Cartesian Relativity

12. Space is different from the aetherspace [extension]

If a stone is removed from the place it occupied, we consider the aetherspace [extension] of the stone itself has been removed.

This is because we judge the aetherspace [extension] and body to be inseparable.

Yet we also believe that the aetherspace [extension] of the former location of the stone persists, despite that area now appearing empty.

This is because we think of extension in a general way.

We think that it can be common to stones, wood, water, air, and all other bodies, and even to the void (if it exists) as long as it keeps the same size, shape, and position relative to the external bodies that define that space.

13. What is external place?

We think of extension as length, width, and height in a general way because the words “place” and “space”:

• merely indicate a body’s size, shape, and location among other bodies.
• do not differ from the body which occupies a place

To determine that location, we must observe other immobile bodies.

Depending on which moving bodies we use as a fixed reference point, we say that the reference point does not move. But it moves after we switch to a new reference point.

And so the same thing both changes place and does not.

For example, imagine a ship being carried out to sea with a person sitting at the stern.

• From the perspective of the ship [with the ship as the reference], he is not moving since he has the same location with respect to the ship..
• From the perspective of the neighbouring shores [with the shores as the reference], he is constantly changing place from one shore towards the other.
• From the perspective of the immovable points in the heavens [with the heavens as the reference] where the earth moves from west to east exactly as the ship moves from east to west, he does not change his place.

But all points in the entire universe are moving.

And so nothing in the world has a place that is fixed and stationary, unless we mentally assign it one.

14. What is the difference between ‘place’ and ‘space’?

Place more expressly indicates position.

Space makes us think more of size and shape.

For example, we say that Body A has taken the place of Body B, even if Body A does not match the Body B’s exact dimensions or form.

• We do not mean that Body A occupies the exact same dimensions as Body B.

Likewise, when an object’s position changes, we say that its place has changed.

• This is even if the new space it occupies has the same size and shape.

So, when we say a thing is in a certain place, we mean only that it is situated in relation to other things.

But if we also say that it occupies a certain space or place, we mean in addition that it has such size and shape that it fully fills it.

15. The surface around a body is its “external place”

We never truly distinguish space from extension in length, width, and heigth.

But sometimes, we regard place as internal to the object.

At other times, we regard place as something external to it.

The interior is in no way different from space.

“Surface” does not include any part of the surrounding body.

Surface is simply the boundary between the boday and the surrounding body.

• It is a mere mode or condition, not a substance.

However, we sometimes treat the exterior as either:

• the surface that immediately surrounds the placed object, or
• a general surface that belongs to no body.

Even if the surrounding body moves elsewhere with its surface, we do not say that the object it surrounded has changed place, as long as it remains in the same position relative to our fixed reference point.

Imagine a boat that is carried in one direction by the current of a stream. It is blown by the wind in the opposite direction with an equal force, causing its location with respect to the banks to not change.*

The boat remains in the same place even if the whole ‘surface’* which surrounds it is incessantly changing.