CHAPTER 73

The common premises laid down by the Mutakallimūn, in spite of the diversity of their opinions and the multiplicity of their methods, that are necessary with a view to establishing what they wish to establish with regard to the four problems in question, are twelve in number. I shall mention them to you and afterwards I shall explain to you the meaning of each of these premises and what necessarily follows from it.¹ [105a]

The first premise: establishing the existence of atoms.2 The second premise: the existence of a vacuum. The third premise: time is composed of instants.³ The fourth premise: that substance⁴ cannot be exempt from a certain number of accidents. The fifth premise: that the accidents that I shall describe subsist in the atom, which cannot be exempt from them. The sixth premise: that an accident does not endure for two units of time. The seventh premise: that the status of the habitus is that of their privation and that the former and the latter are all of them existent accidents requiring an efficient cause. The eighth premise: that nothing except substances and accidents subsist in all that exists—they mean to say, in all the created things—and that natural form is likewise an accident. The ninth premise: that accidents do not support one another.⁵ The tenth premise: that the possibility of a thing should not be considered in establishing a correspondence between that which exists and mental representation. The eleventh premise: that with regard to the impossibility of the infinite, there is no difference between the latter’s existing in actu, in potentia, or by accident; I mean to say that there is no difference between the simultaneous existence of those infinite things, or their being supposed to be made up of what exists and of what has ceased to exist, which is infinity by accident. They say that all these kinds of infinity are impossible. The twelfth premise consists in their saying that the senses commit mistakes and that many of the objects of their apprehension elude them and for this reason their judgment should not be appealed to and they should not be regarded in absolute fashion as principles of demonstration. After having thus enumerated these common premises, I shall start to explain their meanings and to explain what necessarily follows from every one of them. [105b]

THE FIRST PREMISE

Its meaning is that they thought that the world as a whole—I mean to say every body in it—is composed of very small particles that, because of their subtlety, are not subject to division. The individual particle does not possess quantity in any respect. However, when several are aggregated, their aggregate possesses quantity and has thus become a body. If two particles are aggregated together, then according to the statements of some of them, every particle has in that case become a body, so that there are two bodies. All these particles are alike and similar to one another, there being no difference between them in any respect whatever. And, as they say, it is impossible that a body should exist in any respect except it be composed of these particles, which are alike in such a way that they are adjacent to one another. In this way, according to them, generation consists in aggregation, and corruption in separation. They do not, however, call this process corruption, but say that there are the following generations: aggregation and separation, motion and rest. They also say that these particles are not restricted in their existence,6 as was believed by Epicurus and others who affirmed the existence of such particles; for they say that God, may He be exalted, creates these substances constantly whenever He wishes, and that their annihilation is likewise possible. Further on, I shall let you hear their opinions regarding the annihilation of substance.

THE SECOND PREMISE

The assertion concerning the vacuum. The men concerned with the roots [the Mutakallimūn] believe likewise that vacuum exists and that it is a certain space⁷ or spaces in which there is nothing at all, being accordingly empty of all bodies, devoid of all substance. This premise is necessary for them because of their belief in the first premise. For if the world were full of the particles in question, how [106a] can a thing in motion move? It would also be impossible to represent to oneself that bodies can penetrate one another. Now there can be no aggregation and no separation of these particles except through their motions. Accordingly they must of necessity resort to the affirmation of vacuum so that it should be possible for these particles to aggregate and to separate and so that it should be possible for a moving thing to move in this vacuum in which there is no body and none of these substances.8

THE THIRD PREMISE

This is their saying that time is composed of instants, by which they mean that there are many units of time that, because of the shortness of their duration, are not divisible. This premise is also necessary for them because of the first premise. For they undoubtedly had seen Aristotle’s demonstrations, by means of which he has demonstrated that distance, time, and locomotion are all three of them equal as far as existence is concerned. I mean to say that their relation to one another is the same and that when one of them is divided the other two are likewise divided and in the same proportion. Accordingly they knew necessarily that if time were continuous and infinitely divisible, it would follow of necessity that the particles that they had supposed to be indivisible would also be divisible. Similarly if distance were supposed to be continuous, it would follow of necessity that the instant that had been supposed to be indivisible would be divisible—just as Aristotle had made it clear in the “Akroasis.” Therefore they supposed that distance is not continuous, but composed of parts at which divisibility comes to an end, and that likewise the division of time ends with the instants that are not divisible. For example, an hour [106b] consists of sixty minutes, a minute of sixty seconds, and a second of sixty thirds. And thus this division of time ends up accordingly with parts constituting, for instance, tenths or something even briefer, which cannot in any respect be separated in their turn into parts and are not subject to division, just as extension is not subject to it. Consequently, time becomes endowed with position and order. In fact they have no knowledge at all of the true reality of time. And this is only appropriate with regard to them; for seeing that the cleverest philosophers were confused by the question of time and that some of them did not understand its notion—so that Galen could say that it is a divine thing, the true reality of which cannot be perceived—this applies all the more to those who pay no attention to the nature of any thing.

