Definitions by Spinoza

Here the only requirement is that everyone should attend to his perceptions as accurately as possible, so that he may distinguish what is clear from what is obscure.

Definitions

1. Extension [Metaphysical space] is that which consists of 3 dimensions.

But by extension does not mean the act of extending, or anything distinct from quantity.

2. The aether is that which only needs God’s concurrence to exist.

3. An atom is a part of matter indivisible by its own nature.

4. The indefinite is that whose bounds, if it has any, cannot be discovered by human intellect.

5. A vacuum is extension [metaphysical space] without corporeal substance [metaphysical aether].

6. Space is to be distinguished from extension [metaphysical space] only in thought.* In reality, they are the same. Read Art. 10 Part 2 of the Principia.

7. Divisible is that which in our thinking can be divided, at least potentially.

8. Local motion is the transfer of a body, from the vicinity of bodies that are at rest and immediately contiguous to it, to the vicinity of other bodies.

This is the definition used by Descartes to explain local motion. To understand this correctly, we should consider:

8.1. “A part of matter” is all that is transferred together, even if it may consist of many parts.

8.2. Descartes refers only to matter which is constantly in the moving thing in motion, that is, its being transferred.

People often confuse this with the force or action that effects the transfer.

This force or action is commonly thought to be required only for motion and not for rest, an opinion that is plainly wrong.

The same force that is required to move a body at rest is again required to withdraw that motion and put it back to rest.

We use about the same force to propel a boat that is at rest in still water as to halt it when it is moving.

• It would be exactly the same, were we not helped in halting the boat by the weight and resistance of the water displaced by it.

8.3. Descartes says that the transfer takes place from the vicinity of contiguous bodies to the vicinity of others, and not from one place to another.

He explained ‘place’ in Part 2, Art. 13. This ‘place’ is not something real, but depends only on our thought.

In this way, the same body changes and does not change its place.

But it cannot be said to be transferred, and not to be transferred, from the vicinity of a contiguous body.

This is because only certain definite bodies can, at the same moment of time, be contiguous to the same movable body.

8.4. That he does not say, without qualification, that the transfer takes place from the vicinity of contiguous bodies, but only from the vicinity of contiguous bodies that are regarded as at rest.

For in order that a body A may be moved away from a body B, which is at rest, the same force and action are required on the one side as on the other.

This is evident in the example of a boat that is sticking to the mud or sand at the bottom of the water.

To push it forward, an equal force must be applied to the bottom as to the boat. Therefore, the force by which bodies are to be moved is expended equally:

• on the moved body and
• on the body at rest.

The transfer is reciprocal.

If the boat is separated from the sand, the sand is also separated from the boat.

Therefore, when bodies separate from one another, if we were to attribute to them without qualification equal motions in opposite directions, refusing to regard one of them as at rest simply on the grounds that there is the same action in the one case as in the other, then we should also be compelled to attribute to bodies that are universally regarded as at rest (e.g., the sand from which the boat is separated) the same amount of motion as to the moving bodies.

The same action is required on the one side as on the other, and the transfer is reciprocal. But this would be too remote from the normal usages oflanguage.

However, although those bodies from which other bodies are separated are regarded as at rest and are also spoken of in this way, we shall remember that everything in the moving body on account of which it is said to move is also in the body at rest.

8.5. Each body possesses only one motion peculiar to itself because it moves away only from one set of bodies contiguous to it and at rest.

However, if the moving body forms part of other bodies having other motions, then it can also participate in innumerable other motions.

But because it is not easy to understand so many motions at the same time, or even to recognize them all, it will be sufficient to consider in each body that unique motion, which is peculiar to it. See Art. 31 Part 2 Principia.

9. A circle of moving bodies is a formation where the last body, immediately touches the first body.

This is even though the shape formed by all the bodies together through the impulse of a single motion may be very contorted.