Section 6

The term one is used (1.) in an accidental, (2.) in an absolute sense. (1.) In the accidental sense it is used as in the case of Coriscus 1 and cultured and cultured Coriscus (for Coriscus and cultured and cultured Coriscus mean the same);

and cultured and upright and cultured upright Coriscus. For all these terms refer accidentally to one thing; upright and cultured because they are accidental to one substance, and cultured and Coriscus because the one is accidental to the other.

And similarly in one sense cultured Coriscus is one with Coriscus, because one part of the expression is accidental to the other, e.g. cultured to Coriscus; and cultured Coriscus is one with upright Coriscus,

because one part of each expression is one accident of one and the same thing. It is the same even if the accident is applied to a genus or a general term; e.g., man and cultured man are the same, either because cultured is an accident of man, which is one substance, or because both are accidents of some individual, e.g. Coriscus.

But they do not both belong to it in the same way; the one belongs presumably as genus in the substance, and the other as condition or affection of the substance. Thus all things which are said to be one in an accidental sense are said to be so in this way.

(2.) Of those things which are said to be in themselves one, (a) some are said to be so in virtue of their continuity; e.g., a faggot is made continuous by its string, and pieces of wood by glue; and a continuous line, even if it is bent, is said to be one, just like each of the limbs; e.g. the leg or arm. And of these things themselves those which are naturally continuous are one in a truer sense than those which are artificially continuous.

Continuous means that whose motion is essentially one, and cannot be otherwise; and motion is one when it is indivisible, i.e. indivisible in time . Things are essentially continuous which are one not by contact only; for if you put pieces of wood touching one another you will not say that they are one piece of wood, or body, or any other continuous thing.

And things which are completely continuous are said to be one even if they contain a joint, and still more those things which contain no joint; e.g., the shin or the thigh is more truly one than the leg, because the motion of the leg may not be one.

And the straight line is more truly one than the bent. We call the line which is bent and contains an angle both one and not one, because it may or may not move all at once; but the straight line always moves all at once, and no part of it which has magnitude is at rest while another moves, as in the bent line.

(b) Another sense of one is that the substrate is uniform in kind.

Things are uniform whose form is indistinguishable to sensation; and the substrate is either that which is primary, or that which is final in relation to the end. For wine is said to be one, and water one, as being something formally indistinguishable. And all liquids are said to be one (e.g. oil and wine), and melted things; because the ultimate substrate of all of them is the same, for all these things are water or vapor.

(c) Things are said to be one whose genus is one and differs in its opposite differentiae. All these things too are said to be one because the genus, which is the substrate of the differentiae, is one (e.g., horse, man and dog are in a sense one, because they are all animals); and that in a way very similar to that in which the matter is one.

Sometimes these things are said to be one in this sense, and sometimes their higher genus is said to be one and the same (if they are final species of their genus)—the genus, that is, which is above the genera of which their proximate genus is one; e.g., the isosceles and equilateral triangles are one and the same figure (because they are both triangles), but not the same triangles.

(d) Again, things are said to be one when the definition stating the essence of one is indistinguishable from a definition explaining the other; for in itself every definition is distinguishable 〈into genus and differentiae〉. In this way that which increases and decreases is one, because its definition is one; just as in the case of planes the definition of the form is one.

And in general those things whose concept, which conceives the essence, is indistinguishable and cannot be separated either in time or in place or in definition, are in the truest sense one; and of these such as are substances are most truly one. For universally such things as do not admit of distinction are called one in so far as they do not admit of it; e.g., if man qua man does not admit of distinction, he is one man; and similarly if qua animal, he is one animal; and if qua magnitude, he is one magnitude.

Most things, then, are said to be one because they produce, or possess, or are affected by, or are related to, some other one thing; but some are called one in a primary sense, and one of these is substance. It is one either in continuity or in form or in definition; for we reckon as more than one things which are not continuous, or whose form is not one, or whose definition is not one.

Again, in one sense we call anything whatever one if it is quantitative and continuous; and in another sense we say that it is not one unless it is a whole of some kind, i.e. unless it is one in form (e.g., if we saw the parts of a shoe put together anyhow, we should not say that they were one — except in virtue of their continuity; but only if they were so put together as to be a shoe, and to possess already some one form).

Hence the circumference of a circle is of all lines the most truly one, because it is whole and complete.

The essence of one is to be a kind of starting point of number; for the first measure is a starting point, because that by which first we gain knowledge of a thing is the first measure of each class of objects. The one, then, is the starting-point of what is knowable in respect of each particular thing. But the unit is not the same in all classes,

for in one it is the quarter-tone, and in another the vowel or consonant; gravity has another unit, and motion another. But in all cases the unit is indivisible, either quantitatively or formally.

Thus that which is quantitatively and qua quantitative wholly indivisible and has no position is called a unit; and that which is wholly indivisible and has position, a point; that which is divisible in one sense, a line; in two senses, a plane; and that which is quantitatively divisible in all three senses, a body.

And reversely that which is divisible in two senses is a plane, and in one sense a line; and that which is in no sense quantitatively divisible is a point or a unit; if it has no position, a unit, and if it has position, a point.

Again, some things are one numerically, others formally, others generically, and others analogically; numerically, those whose matter is one; formally, those whose definition is one; generically, those which belong to the same category; and analogically, those which have the same relation as something else to some third object.

In every case the latter types of unity are implied in the former: e.g., all things which are one numerically are also one formally, but not all which are one formally are one numerically; and all are one generically which are one formally, but such as are one generically are not all one formally, although they are one analogically; and such as are one analogically are not all one generically.

It is obvious also that many will have the opposite meanings to one. Some things are called many because they are not continuous; others because their matter (either primary or ultimate) is formally divisible; others because the definitions of their essence are more than one.