Hear now what they were compelled to admit as a necessary consequence of these three premises and what they therefore believed. They said that motion is the passage of an atom belonging to these particles from one atom to another that is contiguous to it. It follows that no movement can be more rapid than another movement. In accordance with this assumption, they said that when you see that two things in motion traverse two different distances in the same time, the cause of this phenomenon does not lie in the greater rapidity of the motion of the body traversing the longer distance; but the cause of this lies in the motion that we call slower being interrupted by a greater number of units of rest than is the case with regard to the motion we call more rapid, which is interrupted by fewer units of rest. And when the example of an arrow shot from a strong bow was alleged as an objection against them, they said that the motions of the arrow were also interrupted by units of rest. In fact your thinking that a certain object is moving in continuous motion is due to an error of the senses, for many of the objects of the perception of the senses elude the latter, as they lay down in the twelfth premise. In consequence, it was said to them: Have you seen a millstone making [107a] a complete revolution? Has not the part that is at its circumference traversed the distance represented by the bigger9 circle in the same time in which the part near the center has traversed the distance represented by the smaller¹⁰ circle? Accordingly the motion of the circumference is more rapid than the motion of the inner circle. And there is no opportunity for you to assert that the motion of the latter part is interrupted by a greater number of units of rest as the whole body is one and continuous, I mean the body of the millstone. Their answer to this objection is that the various portions of the millstone become separated from one another in the course of its revolution and that the units of rest that interrupt the motion of all the revolving portions that are near the center are more numerous than the units of rest that interrupt the the motion of the parts that are farther off from the center. Thereupon it was said to them: How then do we perceive the millstone as one body that cannot be broken up even by hammers? One must accordingly assume that when it turns round, it splits into pieces; and when it comes to rest, it is welded up and becomes as it was before. How is it that one does not perceive its portions as separated from one another? Thereupon, in order to reply to this, they had recourse to the same twelfth premise, which states that one should not take into account the apprehensions of the senses, but rather the testimony of the intellect.

You should not think that the doctrines I have explained to you are the most abhorrent of the corollaries necessarily following from those three premises, for the doctrine that necessarily follows from the belief in the existence of a vacuum is even stranger and more abhorrent. Furthermore, the doctrine that I have mentioned to you with regard to motion is not more abhorrent than the assertion going with this view that the diagonal of a square is equal to one of its sides, so that some of them say that the square is a nonexistent thing. To sum up: By virtue of the first premise all geometrical demonstrations become invalid, and they belong to either one or the other of two categories. Some of them are absolutely invalid, as for instance those referring to the properties of incommensurability and commensurability of lines and planes and the existence [107b] of rational and irrational lines and all that are included in the tenth book of Euclid and those that resemble them. As for the others, the demonstrations proving them are not cogent, as when we say we want to divide a line into two equal halves. For in the case in which the number of its atoms11 is odd, the division of the line into two equal parts is impossible according to their assumption. Know, moreover, that the Banū Shakir have composed the famous “Book of Ingenious Devices,” which includes one hundred odd ingenious devices, all of them demonstrated and carried into effect. But if vacuum had existed, not one of them would have been valid, and many of the contrivances to make water flow would not have existed. In spite of this, the lives [of the Mutakallimūn] have been spent in argumentation with a view to establishing the validity of these premises and others resembling them. I shall now return to the explanation of the meaning of their remaining premises that were mentioned.

THE FOURTH PREMISE

This is their saying that the accidents exist, and that they are something superadded to the something that is the substance, and that no body is exempt from one of them. If this premise did not mean more than this, it would be a correct, clear, evident premise, and give rise to no doubt and no difficulty. However, they say that in every substance in which there does not subsist the accident of life, there necessarily subsists the accident of death, for the recipient cannot but receive one of two contraries. They say: similarly it has a color, a taste, motion or rest, aggregation or separation. And if the accident of life subsists in it, there cannot but subsist in it other genera of accidents such as knowledge or ignorance, or will or its contrary, [108b] or power or powerlessness, or apprehension or one of its contraries. To sum up: there must necessarily subsist in it all the accidents that may subsist in a living being or one of their contraries.

