Lecture 21 — “To come from something,” “part,” “whole,” and “mutilated”

“To come from something” means in one sense to come from something as matter, and this in two ways:

in reference either to the first genus or to the ultimate species; for example, all liquefiable things come from water, and a statue comes from bronze.

And in another sense it means to come from a thing as a first moving principle. For example, from what did the fight come? From a jeer, because this was the cause of the fight.

In another sense it means to come from the composite of matter and form, as parts come from a whole, and a verse from the Iliad, and stones from a house.

For the form is an end or goal, and what is in possession of its end is complete. And one thing comes from another in the sense that a species comes from a part of a species, and man from two-footed, and a syllable from an element.

For this is different from the way in which a statue comes from bronze, because a composite substance comes from sensible matter, but a species also comes from the matter of a species.

These are the senses, then, in which some things are said to “come from” something.

But other things are said to come from something if they come from a part of that thing in any of the aforesaid senses.

For example, a child comes from its father and mother, and plants come from the earth, because they come from some part of them.

And some things come from others only because they come one after the other in time, as night comes from day, and a storm from a calm.

And some of these are so described only because they admit of change into each other, as in the cases just mentioned, and some only because they follow one another in time, as a voyage is made from the equinox because it takes place after the equinox.

And feasts come one from another in this way, as the Thargelian from the Dionysian, because it comes after the Dionysian.

“Part” means in one sense that into which a quantity is divided in any way, for what is subtracted from a quantity is always called a part of it. For example, the number two is said in a sense to be a part of the number three.

And in another sense “part” means only such things as measure a whole. And for this reason the number two is said in a sense to be a part of the number three, and in another, not.

Again, those things into which a species is divided irrespective of quantity are also called parts of this species, and it is for this reason that species are said to be parts of a genus.

Again, “parts” means those things into which a whole is divided or of which a whole is composed, whether the whole is a species or the thing having the species, as bronze is a part of a bronze sphere or of a bronze cube (for this is the matter in which the form inheres). An angle also is a part.

And those elements contained in the intelligible expression, which manifests what each thing is, are also parts of a whole. And for this reason the genus is also called a part of the species, although in another respect the species is called a part of the genus.

“Whole” means that from which none of the things of which it is said to consist by nature are missing, and that which contains the things contained in such a way that they form one thing.

But this occurs in two ways: either inasmuch as each is the one in question, or inasmuch as one thing is constituted of them.

For a whole is a universal, or what is predicated in general as being some one thing as a universal is one, in the sense that it contains many things, because it is predicated of each, and all of them taken singly are that one thing, as man, horse, and god, because all are living things.

A whole is something continuous and limited when one thing is constituted of many parts which are present in it, particularly when they are present potentially; but if not, even when they are present in activity.

And of these same things, those which are wholes by nature are such to a greater degree than those which are wholes by art, as we also say of a thing that is one (1015b36; [848]), inasmuch as wholeness is a kind of unity.

Again, since a quantity has a beginning, a middle point, and an end, those quantities to which position makes no difference we designate by the term “all,”

but those to which position makes a difference we designate by the term “whole.”

and those to which both descriptions apply we designate by both terms—all and whole.

Now these are the things whose nature remains the same in being rearranged but whose shape does not, as wax and a garment; for both “all” and “whole” are predicated of them, since they verify both. But water and all moist things and number have “all” applied to them, although water and number are called wholes only in a metaphorical sense. But those things of which the term “every” is predicated with reference to one have the term “all” predicated of them with reference to several—for example, all this number, all these units.

It is not any quantity at all that is said to be “mutilated,” but it must be a whole and also divisible into parts. For two things are not mutilated when one is taken away from the other, because the mutilated part is never equal to the remainder. And in general no number is mutilated, for its substance must remain. If a goblet is mutilated, it must still be a goblet; but a number is not the same when a part is taken away. Again, all things composed of unlike parts are not said to be mutilated. For a number is like something having unlike parts, as two and three. And in general those things to which position makes no difference, such as water and fire, are not mutilated; but they must have position in their substance. And they must be continuous, for a harmony is made up of unlike parts and has position but is not mutilated.

Further, neither is every whole mutilated by the privation of every part. For the parts which are removed must not be things that are proper to the substance or things that exist anywhere at all.

For example, a goblet is not mutilated if a hole is made in it, but only if an ear or some extremity is removed; and a man is not mutilated if his flesh or spleen is removed, but only if an extremity is removed.

