Chapter VI. On the part of logic which certifies the incomplex, and on the requirements for true definition, its faults, and the modes of definition.

for thus act would be signified to precede potency in the same thing, which never happens in any being of a defined thing in which there is potency and act. For in all such things potency immediately precedes act, and therefore through such a definition the being of the defined thing would not be declared as it is. And an example of this is if I were to say that man is living, rational, sensible.

The fourth fault is that the first defining element is not known through itself in substance and power. And this happens in four ways, because a thing is defined either through that which is the same, or through what is equally unknown, or through what is more unknown than it, or through that which cannot be known except through the thing defined, or through that which is known through another. Through that which is the same: the example is as when time is defined as the measure of motion; for what is said of time is said of the measure of motion, because time is nothing other than the measure of motion, and he who is ignorant of time is ignorant of that which is the measure of motion. But when it is defined through what is equally unknown, it is as when whiteness is defined through that which is being contrary to blackness; for it is equally unknown what whiteness is and what its contrary is, namely blackness. And so it is concerning the definition of relatives through one another, as will be manifest below in what follows ¹. But concerning that which is more unknown, the example is as one who defines fire, saying that fire is a thing among bodies most similar to spirit or soul; for he defines fire through soul, which is more unknown than fire by substance and definition. Concerning the case in which a thing is defined through that which cannot be known except through the thing defined, the example is as one who defines the sun, saying that the sun is a planet making the day by its illumination. For since day is the stay of the light of the sun over our hemisphere, it is agreed that the illumination of the day is known through the thing defined; and thus the definition will be circular, which is very unsuitable ². But all agree in one point, namely that the thing is defined through that which ought to be known through another; for in this way it will never stand, but will always be defined through another, and one will go into infinity.

The fifth fault is that the definition does not state the whole being of the thing defined. For if it did not state and explain the whole, it would not state what the being of the defined thing is, and it would certify the defined thing only in part. As one defining triangle says that a triangle is a figure of three angles having three angles equal to two right angles. For since it is not placed in the definition that a triangle is a rectilinear figure having three angles equal to two right angles, the whole being of the defined thing is not stated; for it can be a figure of three angles having three angles greater than three right angles, if the triangular figure is composed from arcs. The stated definition also errs from another cause, because it posits what is not essential to the thing defined. For having three angles equal to two right angles is not the essential constituent of a rectilinear triangle, but is a property consequent upon the essence of the thing defined. Another example of the same, and one more suitable than the one which is stated, is that a circle is a plane figure contained by one line. For this definition does not state the whole being of the thing defined, because it makes no mention of that which is the formal principle of a circle and from which it is produced, that is, of the center. Therefore it will be perfect if it is stated thus: a circle is a plane figure contained by one line, in the middle of which there is a point from which all lines drawn to the circumference continuously and directly are equal. Therefore these are the things which must be attended to and avoided in definitions, if the thing defined ought to be certified through definition.

There are, however, certain other notifications, not proper definitions, sometimes given through matter, sometimes assigned through the efficient cause alone. Unless these are reduced to definitions which are given through genus and essential differences, they cannot be called definitions, but notifications of whatever sort. But they are reduced in this way: matter is not taken as simple matter, but insofar as it is the first potency toward being. For thus it is taken according as in it the essential form is already begun, and in that formal power the constituting and dividing differences are begun. As if it is said that man is constituted from body and rational soul; then body is not taken as freed from form, but rather is called animated sensible body; and this animated sensible body is that from whose potency and beginning rational is produced. And thus it returns to that definition which is from genus and difference, because animated sensible body is animal, and animated by a rational soul is rational. But the definition which is given through the efficient cause is as if it is said that man is what is generated by man. For then the agent is not taken as efficient only, but as agent according to form and univocally. But a univocal agent gives form according as it goes out from formal potency to act. Hence what is generated by man is not living and animal at the same time, nor animal and man at the same time according to act, but first living in act and sensible in potency, and second sensible in act and rational in potency. And also the definition given through the efficient cause is reduced to that which is from genus and difference. If the efficient cause is taken otherwise, it will be of the essence of the thing defined and will not certify it.

But every other declaration of the incomplex which is made through accidental things is not a definition, but is called a description. Such a declaration ought not be made through common accidental things, because these are not convertible, but through proper accidental things, because concerning these is understood what Aristotle says ³, that accidents or cognition of accidents contribute in the greatest part to knowing what a thing is. For these are accidents of nature, and proceed from the aptitude of that very nature, and therefore make known the substance, just as often what is prior is known through what is posterior, not simply, but with respect to us. But this will be manifest in what follows. Nevertheless the logician uses such things in receiving knowledge of the unknown, just as he also uses other argumentations in receiving knowledge of the complex, which certify less than syllogism.

But the logician uses other declarations whenever they are of greater declaration than the name itself or the incomplex diction whose knowledge he seeks. Although they do not perfectly certify, nevertheless in some way they declare that which is sought. And because, as Ptolemy says, he is foolish who, when he cannot perfectly know what he seeks, rejects that through which he can know by conjecturing concerning the thing sought. Therefore it belongs to the logician to give rules and principles of such things for cognition of the incomplex, through which he may begin from principles known through themselves and come into cognition of the things which are sought. For not all things can be unknown, because thus by seeking one would proceed into infinity ⁴. For the first principles are like seeds inserted by nature into the cognition of man, from which, as from seeds, great fruits of the sciences arise concerning those things which are known through them. For when first things have been posited through division, it is known what is in potency in them. And division also leads through to the last; for this reason the very science of division is necessary for the logician, as Boethius says.