THE FIFTH PREMISE

This is their saying that these accidents subsist in the atom and that it cannot be exempt from them. The explanation and the meaning of this premise are as follows. They say that every atom of the atoms that God creates is provided with accidents from which it cannot be exempt; such accidents, for example, as color, smell, motion or rest, but not quantity—since these atoms do not possess quantity. For in accordance with their opinion, they do not call quantity an accident and do not understand that quantity includes the notion of accidentality. In virtue of this premise, they hold with regard to all accidents subsisting in a body that it should not be said that one of them is a proprium of that body as a whole; for the accident in question subsists, according to them, in every atom of the atoms of which that body is composed. For instance, in the case of this piece of snow, the whiteness does not subsist only in the entire whole; rather every single atom of the atoms of the snow is white, and it is because of this that whiteness subsists in their aggregate. In a similar way they say of a body in motion that every atom of its atoms is in motion and that because of this it is in motion as a whole. Similarly life subsists, according to them, in every single part of the living body, and also the senses; every atom is a whole endowed with sensation, being according to them endowed with sensation. [108c] For life, the senses, intellect, and knowledge are, according to them, accidents just as blackness and whiteness are, as we shall make clear on the basis of their doctrines. As regards the soul, they disagree; the opinion of most of them12 is that it is an accident subsisting in one atom that belongs to the whole consisting of the atoms of which man, for example, is composed. This whole is designated as being endowed with a soul because of the fact that that atom subsists in it. Some of them, however, affirm that the soul is a body composed of subtle atoms and that these atoms are doubtless provided with a certain accident, which is their proprium and in virtue of which they become a soul. They affirm that these atoms are mixed with the atoms of the organic body. Accordingly they are not exempt from the belief that the thing that is the soul is an accident. As for the intellect, I consider that they are unanimous in thinking that it is an accident subsisting in an atom belonging to an intellectually cognizing whole. As regards knowledge, there is perplexity among them over whether it is an accident subsisting in every atom belonging to the whole endowed with knowledge, or an accident subsisting in one atom only. Both affirmations entail abhorrent conclusions. It has been objected against them that we find that most minerals and stones have a very intense color, but when they are pulverized this color disappears. Thus when we pulverize the intensely green emerald, it turns into white dust—which is proof that the accident in question resides in the whole and not in every particle included in that whole. It is even more manifest that parts cut off from a living being are not alive—which is proof that this entity13 is constituted by the whole and not by each of the parts included in that whole. In answer to this, they say that the accident in question has no continued existence, but is always created anew, as I shall explain on the basis of their opinion as formulated in the next premise. [109a]

THE SIXTH PREMISE

It consists in their assertion that an accident does not last during two units of time. The meaning of this premise is as follows. They think that God, may He be glorified and magnified, creates an atom and creates together with it, at one and the same time, any accident He wills as an accident subsisting in the atom. For it may not be predicated of Him, may He be exalted, that He has the power to create an atom without an accident, for this is impossible. Now the true reality of an accident and its notion consist in its not enduring or lasting during two units of time, by which they mean: two instants. While this accident is being created, it disappears, having no continued existence. Whereupon God creates another accident of the same species, which accident disappears in its turn; whereupon He creates a third one belonging to the same species, and so on always in the same way in the period during which God wishes the species of that accident to last. If, however, He, may He be exalted, wishes to create in the atom another species of accident, He does so. If, however, He refrains from the act of creation and does not create an accident, the atom in question becomes nonexistent. This is the opinion of some of them—namely, of those who are the majority—this being the creation of accidents, which they affirm. However, some of them belonging to the Muʿtazila assert that some accidents last for a certain time, whereas others do not last during two units of time. As to this, they have no rule to which to refer so as to be able to say: this particular species of accidents lasts and that other does not. What led them to this opinion is that it is not to be said that there is a nature in any respect whatever and that the nature of one particular body may require that this and that accident be attached to that body. Quite the contrary, they wish to say that God, may He be exalted, created the accidents in question now, without the intermediary of nature—without any other thing. But if this is asserted, it follows according to them necessarily that [109b] that accident in question does not last; for if you should say that it lasts for some time and then becomes nonexistent, it becomes necessary to inquire what thing has caused it to become nonexistent. If you should say thereupon that God, if He wills, causes it to become nonexistent, this answer would not be valid according to their opinion. For an agent does not act to bring about nonexistence, since nonexistence does not require an agent. On the contrary, the nonexistence of an act comes about when the agent refrains from acting. This is valid in a certain respect. For this reason, accordingly, their assertions led them—as they wished that there be no nature necessitating the existence or the nonexistence of a thing—to the point of affirming the creation of successive accidents. According to some of them, when God wishes to cause the nonexistence of a substance, He does not create an accident in it, in consequence whereof the substance becomes nonexistent. Others affirm that if God should wish the world to be annihilated, He would create in it the accident of passing-away—an accident that would be without a substratum. Thereupon this accident of passing-away would be opposed to the existence of the world. In accordance with this premise, they assert that when we, as we think, dye a garment red, it is not we who are by any means the dyers; God rather creates the color in question in the garment when the latter is in juxtaposition with the red dye, which we consider to have gone over to the garment. They say that this is not the case, but that God has instituted a habit according to which, for example, black color does not appear except when a garment is juxtaposed with indigo. However, this blackness, which God creates when an object about to turn black is juxtaposed with blackness, does not last, but disappears instantly, and another blackness is created. God has also instituted the habit of not creating, after the disappearance of blackness, redness or yellowness, but a blackness similar to the one before. In conformity with this assumption, they have drawn the corollary that the things we know now [110a] are not identical with the contents of the knowledge known by us yesterday; for that knowledge has become nonexistent, and another knowledge similar to it has been created. They maintain that this is so, because knowledge is an accident. Similarly it necessarily behooves those who believe that the soul is an accident to consider that, to take an example, one hundred thousand souls are created every minute for the requirements of every being endowed with a soul. For as you know, time, according to them, is composed of indivisible instants. In conformity with this premise, they assert that when a man moves a pen, it is not the man who moves it; for the motion occurring in the pen is an accident created by God in the pen. Similarly the motion of the hand, which we think of as moving the pen, is an accident created by God in the moving hand. Only, God has instituted the habit that the motion of the hand is concomitant14 with the motion of the pen, without the hand exercising in any respect an influence on, or being causative in regard to, the motion of the pen. For they maintain that an accident does not go beyond its substratum. There is unanimity among them with regard to their belief that a white garment that has been put into a vat full of indigo and has become dyed, has not been blackened by the indigo, blackness being an accident that is inherent in the body that is the indigo and that does not go beyond it so as to affect something else. According to them, there is no body at all endowed with the power of action. On the other hand, the ultimate agent is God; and it is He who, in view of the fact that He has instituted such a habit, has created the blackness in the body that is the garment when the latter was juxtaposed with indigo.