And this means not any extremity whatever, but those which cannot regenerate when removed from the whole. Hence to have one’s head shaven is not a mutilation.

“Part”

1085. Here he begins to treat the things that pertain to the notion of whole and part.

First, he deals with those which pertain to the notion of part;

and second (1023b26; [1098]), with those which pertain to the notion of whole, at “whole” means.

And because a whole is constituted of parts, he therefore does two things in dealing with the first member of this division.

First, he explains the various ways in which a thing is said to come from something;

second (1023b12; [1093]), he considers the different senses in which the term part is used, at “part” means.

In regard to the first he does three things.

First, he considers the ways in which a thing is said to come from something in the primary and proper sense.

Second [1090], he indicates the ways in which one thing comes from another but not in the primary sense, at but other things.

Third [1091], he considers the ways in which one thing comes from another but not in the proper sense, at and some things.

In dealing with the first part he gives four ways in which a thing is said to come from something.

First, a thing is said to come from something as from matter, and this can happen in two ways.

In one way, inasmuch as matter is taken to be the matter of the first genus (that is, common matter), as water is the matter of all liquids and liquables, all of which are said to come from water.

In another way, in reference to the ultimate species (that is, the lowest species), as the species of statue is said to come from bronze.

1086. In a second way a thing is said to come from something as from a first moving principle, as a fight comes from a jeer, which is the principle moving the soul of the taunted person to fight. And it is in this way too that a house is said to come from a builder, and health from the medical art.

1087. In a third way, one thing is said to come from another as something simple comes from the composite of matter and form. This pertains to the process of dissolution, and it is in this way that we say parts come from a whole, and a verse from the Iliad (that is, from the whole treatise of Homer about Troy). For the Iliad is divided into verses as a whole is divided into parts. And it is in the same way that stones are said to come from a house.

The reason for this is that the form is the goal or end in the process of generation, for it is what has attained its end that is said to be perfect or complete, as was explained above (1021b23; [1039]). Hence it is evident that that is perfect which has a form.

Therefore, when a perfect whole is broken down into its parts, there is motion in a sense from form to matter; and in a similar way when parts are combined, there is an opposite motion from matter to form. Hence the preposition “from,” which designates a beginning, applies to both processes: both to the process of composition (because it signifies a material principle), and to that of dissolution (because it signifies a formal principle).

1088. In a fourth way, a thing is said to come from something as a species comes from a part of a species.

And “part of a species” can be taken in two ways: in reference either to the conceptual order or to the real order.

It is taken in reference to the conceptual order when we say (for example) that two-footed is a part of man, because while it is part of his definition, it is not a real part, otherwise it would not be predicated of the whole. For it is proper to the whole man to have two feet.

And it is taken in reference to the real order when we say (for example) that a syllable comes from an element, or letter, as from a part of the species. But here the fourth way in which the term is used differs from the first. In the first way, a thing was said to come from a part of matter, as a statue comes from bronze. For this substance—a statue—is composed of sensible matter as a part of its substance. But this species is composed of part of the species.

1089. For some parts are parts of a species and some are parts of matter.

Those which are called parts of a species are those on which the perfection of the species depends and without which it cannot be a species. And it is for this reason that such parts are placed in the definition of the whole, as body and soul are placed in the definition of an animal, and an angle in the definition of a triangle, and a letter in the definition of a syllable.

And those parts which are called parts of matter are those on which the species does not depend but are in a sense accidental to the species—for example, it is accidental to a statue that it should come from bronze or from any particular matter at all. And it is also accidental that a circle should be divided into two semi-circles, and that a right angle should have an acute angle as part of it.

Parts of this sort, then, are not placed in the definition of the whole species but rather the other way around, as will be shown in book 7 of this work [1542]. Hence it is clear that in this way some things are said to come from others in the primary and proper sense.

1090. But some things are said to come from something not in the primary sense but according to a part of that thing in any of the aforesaid senses. For example, a child is said to come from its father as an efficient principle, and from its mother as matter, because a certain part of the father (the sperm) causes motion and a certain part of the mother has the character of matter (the menstrual fluid). And plants come from the earth, although not from the whole of it but from some part.

1091. And in another way a thing is said to come from something in an improper sense, namely, from the fact that this implies order or succession alone. In this way one thing is said to come from another in the sense that it comes after it, as night comes from day (that is, after the day), and a storm from a calm (that is, after a calm). And this is said in reference to two things.

