## 11 Jan 2009

### Continuum and Cohesion of Bodies in Aristotle's Physics and Metaphysics

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In "The Theory of Abstract Motion: Fundamental Principles," Leibniz refers to Aristotle's claim that bodies sharing the same limits are continuous or cohesive.

In Metaphysics Book 5, [1016a], Aristotle explains that bodies are continuous if they share the same motion [The full passage found at the end of this entry]:

"Continuous" means that whose motion is essentially one, and cannot be otherwise.

We learn in Physics Book 8 that that if a body moves a second body, that first body is both in motion and is a cause of motion. Moreover, the first body is in contact with and is hence continuous with the other body. [Full passage reproduced below.]

Metaphysics Book 5:

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; [1016a][1] 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.

From Physics Book 8:

For there must be three things-the moved, the movent, and the instrument of motion. Now the moved must be in motion, but it need not move anything else: the instrument of motion must both move something else and be itself in motion (for it changes together with the moved, with which it is in contact and continuous, as is clear in the case of things that move other things locally, in which case the two things must up to a certain point be in contact): and the movement-that is to say, that which causes motion in such a manner that it is not merely the instrument of motion-must be unmoved. Now we have visual experience of the last term in this series, namely that which has the capacity of being in motion, but does not contain a motive principle, and also of that which is in motion but is moved by itself and not by anything else: it is reasonable, therefore, not to say necessary, to suppose the existence of the third term also, that which causes motion but is itself unmoved.

Aristotle. Physics. Transl. R. P. Hardie and R. K. Gaye. Available online at:

Aristotle. Metaphysics. Transl. Hugh Tredennick. Available online at: