Aristotle, The Complete Works
Posterior Analytics, and Mechanics [a preparation for The Politics]
Aristotle wrote:
POSTERIOR ANALYTICS
[Part 1]
All teaching and all intellectual learning come about from already existing knowledge. This is evident if we consider it in every case; for the mathematical sciences are acquired in this fashion, and so is each of the other arts. And similarly too with arguments—both deductive and inductive arguments proceed in this way; for both produce their teaching through what we are already aware of, the former getting their premisses as from men who grasp them, the latter proving the universal through the particulars being clear. (And rhetorical arguments too persuade in the same way; for they do so either through examples, which is induction, or through enthymemes, which is deduction.)
It is necessary to be already aware of things in two ways: of some things it is necessary to believe already that they are, of some one must grasp what the thing said is, and of others both—e.g. of the fact that everything is either affirmed or denied truly, one must believe that it is; of the triangle, that it signifies this; and of the unit both (both what it signifies and that it is). For each of these is not equally clear to us.
But you can become familiar by being familiar earlier with some things but getting knowledge of the others at the very same time—i.e. of whatever happens to be under the universal of which you have knowledge. For that every triangle has angles equal to two right angles was already known; but that there is a triangle in the semicircle here became familiar at the same time as the induction. …
… Before the induction, or before getting a deduction, you should perhaps be said to understand in a way—but in another way not. For if you did not know if it is simpliciter, how did you know that it has two right angles simpliciter? But it is clear that you understand it in this sense—that you understand it universally—but you do not understand it simpliciter …
… For one should not argue in the way in which some people attempt to solve it: Do you or don’t you know of every pair that it is even? And when you said Yes, they brought forward some pair of which you did not think that it was, nor therefore that it was even. For they solve it by denying that people know of every pair that it is even, but only of anything of which they know that it is a pair.—Yet they know it of that which they have the demonstration about and which they got their premisses about; and they got them not about everything of which they know that it is a triangle or that it is a number, but of every number and triangle simpliciter. For no proposition of such a type is assumed …
… But nothing, I think, prevents one from in a sense understanding and in a sense being ignorant of what one is learning; for what is absurd is not that you should know in some sense what you are learning, but that you should know it in this sense, i.e. in the way and sense in which you are learning it.
MECHANICS
[Part 1]
Our wonder is excited, firstly, by phenomena which occur in accordance with nature but of which we do not know the cause, and secondly by those which are produced by art despite nature for the benefit of mankind. Nature often operates contrary to human interest; for she always follows the same course without deviation, whereas human interest is always changing. When, therefore, we have to do something contrary to nature, the difficulty of it causes us perplexity and art has to be called to our aid. The kind of art which helps us in such perplexities we call Mechanical Skill.
The words of the poet Antiphon are quite true: Mastered by Nature, we o’ercome by Art.
Instances of this are those cases in which the less prevails over the greater, and where forces of small motive power move great weights—in fact, practically all those problems which we call Mechanical Problems. …
… Among questions of a mechanical kind are included those which are connected with the lever. It seems strange that a great weight can be moved with but little force, and that when the addition of more weight is involved; for the very same weight, which one cannot move at all without a lever, one can move quite easily with it, in spite of the additional weight of the lever.
The original cause of all such phenomena is the circle. It is quite natural that this should be so; for there is nothing strange in a lesser marvel being caused by a greater marvel, and it is a very great marvel that contraries should be present together, and the circle is made up of contraries.
For to begin with, it is formed by motion and rest, things which are by nature opposed to one another. Hence in examining the circle we need not be much astonished at the contradictions which occur in connexion with it. Firstly, in the line which encloses the circle, being without breadth, two contraries somehow appear, namely, the concave and the convex.
These are as much opposed to one another as the great is to the small; the mean being in the latter case the equal, in the former the straight. Therefore just as, if they are to change into one another, the greater and smaller must become equal before they can pass into the other extreme; so a line must become straight in passing from convex into concave, or on the other hand from concave into convex and curved. This, then, is one peculiarity of the circle.
Another peculiarity of the circle is that it moves in two contrary directions at the same time; for it moves simultaneously to a forward and a backward position. Such, too, is the nature of the radius which describes a circle. For its extremity comes back again to the same position from which it starts; for, when it moves continuously, its last position is a return to its original position, in such a way that it has clearly undergone a change from that position.
Therefore, as has already been remarked, there is nothing strange in the circle being the origin of any and every marvel. The phenomena observed in the balance can be referred to the circle, and those observed in the lever to the balance; while practically all the other phenomena of mechanical motion are connected with the lever. Furthermore, since no two points on one and the same radius travel with the same rapidity, but of two points that which is further from the fixed centre travels more quickly, many marvellous phenomena occur in the motions of circles …
The Source:
Aristotle, The Complete Works of Aristotle, edited by Jonathan Barnes, Princeton University Press (1984) 1995
Evolutions of social order from the earliest humans to the present day and future machine age.