For in those cases in which one thing is said to come from another, order is sometimes noted in reference to motion and not merely to time. For either they are the two extremes of the same motion, as when it is said that white comes from black, or they are a result of different extremes of the motion, as night and day are a result of different locations of the sun. And the same thing applies to winter and summer. Hence in some cases one thing is said to come from another because one is changed into the other, as is clear in the above examples.

1092. But sometimes order or succession is considered in reference to time alone; for example, it is said that a voyage is made from the equinox, that is, after the equinox. For these two extremes are not extremes of a single motion, but pertain to different motions. And similarly it is said that the Thargelian festival comes from the Dionysian because it comes after the Dionysian. (These are two feasts which were celebrated among the gentiles, one of which preceded the other in time.)

1093. “Part” means (1023b12). He now gives four senses in which something is said to be a part.

In one sense, “part” means that into which a thing is divided from the viewpoint of quantity, and this can be taken in two ways.

For in one way, no matter how much smaller that quantity may be into which a larger quantity is divided, it is called a part of this quantity. For anything that is taken away from a quantity is always called a part of it—for example, the number two is in a sense a part of the number three.

And, in another way, only a smaller quantity which measures a larger one is called a part. In this sense the number two is not a part of the number three, but a part of the number four, because two times two equals four.

1094. In a second sense, “parts” means those things into which something is divided irrespective of quantity, and it is in this sense that species are said to be parts of a genus. For a genus is divided into species, but not as a quantity is divided into quantitative parts. For a whole quantity is not in each one of its parts, but a genus is in each one of its species.

1095. In a third sense, “parts” means those things into which some whole is divided or of which it is composed, whether the whole is a species or the thing having a species (the individual). For, as has been pointed out already [1089], there are parts of the species and parts of matter, and these (species and matter) are parts of the individual. Hence bronze is a part of a bronze sphere or of a bronze cube as the matter in which the form is received, and thus bronze is not a part of the form, but of the thing having the form. And a cube is a body composed of square surfaces. And an angle is part of a triangle as part of its form, as has been stated above [1099].

1096. In a fourth sense, “parts” means those things that are placed in the definition of anything, and these are parts of its intelligible structure—for example, animal and two-footed are parts of man.

1097. From this it is clear that a genus is part of a species in this fourth sense, but that a species is part of a genus in a different sense, in the second sense. For in the second sense, a part was taken as a subjective part of a universal whole, whereas in the other three senses, it was taken as an integral part. And in the first sense it was taken as a part of quantity, and in the other two senses as a part of substance, yet in such a way that a part in the third sense means a part of a thing (whether it be a part of the species or of the individual). But in the fourth sense, it is a part of the intelligible structure.

“Whole”

1098. “Whole” means (1023b26). He proceeds to treat the things that pertain to a whole.

First, he considers a whole in a general way;

second (1024a29; [1119]), he deals with a particular kind of whole, namely, a genus, at the term “genus.”

In regard to the first part he does two things.

First, he proceeds to deal with the term “whole”;

second (1024a11; [1109]), with its opposite, “mutilated,” at it is not any quantity at all.

In regard to the first he does three things.

First, he states the common meaning of “whole,” which involves two things.

The first is that the perfection of a whole is derived from its parts. He indicates this when he says a whole means that from which none of the things—that is, the parts—of which it is said to consist by nature—that is, of which the whole is composed according to its own nature—are missing.

The second is that the parts become one in the whole. Thus he says that a whole is that which contains the things contained, namely, the parts, in such a way that the things contained in the whole are some one thing.

1099. But this occurs (1023b28). Second, he notes two ways in which a thing is a whole. He says that a thing is said to be a whole in two ways.

First, in the sense that each of the things contained by the containing whole is the one in question, that is, the containing whole, which is in the universal whole that is predicated of any one of its own parts.

Second, in the sense that it is one thing composed of parts in such a way that none of the parts are that one thing. This is the notion of an integral whole, which is not predicated of any of its own integral parts.

1100. For a whole (1023b29). Third, he explains the foregoing senses of “whole.”

First, he explains the first sense. He says that a whole is a universal or what is predicated in general, that is, a common predicate, as being some one thing—just as the universal, which contains many parts, is predicated of each of its parts. And all of these are one in a universal whole in such a way that each of them is that one whole. For example, “living thing” contains man and horse and god, because all are living things, since “living thing” is predicated of each. By a “god” he means here a celestial body, such as the sun or the moon, which the ancients said were living bodies and considered to be gods. Or he means certain ethereal living beings, which the Platonists called demons, and which were worshipped by the pagans as gods.