To sum up: it should not be said in any respect that this is the cause of that. This is the opinion of the multitude [of the Mutakallimūn]. One15 of them, however, maintained the doctrine of causality and in consequence was regarded as abhorrent by them. As for the actions of man, they are in disagreement about them. The doctrine of the majority and in particular that of the multitude of the Ashʿariyya is that when the pen is put into motion, God creates four accidents, no one of which is a cause of any other—all of them being concomitant [110b] in regard to their existence, not otherwise. The first accident is my will to put the pen into motion; the second accident, my power to put it into motion; the third accident, human motion itself—I mean the motion of the hand; the fourth accident, the motion of the pen. For they think that when a man wills a thing and, as he thinks, does it, his will is created for him, his power to do that which he wills is created for him, and his act is created for him. For he does not act in virtue of the power created in him, and the power has no influence on the action. On the other hand, the Muʿtazila maintain that man acts in virtue of the power created in him; and one of the Ashʿariyya says that this created power has a certain influence on, and connection with, the act. But they regard this as abhorrent. As all of them think, the created will and the created power and—in the opinion of some of them—also the created act, are accidents that do not last, God constantly creating in that way motion after motion in the pen in question as long as the pen is in motion. Thereafter, when it comes to rest, it does so only after He has created in it a unit of rest. And He does not cease to create in it one unit of rest after another as long as the pen is at rest. Accordingly God creates at every one of the instants—I mean the separate units of time—an accident in every individual among the beings, whether that individual be an angel, a heavenly sphere, or something else. This He does constantly at every moment of time. They maintain that this is the true faith in God’s activity; and in their opinion, he who does not believe that God acts in this way denies the fact that God acts. With regard to beliefs of this kind, it has been said in my opinion and in that of everybody endowed with an intellect: Or as one mocketh [111a] a man, do ye so mock him16—this being in truth the very essence of mockery.

THE SEVENTH PREMISE

It consists in their belief that privations of habitus are things that exist in a body, being superadded to its substance, and are accordingly also existent accidents. In consequence they are always being created, and whenever one of them disappears, another is created. The explanation is as follows. They do not hold that rest is the privation of motion, that death is the privation of life, and that blindness is the privation of sight; in fact they do not believe this with regard to any privations of habitus similar to those mentioned. For according to them, the status¹⁷ of motion and rest is the same as that of heat and cold. For just as heat and cold are accidents existing in the hot and cold substrata, motion is an accident created in the moving body, and rest an accident which God creates in the body that is at rest, which accident likewise does not last for two units of time, as has been set forth before in the preceding premise. According to them, God has created a unit of rest in every particle of the body that is at rest and, as long as it is at rest, creates another unit of rest every time a unit of it becomes nonexistent. The position is completely analogous, according to them, with regard to knowledge and ignorance. According to them, the latter exists and is an accident. In consequence, a unit of ignorance continually disappears and another is created as long as a particular ignorant individual continues to be ignorant in anything. The position is also completely analogous with regard to life and death. For both of these are, according to them, accidents, and they clearly assert that a unit of life disappears and another is created as long as a particular living being is alive. Then, when God wills its death, He creates in it the accident of death following upon the disappearance of the accident of life, which [111b] does not last two units of time. All this they assert clearly. Now according to this assumption, it clearly follows that the accident of death, which God creates, likewise becomes nonexistent after a moment of time, so that God creates another unit of death. But for that, death would not last. However, as one unit of life is created after another, one unit of death is created after another. Would that I knew till when God creates the accident of death in a dead individual; does He do so as long as that individual’s external form endures, or as long as one of that individual’s atoms endures? For, according to what they wish, God creates the accident of death in every single atom of the atoms of the individual in question. Now we find molars of dead individuals that are thousands of years old. Accordingly this is a proof that God has not annihilated that substance. In consequence, He should be creating in it the accident of death all through these thousands of years, creating a unit of death as soon as another unit of it disappears. This is the doctrine of the multitude of them. However one Muʿtazilite says that certain privations of habitus are not existent things. He does not, however, say this consistently with regard to every privation. Thus he does not say that darkness is the privation of light, that rest is the privation of motion. In fact he regards some of the privations as existent and some others as being merely a privation of habitus, just as it suits him with respect to his belief. They did a similar thing with regard to the continued existence of accidents. For according to them, some of the accidents last for some time, whereas others do not last for two units of time. For the purpose of all of them is to suppose an existent universe,18 the nature of which fits in with our opinions and teachings.

