Form, not Genus, is Principle
If the universals are always more of the nature of principles, evidently the uppermost of the genera are the principles; for these are predicated of all things. Both being and unity will be principles and substances. But it is not possible that either unity or being should be a single genus of things; for the differentiae of any genus must each of them both have being and be one, but it is not possible for the genus taken apart from its species (any more than for the species of the genus) to be predicated of its proper differentiae; so that if unity or being is a genus, no differentia will either have being or be one.
The differentiae of any genus are other genera, all of which are derived from Unity and Being. It follows that the individual is the opposite of One, for it combines numerous, if not infinite, Forms.
Being and Coming to Be
If there is nothing eternal, neither can there be a process of coming to be; for there must be something that comes to be, since the series has a limit and nothing can come to be out of that which is not. Further, if generation and movement exist there must also be a limit; for no movement is infinite; and that which has completed its coming to be must be.
Beginning is the first point from which a thing either is or comes to be or is known; but of these some are immanent in the thing and others are outside. Hence the nature of a thing is a beginning, and so is the element of a thing, and thought and will, and essence, and the final cause-for the good and the beautiful are the beginning both of the knowledge and of the movement of many things.
(1) continuous generation of the same kind, (2) the first mover which is of the same kind as the things it moves, (3) as matter; for that to which the differentia or quality belongs is the substratum, which we call matter
1) the differentia of essence
As ‘male’ attaches to animal, ‘equal’ to quantity, and ‘odd’ to number, and as all so-called ‘attributes propter se’ attach to their subjects. Such attributes are those in which is involved either the formula or the name of the subject of the particular attribute, and which cannot be explained without this.
2) the sense in which the numbers have a certain quality, e.g. the composite numbers which are not in one dimension only, but of which the plane and the solid are copies (these are those which have two or three factors); and in general that which exists in the essence of numbers besides quantity is quality; for the essence of each is what it is once.
Substance and Individuality
Substance is that which is not predicated of a stratum, but of which all else is predicated; The ultimate substratum is of itself neither a particular thing nor of a particular quantity nor otherwise positively characterized; nor yet is it the negations of these, for negations also will belong to it only by accident; It follows that matter is substance. But this is impossible; for both separability and ‘thisness’ are thought to belong chiefly to substance.
Of the individual substances, whether perceptible or intelligible, of these there is no definition, but they are known by the aid of intuitive thinking or of perception; and when they pass out of this complete realization it is not clear whether they exist or not; but they are always stated and recognized by means of the universal formula. But matter is unknowable in itself.
Being, Individual and Knowledge
Are the substance of all the individuals one?
How does matter become each of the individuals?
How do numbers and spatial magnitude proceed from Unity?
For all things that we come to know, we come to know in so far as they have some unity and identity, and in so far as some attribute belongs to them universally. If the first principles are one in kind only, nothing will be numerically one (that is, there will be no individuals), not even unity-itself and being-itself; and how will knowing exist, if there is not to be something common to a whole set of individuals? But if there is a common element which is numerically one, and each of the principles is one, and the principles are the same in kind (not as in the case of perceptible things different for different things) –if it is not like this but the principles of things are numerically one, there will be nothing else besides the elements.
Thinking or Being Thought
If in relation to that which thinks, man and that which is thought are the same, man will not be that which thinks, but only that which is thought. And if each thing is to be relative to that which thinks, that which thinks will be relative to an infinity of specifically different things.
Parmenides and the Law of Non-Contradiction
If Being and Unity are substances, what is different from being does not exist, so that it necessarily follows, according to the argument of Parmenides, that all things are one and this is being.
If Unity is indivisible, according to Zeno’s postulate, it will be nothing. For that which neither when added makes a thing greater nor when subtracted makes it less, has no being.
If contradictory statements are both true, we get the doctrine of Anaxagoras, that all things are mixed together, so that nothing exists. They seem to be speaking of the indeterminate, and, while fancying themselves to be speaking of being, they are speaking about non-being; for it is that which exists potentially and not in complete reality that is indeterminate. Those who say that things at the same time are and are not, should in consequence say that all things are at rest rather than that they are in movement; for there is nothing into which they can change, since all attributes belong already to all subjects.
All contraries are reducible to being and non-being, and to unity and plurality, as for instance rest belongs to unity and movement to plurality. Being and substance are composed of contraries; the unity is in some cases that of common reference, in some cases that of serial succession.
Aristotle’s Use of Satire
When expounding the Law of Non-Contradiction, Aristotle satirizes those who believe things can be both true and false. He first compares them to vegetables, and then tells them to “walk early one morning into a well or ravine”. I’ve always suspected he has a mean streak in him. and he shows it here.