1101. A whole is something (1023b32). Second, he explains the meaning of “whole” in the sense of an integral whole; and in regard to this he does two things.

First, he gives the common meaning of this kind of whole, and particularly of that which is divided into quantitative parts, which is more evident to us. He says that a whole is something continuous and limited, perfect or complete. For what is unlimited does not have the character of a whole, but of a part, as is said in Physics 3, when one thing is composed of many parts which are present in it. He says this in order to exclude the sense in which one thing comes from another as from a contrary.

1102. Now the parts of which a whole is composed can be present in it in two ways: in one way potentially, and in another actually.

Parts are potentially present in a whole which is continuous, and actually present in a whole which is not continuous, as stones are actually present in a heap. But that which is continuous is one to a greater degree, and therefore is a whole to a greater degree, than that which is not continuous. Hence he says that parts must be present in a whole, especially potential parts, as they are in a continuous whole; and if not potentially, then at least in activity, or actually. For “activity” means interior action.

1103. Now, although a thing is a whole to a greater degree when its parts are present potentially than when they are present actually, nonetheless if we look to the parts, they are parts to a greater degree when they exist actually than when they exist potentially.

Hence another text reads, especially when they are present perfectly and actually; but otherwise, even when they are present potentially. And it also adds the words given above: particularly when they are present potentially; but if not, even when they are present in activity.

Hence it seems that the translator found two texts, which he translated, and then made the mistake of combining them so as to make one text. This is clear from another translation, which contains only one of these statements; for it reads as follows: and a whole is continuous and limited when some one thing is composed of many intrinsic parts, especially when they are present potentially; but if not, when they are present actually.

1104. And of these same things (1023b34). Second, he indicates two differences within this second sense of “whole.”

The first is that some continuous things are such by art and some by nature. Those which are continuous by nature are such (wholes), to a greater degree than those which are such by art. And since we spoke in the same way above [848] about things that are one, saying that things that are continuous by nature are one to a greater degree (as though wholeness were oneness), it is clear from this that anything which is one to a greater degree is a whole to a greater degree.

1105. Again, since a quantity (1024a1). He gives the second difference. For since it is true that there is an order of parts in quantity, because a quantity has a beginning, a middle point, and an end, and the notion of position involves these, the positions of the parts in all these quantities must be continuous. But if we consider the position of the parts, a whole is found to be continuous in three ways. For there are some wholes which are unaffected by a difference of position in their parts. This is evident in the case of water, for it makes no difference how the parts of water are interchanged. The same thing is true of other liquids, as oil and wine and the like. And in these things, a whole is signified by the term “all” and not by the term “whole.” For we say all the water or all the wine or all the numbers, but not the whole, except metaphorically. (This perhaps applies to the Greek idiom, but in Latin it is a proper way of speaking.)

1106. And there are some things to which the position of the parts does make a difference—for example, a man and any animal and a house and the like. For a thing is not a house if its parts are arranged in just any way at all, but only if they have a definite arrangement; and of these we use the term “whole” and not the term “all.” And similarly a thing is not a man or an animal if its parts are arranged in just any way at all. For when we speak of only one animal, we say “the whole animal,” and not “all the animal.”

1107. And there are some things to which both of these apply, because in a sense the position of their parts accounts for their differences. Of these we use both terms (“all” and “whole”). And these are the things in which the matter, but not the form or shape, remains the same when the parts are interchanged.

This is clear, for example, in the case of wax, for no matter how its parts are interchanged, the wax still remains, but it does not have the same shape. The same is true of a garment and of all things that have like parts and take on a different shape. For even though liquids have like parts, they cannot have a shape of their own, because they are not limited by their own boundaries, but by those of other things. Hence when their parts are interchanged, no change occurs in anything that is proper to them.

1108. The reason for this difference is that the term “all” is distributive and therefore requires an actual multitude or one in proximate potency to act. And because those things have like parts, they are divided into parts entirely similar to the whole, and in that manner multiplication of the whole takes place.