THE EIGHTH PREMISE

It consists in their assertion that there exists nothing except substances and accidents and that the natural forms [112b] are likewise accidents. The explanation of this premise is as follows. According to them, all bodies are composed of atoms resembling one another, as we have made clear when setting out the first of their premises. These atoms differ from one another only with regard to accidents and in nothing else. Thus according to them, animality, humanity, sensation, and rationality are all accidents having the same status as whiteness, blackness, bitterness, and sweetness, so that the difference existing between an individual belonging to one species and an individual belonging to another is like the difference between individuals belonging to the same species. In consequence, the body of heaven, even the body of the angels, or even the body of [God’s] throne, as it is imagined in fantasy, and the body of any insect you like from among the insects of the earth or of any plant you like, are, according to them, of one substance, differing only with regard to accidents and in nothing else. And the substances of which the universe is composed are the atoms.

THE NINTH PREMISE

It consists in their assertion that accidents do not serve as a substratum for one another. According to them, it may not be said that one accident has as its substratum another, which latter has as its substratum a substance. In their opinion all accidents, in the first place and in the same way, have substance as a substratum.19 They avoid the opposing doctrine because it has as its necessary consequence that an ultimate accident may not subsist in a substance unless a primary accident precedes it in subsisting in it. They do not wish to admit this in the case of certain accidents, desiring to create the possibility that certain accidents may subsist in any substance that they may happen to encounter without any need for another accident previously providing the substance with a proprium. This is in accordance with their view that all accidents provide a proprium. Furthermore, from [112c] another angle it may be seen that the substratum to which an accident may attach itself20 has to be stable and has to endure for a certain time. However, as an accident, according to them, does not last for two units of time—I mean for two instants—how can it be possible according to this hypothesis that it should serve as a substratum for something other than itself?

THE TENTH PREMISE

It consists in the affirmation of admissibility that they mention. This is the main proposition of the science of kalām. Listen to its meaning. They are of the opinion that everything that may be imagined is an admissible notion for the intellect. For instance, it is admissible from the point of view of intellect that it should come about that the sphere of the earth should turn into a heaven endowed with circular motion and that the heaven should turn into the sphere of the earth. Or to take another example, it is admissible that the sphere of fire should move toward the center of the earth and that the sphere of the earth should move toward the encompassing heaven. For as they say, according to intellectual admissibility, one place is not more appropriate for one particular body than another place. They also say with regard to all things that are existent and perceptible that supposing anything among them should be bigger than it is or smaller or different from what it is in shape or place—should a human individual, for instance, have the size of a big mountain having many summits overtopping the air, or should there exist an elephant having the size of a flea, or a flea having the size of an elephant—all such differences would be admissible from the point of view of the intellect. The whole world is involved in this method of admissibility as they practice it. For whatever thing of this kind they assume, they are able to say: it is admissible that it should be so, and it is possible that it should be otherwise; and it is not more appropriate that one particular thing should be so than that it should be otherwise. And they say this without paying attention to the correspondence or lack of correspondence of that which exists to their assumptions. For they say of the existent things—provided with [113a] known forms and determinate sizes and necessarily accompanying modes that are unchangeable and immutable—that their being as they are is merely in virtue of the continuance of a habit. In the same way it is the habit of a sultan not to pass through the market places of the city except on horseback, and he has never been seen doing it in a way other than this. However, it is not held impossible by the intellect that he should walk on foot in the city; rather is it undoubtedly possible, and it is admissible that this should occur. They say that the fact that earth moves toward the center and fire upwards or the fact that fire burns and water cools is in a similar way due to the continuance of a habit. It is, in consequence, not impossible from the point of view of the intellect that this habit should undergo a change so that fire should cool and move downwards, while still being fire, and so that similarly water should warm and move upwards, while still being water. The whole edifice21 is founded on this assumption. At the same time they are unanimous in holding that the coming-together of two contraries in the same substratum²² and at the same instant is impossible, cannot be true, and cannot be admitted by the intellect. They further assert that it is impossible and cannot be admitted by the intellect that a substance should exist without there being any accident in it; or, as some of them say, it is also impossible and cannot be admitted by the intellect that an accident should exist without being in a substratum. Similarly they say that it cannot be true that a substance should be transformed into an accident or an accident into a substance or that a body should compenetrate another body; they acknowledge that these are impossibilities from the point of view of the intellect. Now it is a true assertion that none of the things that they consider as impossible can be mentally represented to oneself in any way whatever, whereas the things they call possible can be. Yet the philosophers say that when you call a thing “impossible,” it is because it cannot be imagined, and when you call a thing “possible,” it is because it can be imagined. Thus what is possible according to you is possible only from the point of view of the imagination and not from that of the intellect. Accordingly in this premise you consider that which is necessary, admissible, or impossible, sometimes [113b] with the imagination and not with the intellect and sometimes with the first suggestions of common opinion—just as Abū Naṣr23 has noted when speaking of the notion to which the Mutakallimūn apply the term “intellect.” Thus it has already been made clear that that which can be imagined is, according to them, something possible, whether something existent corresponds to it or not. On the other hand, everything that cannot be imagined is impossible. Now this premise cannot be true except in virtue of the nine premises previously mentioned. Undoubtedly it was because of it that they had recourse to expounding these nine premises before it. The explanation of this is in accordance with what I shall set forth to you while I reveal to you the secrets of these matters in the form of a dispute taking place between a Mutakallim and a philosopher.

