Natural Right

Having thus set forth the most universal principles of natural things, we must now go on to explain what follows from them. However, because the things that follow from these principles exceed all that our mind can ever survey in thought, and because we are not determined by them to consider some in particular rather than others, we should first of all present a brief account of the most important phenomena whose causes we shall here be investigating. But this you have in Arts.

In Arts. 20-43 is set out the hypothesis that Descartes judges most suitable not only for understanding the phenomena of the heavens but also for seeking out their natural causes.

Then again, because the best way to understand the nature of Plants or Man is to consider in what way they gradually come into existence and are generated from their seeds, we must devise such principles as are the simplest and easiest to know, from which we may demonstrate that the stars, the earth, in short, everything we observe in this visible world, could have arisen as from certain seedsalthough we may well know that they never did thus arise. For in this way we shall explain their nature far better than if we were to describe them only as they are now.

We seek principles that are simple and easy to know. Unless they are such, we shall not be in need of them.

The only reason why we assign seeds to things is to get to know their nature more easily and, like mathematicians, to ascend from the clearest to the more obscure and from the simplest to the more complex.

The principles we seek are such that we may demonstrate that from them the stars, the earth, etc., could have arisen. For we do not seek causes that suffice only to explain the phenomena of the heavens, as is the common practice of astronomers, but such as may also lead us to knowledge of the things on earth.

For we hold that everything we observe to happen above the earth should be counted as phenomena of nature. Now to discover these causes, the following are the requirements of a good hypothesis.

1. Considered only in itself, it must not imply any contradiction.
2. It must be the simplest that can be.

Part 3, Postulate 175 3. FoIl owing from (2), it must be very easy to know. 4. Everything that is observed in the whole of nature must be able to be deduced from it.

We have said, finaIly, that it is aIlowable for us to assume a hypothesis from which we can deduce, as from a cause, the phenomena of nature, even though we well know that they did not arise in that way. For this to be understood, I shaIl make use of the foIl owing example.

If someone were to find drawn on a sheet of paper the curved line we call a parabola and wished to enquire into its nature, it would make no difference whether he were to suppose that the line was first cut from a cone and then imprinted on the paper, or that the line was described as a result of the motion of two straight lines, or that it arose in some other way, provided that his supposition enabled him to demonstrate all the properties of a parabola.

Even though he may know that it originated from the imprinting of a conic section on the paper, he can nevertheless assume any other cause he pleases that seems to him most convenient for explaining all the properties of a parabola.

So too, in order to explain the features of nature, we are permitted to assume any hypothesis we please, provided we deduce from it by mathematical inference all the phenomena of nature.

A more important point to note is this, that there is hardly any assumption we can make from which the same effects cannot be deduced-although perhaps with more trouble-from the laws of nature explained previously.

For because, by the operation of those laws, matter assumes successively all the forms of which it is capable, if we consider those forms in due order, we shaIl finally be able to arrive at the form that is the form of this world. So one need fear no error from a false hypothesis.

Postulate

It is requested that the following be taken for granted.

All the matter of which this visible world is composed was in the beginning divided by God into particles as near as possible equal to one another. These were not spherical because a number of tiny spheres joined together do not fill a continuous space.

These parts were of different shapes and medium size; that is, of a size intermediate between all those of which the heavens and the stars are now composed. The parts possessed in themselves the same amount of motion as is now found in the world and moved with equal speed.

Individually, they moved about their own centers, each independently of the others, so as to compose a fluid body such as we think the heavens to be. Many also moved in unison around certain other points, equidistant from one another and arranged in the same way as are now the centers of the fixed stars. Others, again, moved about a somewhat greater number of other points that are equal to the number of the planets, thus forming as many different vortices as there now are stars in the world. See the diagram in Art. 47 Part 3 of the Principia.

This hypothesis, regarded in itself, implies no contradiction, for it ascribes to matter nothing except divisibility and motion, modifications that we have already shown to exist in reality in matter.

Matter is boundless, and one and the same in the heavens and on earth, we can suppose these modifications to have been in the whole of matter without any danger of contradiction.

Again, this hypothesis is the simplest because it supposes no inequality or dissimilarity in the particles into which matter was divided in the beginning, nor yet in their motion.

From this it follows that this hypothesis is also very easy to know.

This is also evident from the fact that by this hypothesis nothing is supposed to have been in matter except what everyone immediately knows from the mere concept of matter, divisibility, and local motion.

That everything observed in nature can be deduced from this hypothesis, we shall try to show as far as possible in actual fact, adopting the following order.

First, we shall deduce from it the fluidity ofthe heavens, explaining how this is the cause oflight. Then we shall proceed to the nature of the sun, and at the same time to what is observed in the fixed stars. After that we shall speak of comets, and lastly of the planets and their phenomena.

Definitions

1. Ecliptic - the part of a vortex that, in rotating about its axis, describes the greatest circle.
2. Poles - the parts of a vortex that are farthest away from the ecliptic or that describe the smallest circles.
3. Conatus to motion - not some thought, but that a part of matter is so situated and stirred to motion that it would in fact be going in some direction if it were not impeded by any cause.
4. Angle - whatever in any body projects beyond a spherical shape.

Axioms

1. A number of small spherical bodies joined together cannot occupy a continuous space.
2. A portion of matter divided into angular parts, if its parts are moving about their own centers, requires more space than if its parts were all at rest and all their sides were immediately contiguous to one another.
3. The smaller a part of matter is, the more easily it is divided by the same force.
4. Parts of matter that are moving in the same direction and in that motion do not withdraw from one another are not in actuality divided.

PROPOSITION 1

Appendix Containing Metaphysical Thoughts, Part I, Chapter I 177

The parts into which matter was {irst divided were not round but angular.

Proof All matter was in the beginning divided into equal and similar parts (Postulate). Therefore (Ax. I and Prop. 2 Part 2) they were not round; and so (Def. 4) they were angular. Q.E.D.

PROPOSITION 2

The force that brought it about that the particles of matter should move about their own centers, at the same time brought it about that the angles of the particles should be worn away by collision with one another.

Proof In the beginning, all matter was divided into equal (Postulate) and angular (Prop. I Part 3) parts. Therefore, if their angles had not been worn away as soon as they began to move about their own centers, then of necessity (Ax. 2) the whole of matter would have had to occupy more space than when it was at rest. But this is absurd (Prop. 4 Part 2). Therefore their angles were worn away as soon as they began to move. Q.E.D.