Isagoge Philosophica

One further point must not be passed over: universal things have a twofold unity, one usually called formal unity and the other, in our present terminology, called unity of precision.

Formal unity is nothing other than the indivision of a universal thing in itself—that is, in its nature or account. Such is the indivision of animal insofar as it is animal, and of man insofar as he is man. The senate, the people, and a team of four horses are not indivisible in this way, because in their accounts they are divided and many even in actuality. This unity is called formal because it is communicable to many, just as the universal thing itself, of which it is the unity, is communicable and is its first property.

Unity of precision, by contrast, is the indivision of a universal thing not in itself but in its particulars. Such is the indivision of animal in man and beast, and of man in Socrates and the other individual men. It is called unity of precision because it does not belong to a universal thing in whatever state it is taken. Formal unity belongs to it in every state: before it is contracted to its particulars, while it is already contracted in them, and after it has been abstracted from them and, as it were, plucked away by the intellect. Unity of precision belongs to it only in the state in which it is apt to descend to its particulars and be divided and multiplied in them. For insofar as a thing is apt to be in many and to be divided among them and called many, but has not yet been divided and multiplied in the order of nature, it is individed in relation to them and therefore one by this unity of precision. But if it is taken as it already exists in its particulars, divided and countable in them, it is already many, not one, by this kind of unity.

These two kinds of unity differ chiefly in three respects. First, formal unity is a property of universal things insofar as they are things; unity of precision is a property of them insofar as they are universal, that is, insofar as they are apt to be in many. For the whole essence of universality lies in this aptitude, to the extent that it can be called an essence.

Accordingly, in the earlier definition in which the universal is said to be one thing apt to be in many, the word “one,” which is put in place of the genus and stands for the thing underlying universality, is to be understood as formal unity—or rather as unity common to formal unity and the numerical unity of singular things. Unity of precision is not expressed in that definition, but it necessarily follows from the aptitude to be in many, which completes the account of universality. For, as we just said, while a thing retains its aptitude to be in many, it remains undivided into many and therefore one by this kind of unity.

They also differ in that formal unity is an indivision that is purely negative, whereas unity of precision is privative.

Formal unity presupposes no aptitude in the universal thing to be many within itself: what is undivided in itself cannot in any way be divided in itself. Unity of precision, however, presupposes an aptitude by which a universal thing can be divided and multiplied in its particulars. In the same way, we say that a stone’s lack of sight is a pure negation, because a stone has no aptitude for seeing; but a blind man’s lack of sight is a privation, because a man is by nature apt to see.

Finally, they differ in this: formal unity is multiplied along with the universal things themselves in their particulars, whereas unity of precision is not. There are as many formal unities of the nature of animal in particular animals, and of human nature in individual human beings, as there are particular animals and individual human beings. But there is only one unity of precision for one common nature taken in its commonness, which does not descend together with that commonness into its particulars. This difference shows that formal unity is itself universal, just as the thing whose unity it is is universal; unity of precision is singular, just as the aptitude it presupposes and follows is singular. Hence it is only by unity of precision that we can say animal is one genus in number and man one species in number, and that the number of primary objects of our intellect is the same as the number of universal things.

Since unity taken generally is divided into formal and numerical unity, and formal unity belongs properly to universal things taken absolutely, while unity of precision is their numerical unity insofar as they are universal, it remains that numerical unity taken simply and absolutely belongs properly and peculiarly to singular things. This will suffice for what we have said in general about the five species or forms of universals.

We must now treat each one separately, but first let us warn readers that whatever in this little book has been said so far, or will be said later, that seems harder to understand is not to be explained more precisely here by teachers, still less debated at length and in detail. It should be presented through familiar examples and provisionally taken on trust, so that it may help students understand what is taught throughout the course of philosophy. If students wholly fail to grasp these matters, they will often be led astray and stumble midway through the course. But if they are burdened at the very outset with long and weighty debates so that they may understand them more deeply, they lose heart and give up their undertaking under something like compulsion; or at least they become so weary and disheartened that, needing still greater support in philosophy, they do not finally understand these matters and approach what follows with less interest and zeal. It will therefore be enough at this stage to grasp them as best one can, commit them to memory, and hold them largely on the authority of teachers until they are explained more clearly in their proper places. For, as Aristotle teaches, the learner must believe; this is especially clear of those who are at the very beginnings of the sciences. The same rule should be observed in the treatment of the categories, in the account of future contingents given in On Interpretation, and in similar places. To demand that minds still untrained and little practiced reduce all these matters, as the saying goes, to exact calculation, and to require a precise account of them from new students, is quite inept and unbecoming. It is disgraceful to demand from beginners what even veterans often scarcely manage to provide adequately.

But now let us say what genus is and what force it has.