The Mutakallim said to the philosopher: Why is it that we find this body, which is iron, is endowed with extreme hardness and strength, while being black; whereas that other body, which is cream, is endowed with extreme softness and looseness, while being white?

The philosopher replied to him: Every natural body has two species of accidents: those that are attached to it in respect to its matter, such as those making man healthy and ill; and those that are attached to it in respect to its form, such as man’s feeling of wonder and his laughing. Now the various kinds of matter found in bodies that are in the stage of ultimate composition differ greatly because of the forms, which particularize these various kinds of matter, so that the substance of iron becomes different from that of cream and so that each of these substances has attached to it the differing accidents that you see. Thus strength subsisting in the one substance and softness subsisting in the other are accidents that follow from the difference of their forms, and blackness and whiteness are accidents that follow from the difference of their ultimate matter.

Thereupon the Mutakallim controverted this entire reply by means of the premises of his doctrine as I shall set forth to you. In effect he said: There does not exist at all, contrary to what you think, any form constituting a substance so that a variety of substances is thereby brought about. [114a] On the contrary, everything that you consider as a form is an accident—as we have made clear from their assertion in the eighth premise. Then he said: There is no difference between the substance of iron and the substance of cream, the whole being composed of atoms similar to one another—as we have made clear from their opinions set forth in the first premise, from which, as we have explained, the second and the third follow necessarily. Similarly the twelfth premise is required for establishing the existence of atoms. Furthermore, it is not true, in the opinion of a Mutakallim, that there are certain accidents that particularize a substance so that because of them it is disposed and prepared to receive other secondary accidents. For in his opinion, one accident cannot serve as a substratum for another—as we have made clear in the ninth premise—and moreover, an accident has no continued existence—as we have made clear in the sixth premise. Then when, according to the Mutakallim, everything he wishes with regard to his premises is established as true, the resultant conclusion is that the substances of the iron and the cream are the same substances,24 substances similar to one another in every respect. Each of these substances has the same relation with any accident,²⁵ one particular substance not being more appropriate for one particular accident than another. And just as one atom is not more fitted to move than to be at rest, so one particular atom is not more appropriate for the reception of the accident of life, the accident of the intellect, the accident of sense, than any other atom. The greater or smaller number of the atoms does not in this point constitute a significant addition to the final result, as an accident subsists in every atom—as we have made clear on the basis of their assertion in the fifth premise. Accordingly it follows necessarily from all these premises that man is not more fitted to cognize intellectually than a beetle. And thus the admissibility of which [the Mutakallimūn] speak in the present premise follows necessarily. In fact it was with a view to this premise [114b] that the whole endeavor was made, because this premise is more firm than any other thing for establishing everything that there is a wish to establish, as shall be made clear.

A CALL UPON THE READER’S ATTENTION

Know, thou who studiest this Treatise: if you are of those who know the soul and its powers and have acquired true knowledge of everything as it really is, you already know that imagination exists in most living beings. As for the perfect animal, I mean the one endowed with a heart, the existence of imagination in it is clear. Accordingly, man is not distinguished by having imagination; and the act of imagination is not the act of the intellect but rather its contrary. For the intellect divides the composite things and differentiates their parts and makes abstractions of them, represents them to itself in their true reality and with their causes, and apprehends from one thing very many notions, which differ for the intellect just as two human individuals differ in regard to their existence for the imagination. It is by means of the intellect that the universal is differentiated from the individual, and no demonstration is true except by means of universals. It is also through the intellect that essential predicates are discerned from accidental ones. None of these acts belongs to the imagination. For the imagination apprehends only that which is individual and composite as a whole, as it is apprehended by the senses; or compounds things that in their existence are separate, combining one with another; the whole26 being a body or a force of the body. Thus someone using his imagination imagines a human individual having a horse’s head and wings and so on. This is what is called a thing invented and false, for nothing existent corresponds to it at all. In its apprehension, imagination is in no way able to hold itself aloof from matter, even if it turns a form into the extreme of abstraction. For this reason there can be no critical examination in the imagination.

