Axioms

1. We arrive at the knowledge and certainty of some unknown thing only through the knowledge and certainty of another thing that is prior to it in certainty and knowledge.

2. There are reasons that make us doubt the existence of our bodies.

This has in fact been shown in the Prolegomenon, and so is here posited as an axiom.

3. If we have anything besides mind and body, this is less known to us than mind and body.

Axioms Taken from Descartes

4. There are different degrees of reality or being.

Substance has more reality than accident or mode, and infinite substance, more than finite substance.

Therefore there is more objective reality in the idea of substance than in the idea of accident, and in the idea of infinite substance than in the idea of finite substance.25"

This axiom is known simply from contemplating our ideas, of whose existence we are certa in because they are modes of thinking. For we know how much reality or perfection the idea of substance affirms of substance, and how much the idea of mode affirms of mode.

This being so, we also necessarily realize that the idea of substance contains more objective reality than the idea of some accident, etc. See Scholium Prop. 4.

5. A thinking thing, if it knows of any perfections that it lacks, will immediately give these to itself, if they are within its power.26

This everyone observes in himself insofar as he is a thinking thing. Therefore (Scholium Prop. 4) we are most certain of it. And for the same reason, we are just as certa in of the following:

6. In the idea or concept of every thing, there is contained either possible or necessary existence. (See Axiom 10, Descartes.)

Necessary existence is contained in the concept of God, or a supremely perfect being; for otherwise he would be conceived as imperfect, which is contrary to what is supposed to be conceived. Contingent or possible existence is contained in the concept of a limited thing.

7. No thing, nor any perfection of a thing actually existing, can have nothing, or a nonexisting thing, as the cause of its existence.

I have demonstrated in the Scholium Prop. 4 that this axiom is as clear to us as is ‘I am, when thinking’.

8. Whatever there is of reality or perfection in any thing exists formally or eminently in its first and adequate cause.27

By ’eminently’ I understand: when the cause contains all the reality of the effect more perfectly than the effect itself. By ‘formally’: when the cause contains all the reality of the effect equally perfectly.

This axiom depends on the preceding one. For if it were supposed that there is nothing in the cause, or less in the cause than in the effect, then nothing in the cause would be the cause of the effect. But this is absurd (Ax. 7).

Therefore it is not the case that anything whatsoever can be the cause of a certain effect; it must be precisely a thing in which there is eminently or at least formally all the perfection that is in the effect.

9. The objective reality of our ideas requires a cause in which that same reality is contained not only objectively but also formally or eminently.28

This axiom, although misused by many, is universally admitted, for when somebody conceives something new, everyone wants to know the cause of this concept or idea. Now when they can assign a cause in which is contained formally or eminently as much reality as is contained objectively in that concept, they are satisfied.

This is made quite clear by the example of a machine, which Descartes adduces in Art. 17 Part I Principia.29 Similarly, if anyone were to ask whence it is that a man has the ideas of his thought and of his body, no one can fail to see that he has them from himself, as containing formally everything that his ideas contain objectively.

Therefore if a man were to have some idea that contained more of objective reality than he himself contained of formal reality, then of necessity we should be driven by the natural light to seek another cause outside the man himself, a cause that contained all that perfection formally or eminently. And apart from that cause no one has ever assigned any other cause that he has conceived so clearly and distinctly.

Furthermore, as for the truth of this axiom, it depends on the previous ones.

By Axiom 4 there are different degrees of reality or being in ideas. Therefore (Ax. 8) they need a more perfect cause in accordance with their degree of perfection.

But because the degrees of reality that we observe in ideas are not in the ideas insofar as they are considered as modes of thinking but insornr as one presents substance and another merely a mode of substance-or, in brief, insornr as they are considered as images of things-hence it clearly follows that there can be granted no other first cause of ideas than that which, as we have just shown, all men understand clearly and distinctly by the natural light, namely, one in which is contained formally or eminently the same reality that the ideas have objectively. 30

To make this conclusion more clearly understood, I shall illustrate it with one or two examples.

If anyone sees some books (imagine one to be that of a distinguished philosopher and the other to be that of some trifler) written in one and the same hand, and if he pays no attention to the meaning ofthe words (i.e., insofar as they are symbols) but only to the shape of the writing and the order of the letters, he will find no distinction between them such as to compel him to seek different causes for them.

They will appear to him to have proceeded from the same cause and in the same manner. But if he pays attention to the meaning of the words and of the language, he will find a considerable distinction between them. He will therefore conclude that the first cause of the one book was very different from the first cause of the other, and that the one cause was in fact more perfect than the other to the extent that the meaning of the language of the two books, or their words considered as symbols, are found to differ from one another.

I am speaking of the first cause of books, and there must necessarily be one although I admit- indeed, I take for granted-that one book can be transcribed from another, as is self-evident.

The same point can also be clearly illustrated by the example of a portrait, let us say, of some prince. If we pay attention only to the materials of which it is made, we shall not find any distinction between it and other portraits such as to compel us to look for different causes.

There will be nothing to prevent us from thinking that it was copied from another likeness, and that one again from another, and so ad infinitum. For we shall be qu ite satisfied that there need be no other cause for its production. But if we attend to the image insofar as it is the image of something, we shall immediately be compelled to seek a first cause such as formally or eminently contains what that image contains representatively. I do not see what more need be said to confirm and elucidate this axiom.

10. To preserve a thing, no lesser cause is required than to produce it in the first place.

From the fact that at this moment we are thinking, it does not necessarily follow that we shall hereafter be thinking. For the concept that we have of our thought does not involve, or does not contain, the necessary existence of the thought.

I can clearly and distinctly conceive the thought even though I suppose it not to exist.

The nature of every cause must contain in itself or involve the perfection of its effect (Ax. 8). Hence it clearly follows that there must be something in us or external to us that we have not yet understood, whose concept or nature involves existence, and that is the reason why our thought began to exist and also continues to exist.

For although our thought began to exist, its nature and essence does not on that account involve necessary existence any the more than befure it existed, and so in order to persevere in existing it stands in need of the same force that it needs to begin existing.

What we here say about thought must be said about every thing whose essence does not involve necessary existence.

11. Of every thing that exists, it can be asked why it exists.

See Descartes, Axiom I.

To exist is something positive. We cannot say that it has no cause (Ax. 7).

Therefore, we must assign some positive reason why it exists.

This must be either:

• external (Le., outside the thing itself) or
• internal (Le., included in the nature and definition of the existing thing itself).

Propositions 5-8 that follow are taken from Descartes.