something else must be moved before the things that come to be, itself being and not coming to be, and before this another.” If what grows is generated, and locomotion grows by the quantity of motion, locomotion is not eternal. For the body that is carried has different places, in which, extending the change of its measures as it is carried, it produces growth of motion by locomotion. If locomotion has in itself growth by the quantity of motion, how is locomotion said to be prior to the motion of growth? If it is impossible for what has no beginning and limit to receive growth by addition, then locomotion is not without beginning, since it always becomes greater by the quantity of motion. If locomotion has its being in coming to be and ceasing to be, locomotion is not eternal, since its not being always precedes its being. For every motion comes about by the change of what is not yet but is going to be. If every locomotion is finite with respect to the past, and everything finite necessarily has a beginning, and everything that has a beginning is generated, then locomotion is generated. And if locomotion is not prior to the body that is carried, the body that is carried is generated too. If among eternal things one only moves and the other is only moved, eternally, with the motion of locomotion, how is it not impossible for what is without beginning to be moved with a motion that has a beginning? If that without which nothing else is is first of the others both in substance and in time, how is it not ungenerated? For the first mover was posited to be first of all and ungenerated; and further the heaven and the things that appear and move in the heaven to be all ungenerated; which is absurd, to say that something ungenerated is prior to something eternal among eternal things. If the first mover [moves] the continuous motion, but moves neither the motion according to nature nor that contrary to nature (the former as superfluous, as was said, the latter as being secondary to the motion according to nature), then nothing moves the continuous motion. If, among things eternally moved, neither is the motion prior to the things moved nor the things moved prior to the motion, and every motion is by change of what is not yet but is going to be, then all the things moved will be from the change of what is not yet but … and later; there will then be a time when the ungenerated was not ungenera[ted] … locomotion is the last of motions, but there must be something else, moved by locomotion, prior, which is also the cause of generation, being ungenerated. How is it possible for the same thing to be the cause of generation according to nature and of generation beyond nature? For the one first begotten … was begotten. Yet the prior moved thing was moved for the generation of what first came to be in the same way as it was later moved for the generation of the things that come from that. Either, then, what is thus moved ungeneratedly is not the cause of all generation, or the first mover does not move the continuous motion, since a difference of generation is seen in the things that come to be, by which some came to be beyond nature and others according to nature. If what is prior and later is ungenerated, there will be a time when the ungenerated …

From the same: “In the continuous there are infinitely many halves, but not in actuality, only in potentiality.” If nothing is infinite in actuality, clearly neither motion nor time is infinite. Since motion and time are finite with respect to the past, they necessarily have a beginning; and having a beginning, they are necessarily generated. And if motion and time are generated, necessarily the moved body too. … [nor if,] of a time taken, its halves can be taken from the future and added to the past; not even so can time with respect to the past ever be infinite in actuality.

From Aristotle, from the first book On the Heaven: “There must be some simple body which is of a nature to move with circular motion according to its own nature.” What need, then, is there of the first mover to move such a body, which according to its own nature [moves] with circular motion …

From the same book: “It is evident that there is by nature some other substance of body besides those constituted here, more divine than and prior to all of these.” If this body moves eternally and without beginning around the earth, the substance that is here, how can it be prior to the earth, without which it would not move in its circular motion? And if being eternal and ungenerated, and useful for the constitution of the things that come to be here, belongs to the earth just as it belongs to such a body, how is that body more honorable than the earth and prior to it?

From the same book: “The body that moves in a circle cannot have heaviness or lightness.” If what has no heaviness and lightness cannot be tangible (for the tangible is among the things that have heaviness and lightness), how does it have what cannot be without those, and yet not have those? And how by its motion does it produce a heating power in the air, like the bodies here that have heaviness and lightness, which by their motions [produce] heating …

From the same: “The contrarieties of locomotion correspond to the contrarieties of places. For if they were equal, there would be no motion of them; and if one motion prevailed, the other would not be. So if both existed, one body would be in vain, not moving with its own motion. For we call a sandal in vain when it is not worn. But God and nature do nothing in vain.” If in the locomotion of bodies there were contrary motions, either equal, hindering one another's motions by counter-pressure, or unequal, so that through the prevailing of one the other became motionless, the overpowered one being forced by the prevailing one and not completing its own natural motion, then the things so hindered in their own natural motions would have come to be in vain, and these would not be works of God, nor clearly of nature. If God is not the maker of the things that come to be in vain, nor is nature, then God and nature are the maker of the things that come to be not in vain but complete their natural motions unhindered. How then is it not most absurd to call these ungenerated, eternal, and without beginning, when God and nature are their maker? And if we call sandals that are worn works of a craftsman, why do we not also call the bodies that complete their own natural motions thoughts of God and nature?

From the same book: “That the formula without matter is different from the formula of the shape in matter is well said, and let this be true; but nonetheless there is no necessity on this account that there should be more worlds, nor is it possible that more should come to be, since this world is made from all the matter, as indeed it is.” If the difference of formula from formula is that one is without matter and the other in matter, clearly the formula in matter is later than the formula without matter. How then is the world ungenerated, when it has its constitution from the later formula? If matter is formless and without substance, and deprived of being a “this,” before it receives the form and becomes a substance and a “this,” how is the world ungenerated, when it has come to be from such matter? If the one who had the formula of one world also had the formulas of more worlds, … the making according to his own will, but by the abundance of matter was able to make one world and by its lack was not able to make more worlds, how does he not seem to have had the formulas of more worlds in vain, when he could not make them because of the lack of matter? If it is impossible for the ungenerated to come to be from the ungenerated, how, if matter is ungenerated and the world is ungenerated too, does the world come to be from matter? If God did not make matter as he made the things that come from matter, then God does not make whatever he wishes, but whatever he is able. But if he has power equal to his will in all things, then God is the maker of matter, as also of the things that come from matter. If matter, lying under God for the making of the things that come from it, formless and without substance, without quality and without quantity, was changed by God's power into all these things and became substance with quality and quantity, how was it not increased by the same power of God, which wrought such great changes in it, so far that more worlds too should come to be from it, but, being spread out for the generation of one world, prevented God against his will from making more worlds?

From the same: “The heaven is among the particular things and those that come from matter; but if it is constituted not from a part of matter but from all of it, then being heaven and being this heaven are different; yet there would not be another, nor could more come to be, because this one has embraced all the matter.” [If the heaven is] composed of matter and formula, so that being heaven is different from the immaterial formula, how is it not generated, when it has as the beginning of its own substance the composition of matter and formula from which it is? If matter by itself has neither heaviness nor lightness (for these are affections of the bodies that come to be from it), and if the heaven, which has neither heaviness nor lightness, came to be from all such matter, from where did all the other things come to be, when all the matter was used up in making the heaven? If, before matter was formed by the form of the heaven, it had no heaviness and lightness, just as now, after it has been formed, it has none, how was it not moved before the forming, as it is moved now after the forming? If being moved belongs to substance, and not having heaviness and lightness belongs to matter and not to substance, and the heaven moves with circular motion because it has no heaviness and lightness, clearly the heaven has its moving in this way because of the matter and not because of the form. How then was matter unmoved with circular motion before the form, having neither heaviness nor [lightness]?