Hear what [115a] the mathematical sciences have taught us and how capital are the premises we have obtained from them. Know that there are things that a man, if he considers them with his imagination, is unable to represent to himself in any respect, but finds that it is as impossible to imagine them as it is impossible for two contraries to agree; and that afterwards the existence of the thing that is impossible to imagine is established by demonstration as true, and existence manifests it as real. Thus if you imagine a big sphere of any size you like, even if it be the size of the encompassing heaven; imagine further a diameter passing through the center of the sphere; and thereupon imagine the two human individuals standing upon the two extremities of the diameter so that their feet are put in a straight line with respect to the diameter, so that their feet and the diameter form one and the same straight line—then one of two possibilities must be true: either the diameter is parallel to the horizon or it is not. Now if it is parallel, both individuals should fall. If it is not parallel, one of them—namely the lower one—should fall, while the other is firmly placed. It is in that way that imagination would apprehend the matter. Now it has been demonstrated that the earth is spherical in form and that portions of the inhabited part of it lie at both extremities of its diameter. Thus the head of every individual from among the inhabitants of the two extremities is near heaven while his feet are near the feet of another individual who is opposite him. It is thus impossible in every way that either of them would fall. This cannot even be represented to oneself; for one of them is not placed above and the other below, but each of them is both above and below in relation to the other. Similarly it has been made clear in the second book of the “Conic Sections”27 that two lines, between which there is a certain distance at the outset, may go forth in such a way that the farther they go, this distance diminishes and they come nearer to one another, but without it ever being possible for them to meet even if they are drawn forth to infinity and even though they come nearer to one another the farther they go. This cannot be [115b] imagined and can in no way enter within the net of the imagination. Of these two lines, one is straight and the other curved, as has been made clear there in the above-mentioned work.

Accordingly it has been demonstrated that something that the imagination cannot imagine or apprehend and that is impossible from its point of view, can exist. It has similarly been demonstrated that something the imagination considers as necessary is impossible—namely, that God, may He be exalted, should be a body or a force in a body. For according to the imagination, there are no existents28 except bodies²⁸ or things²⁸ in bodies.²⁸

Accordingly it is clear that there is something else by means of which that which is necessary, that which is admissible, and that which is impossible, can be discerned, something that is not the imagination. How excellent is this speculation and how great its utility for him who wishes to awaken from this dormancy, I mean the state of following the imagination! Do not think that the Mutakallimūn are not aware of anything concerning this point. On the contrary, they are aware of it to a certain extent; they know it and call that which may be imagined while being at the same time impossible—as for instance God’s being a body—a fantasy and a vain imagining. And often do they clearly state that fantasies are false. For this reason they have recourse to the nine premises we have mentioned, so as to be able to establish with their help the truth of this tenth premise—which asserts the admissibility of those imaginings that they wanted to be declared admissible—in order to maintain the similarity of the atoms to one another and the equality of the accidents with respect to “accidentally,” as we have made clear.

Consider, thou who art engaged in speculation, and perceive that a method of profound speculation has arisen. For with regard to particular mental representations, one individual claims that they are intellectual representations, whereas another affirms that they are imaginative representations. We wish consequently to find something that would enable us to distinguish the things cognized intellectually from those imagined. For if the philosopher says, as he does: That which exists²⁹ is my witness and by means of it we discern the necessary, the possible, and the impossible; the adherent of the Law says to him: The dispute between us is with regard to this point. For we claim³⁰ that that which exists [116a] was made31 in virtue of will and was not a necessary consequence. Now if it was made in this fashion, it is admissible that it should be made in a different way, unless intellectual representation decides, as you think it decides, that something different from what exists at present is not admissible. This is the chapter of admissibility. And about that I have something to say, which you will learn32 in various passages of this Treatise. It is not something one hastens to reject in its entirety with nonchalance.