For if every part of water is water, then in each part of water there are many waters, although they are present potentially, just as in one number there are many units actually. But “a whole” signifies a collection of parts into some one thing; therefore, in those cases in which the term “whole” is properly used, one complete thing is made from all the parts taken together, and the perfection of the whole belongs to none of the parts. A house and an animal are examples of this. Hence, “every animal” is not said of one animal, but of many.

Therefore, at the end of this part of his discussion he says that those wholes of which the term “every” is used—as is done of one thing when reference is made to a whole—can have the plural term “all” used of them, as is done of several things when reference is made to them as parts.

For example, one says “all this number,” and “all these units,” and “all this water,” when the whole has been indicated, and “all these waters” when the parts have been indicated.

1109. It is not any quantity (1024a11). Here he clarifies the issue about the opposite of “whole,” which is “mutilated.” In place of this, another translation reads diminished by a member, but this translation does not always fit. For the term “mutilated” is used only of animals, which alone have members. Now “mutilated” seems to mean “cut off,” and thus Boethius translated it maimed, that is, “defective.” Hence the Philosopher’s aim here is to show what is required in order that a thing may be said to be mutilated.

First, he gives what is required on the side of the whole;

second (1024a22; [1117]), what is required on the side of the part which is missing, at further, neither.

1110. Now in order that a whole can be said to be mutilated, seven things are required.

First, the whole must be a quantified being having parts into which it may be divided quantitatively. For a universal whole cannot be said to be mutilated if one of its species is removed.

1111. Second, not every kind of quantified being can be said to be mutilated, but it must be one that is divisible into parts, that is, capable of being separated, and be a whole, something composed of different parts. Hence the ultimate parts into which any whole is divided, such as flesh and sinew, cannot be said to be mutilated even though they have quantity.

1112. Third, two things are not mutilated—that is, anything having two parts—if one of them is taken away from the other. And this is true because a mutilated part, whatever is taken away from the mutilated thing, is never equal to the remainder, but the remainder must always be larger.

1113. Fourth, no number can be mutilated, no matter how many parts it may have, because the substance of the mutilated thing remains after the part is taken away. For example, when a goblet is mutilated it still remains a goblet, but a number does not remain the same no matter what part of it is taken away. For when a unit is added to or subtracted from a number, it changes the species of the number.

1114. Fifth, the thing mutilated must have unlike parts. For those things that have like parts cannot be said to be mutilated, because the nature of the whole remains verified in each part. Hence, if any of the parts are taken away, the others are not said to be mutilated. Not all things having unlike parts, however, can be said to be mutilated. A number cannot, as has been stated, even though in a sense it has unlike parts—for example, the number twelve has the number two and the number three as parts of it. Yet in a sense every number has like parts because every number is constituted of units.

1115. Sixth, none of those things in which the position of the parts makes no difference can be said to be mutilated—for example, water or fire. For mutilated things must be such that the intelligible structure of their substance contains the notion of a determinate arrangement of parts, as in the case of a man or of a house.

1116. Seventh, mutilated things must be continuous. For a musical harmony cannot be said to be mutilated when a note or a chord is taken away, even though it is made up of low- and high-pitched sounds, and even though its parts have a determinate position. For it is not any low- and high-pitched sounds arranged in any way at all that constitute such a harmony.

1117. Further, neither is (1024a22). Then he indicates the conditions which must prevail with regard to the part cut off in order that a thing may be mutilated; there are three of these. He says that just as not every kind of whole can be said to be mutilated, so neither can there be mutilation by the removal of every part.

First, the part which is removed must not be a principal part of the substance—that is, one which constitutes the substance of the thing and without which the substance cannot be—because the thing that is mutilated must remain when a part is removed, as has been stated above [1113]. Hence a man cannot be said to be mutilated when his head has been cut off.

1118. Second, the part removed should not be everywhere, but in some extremity. Thus, if a goblet is perforated about the middle by removing some part of it, it cannot be said to be mutilated. But this is said if someone removes the ear of a goblet, that is, a part which is similar to an ear, or any other extremity. Similarly, a man is not said to be mutilated if he loses some of his flesh from his leg or from his arm or from his waist, or if he loses his spleen or some part of it, but if he loses one of his extremities, such as a hand or a foot.

Third, a thing is not said to be mutilated if just any part that is an extremity is removed, but if it is such a part which does not regenerate if the whole of it is removed, as a hand or a foot. But if a whole head of hair is cut off, it grows again. So if such parts are removed, the man is not said to be mutilated, even though they are extremities. And for this reason people with shaven heads are not said to be mutilated.