THE ELEVENTH PREMISE

This is their saying that the existence of that which is infinite in any mode whatever is impossible. The explanation of this is as follows. The impossibility of the existence of an infinite magnitude has already been demonstrated, or the existence of magnitudes infinite in number—even if each of them is of finite magnitude—provided that those magnitudes infinite in number are supposed to coexist in time. Similarly the existence of an infinite number of causes is impossible—I mean to say that a thing should be the cause of something, that this thing should have a cause³³ in its turn, that that cause should again have a cause, and so forth to infinity, so that an infinite number of numerable³⁴ things should exist in actu; and it is indifferent whether these be bodies or things separate from matter, provided only that some of them are the causes of others. It is this natural and essential orderly arrangement with regard to which it has been demonstrated that the infinite is impossible in it. But as for what is infinite in potentia or accidentally, the existence of such an infinite has, in some cases, been demonstrated: thus it has been demonstrated that the division of magnitudes to infinity is possible in potentia, and likewise the division of time to infinity. Another case is an object of speculation: namely, the existence of what is infinite by way of succession. This is what is called the infinite by accident. And it consists in a thing coming to exist after the passing-away [116b] of another thing, the latter’s coming to exist after the passing-away of a third thing, and so forth to infinity. About this there is an extremely profound speculation. Thus he who claims to have demonstrated the eternity of the world says that time is not finite, and nothing absurd follows necessarily for him therefrom. For as soon as a portion of time is actualized, another portion passes away. Similarly the succession of accidents, which attach themselves to matter, goes on, in his opinion, to infinity, without an absurdity necessarily following for him from this assertion. For the accidents do not all exist simultaneously, but in succession; and the impossibility of this has not been demonstrated. As for the Mutakallimūn, there is no difference, in their opinion, between saying that a certain infinite magnitude exists and saying that bodies and time are liable to be divided to infinity. There likewise is no difference, in their opinion, between asserting the simultaneous existence of things infinite in number, arranged, [at the same time] in orderly fashion—your saying this, for instance, as it were, about the human individuals existing at present—or your asserting that things infinite in number came into existence, but passed away one after the other. It is as if you said: Zayd is the son of Umar, Umar is the son of Khālid, Khālid is the son of Bakr, and so forth to infinity. This position is likewise absurd according to them, just as the first was. Thus these four divisions of the infinite are equivalent according to them. Some of them wish, in a way that I shall explain to you in the present Treatise, to establish the correctness of the last of these divisions—I mean to say, they wish to make clear its impossibility. Others say that this impossibility is self-evident for the intellect through the spontaneous perception of the mind and that it does not require demonstration. Now if it is a clear absurdity that things infinite in number should exist successively, even though those of them that exist at present are finite in number, the eternity of the world can be considered [117a] through the spontaneous perception of the mind as absurd. And there is no need in any respect for any other premise. However, this is not the place for the investigation of this subject.

THE TWELFTH PREMISE

This is their saying that the senses do not always procure certain knowledge. For the Mutakallimūn have been suspicious with regard to the apprehension of the senses on two counts. One of them arises from the fact that, as they say, the senses miss many of the objects of their sensations either because of the subtlety of the body of the object of apprehension—as they mention with regard to the atoms and what pertains to them, as we have made clear—or because of the distance of the objects of apprehension from the apprehending subject. Thus a man does not see, hear, and smell at a distance extending to several parasangs, and it is impossible to apprehend the motion of the heaven. The second count arises from their saying that the senses can be mistaken with regard to the object of their apprehension. Thus a man, when he is far off, sees a big thing as small; a small thing as big, if it is in water; and a crooked thing as straight, if part of it is in water and part of it outside. Similarly someone suffering from jaundice sees things as yellow, and one whose tongue is steeped with yellow bile tastes sweet things as bitter. They enumerate many things of that kind. They say: for this reason the senses should not be trusted to the extent of adopting them as the principles of demonstration. Do not think that agreement of the Mutakallimūn in affirming this premise is gratuitous. That would be similar to the belief35 of the majority of the later Mutakallimūn that the wish of their predecessors to establish the existence of the indivisible particle did not correspond to a need. In fact, all their assertions that we have set forth in the foregoing passages are necessary; and if one premise were to be destroyed, the whole purpose would be destroyed. Indeed this [117b] last of the premises is most necessary. For whenever we apprehend with our senses things controverting their assumptions, they are able to say: no attention should be paid to the senses as the matter—which, as they think, has been proven by the testimony of the intellect—is demonstrated. This is the case with regard to their claim that continuous motion is interrupted by units of rest, with regard to their other claim that the millstone undergoes a division when revolving, and with regard to still another claim of theirs that the whiteness of this garment has become nonexistent at this instant and that this whiteness is another whiteness. These are assertions that run counter to what can be seen. There are furthermore many things necessarily following from the existence of vacuum, all of which are contradicted by the senses. Consequently the answer to all this is, when this answer is possible, that the particular thing one is concerned with has been missed by the senses. In other cases, the answer is given that it is one of the errors of the senses. You already know that all these are ancient opinions, which had been held by the Sophists. About the latter, Galen, in his book “On the Natural Faculties,”36 states that they taxed the senses with lying and relates everything that you already know.³⁷

After having prefaced these premises, I shall begin to make clear their methods with regard to the four above-mentioned problems.