The Infinite Versus the Indefinite

26. We do not need to enter into disputes regarding the infinite.

We merely hold all that in which we can find no limits are indefinite, such as:

• the size of the universe
• the divisibility of matter
• the number of the stars, etc.

We will thus never enter disputes about the infinite. This is because we are finite. It would be absurd for us to try to determine the infinite.

We will accordingly not care to reply to those who demand whether:

• the half of an infinite line is also infinite
• an infinite number is even or odd, and the like

This is because only those who imagine their minds to be infinite entertain questions of this sort.

When we see things that have no limits, we will not affirm that they are infinite. Instead, we call them as indefinite*.

We cannot imagine a space so great that we cannot think of a larger space. We will say that the magnitude of possible things is indefinite.

A body cannot be divided into parts so small that we cannot think of each of these to again be divided into smaller parts. Thus, let us regard quantity as divisible into an indefinite number of parts.

We cannot imagine so many stars that it would seem impossible for God to create more, we say that their number is indefinite.

27. What is the difference between the indefinite and the infinite?

Instead of calling infinite things as ‘infinite’, we call them ‘indefinite’. Only God can call things infinite because:

• we discover in him alone no limits on any side and we positively conceive that he admits of none
• we do not in the same way positively conceive that other things are in every part unlimited, but merely negatively admit that their limits, if they have any, cannot be discovered by us.

28. We look for the efficient causes of created things, not the final causes.

We will not seek reasons of natural things from the end which God or nature proposed to himself in their creation (i. e., final causes),

we should not think that we are sharers in the counsels of Deity. Instead, we consider him as the efficient cause of all things.

With this in mind, let us try to discover by the natural light which he has planted in us. Let us apply it to his attributes which we already know, so that we can have some conclusion on those effects we perceive by our senses.

bearing in mind, however, what has been already said, that we must only confide in this natural ight so long as nothing contrary to its dictates is revealed by God himself.

[Footnote: The last clause, beginning “bearing in mind.” is omitted in the French.]

[Footnote: “We will not stop to consider the ends which God proposed to himself in the creation of the world. We entirely reject from our philosophy the search of final causes!”]

[Footnote: “Faculty of reasoning."—FRENCH.]

29. God is not the cause of our errors.

The first attribute of God is that he is absolutely veracious and the source of all light.

It is plainly repugnant for him:

• to deceive us, or
• to be properly and positively the cause of the errors to which we are consciously subject

“To deceive” has some mark of subtlety. But it comes from malice, or from fear and weakness. Consequently, it cannot be attributed to God.

30. Consequently, all which we clearly perceive is true.

This delivers us from the above doubts.

It follows that the light of nature, or faculty of knowledge given us by God, can never compass any false object, as long as we can clearly and distinctly apprehend that object.

God would be a deceiver if he had given us this faculty perverted, that it led us to take falsity for truth.

The same principle should also be of avail against all the other grounds of doubting that have been already enumerated. For mathematical truths ought now to be above suspicion, since these are of the clearest.

If we perceive anything by our senses, whether while awake or asleep, we will easily discover the truth provided we separate what there is of clear and distinct in the knowledge from what is obscure and confused.

This is explained further in my work metaphysical Meditations.

31. Our errors regarding God are merely negations. Our errors regarding ourselves are merely privations.

God is no deceiver, yet we frequently fall into error.

Our errors depend more on our will, than on our understanding.

They have no need of the actual concourse of God, in order to their production.

When considered in reference to God, they are merely negations, but in reference to ourselves, privations.

32. There are only 2 modes of thinking in us: the perception of the understanding and the action of the will

For all the modes of thinking of which we are conscious may be referred to two general classes, the one of which is the perception or operation of the understanding, and the other the volition or operation of the will.

Thus, to perceive by the senses (SENTIRE), to imagine, and to conceive things purely intelligible, are only different modes of perceiving (PERCIP IENDI); but to desire, to be averse from, to affirm, to deny, to doubt, are different modes of willing.

33. We never err unless when we judge of something which we do not sufficiently apprehend.

When we apprehend anything we are in no danger of error if we refrain from judging of it in any way.

Even when we have formed a judgment regarding it, we would never fall into error, provided we gave our assent only to what we clearly and distinctly perceived.

We are usually deceived because we judge without having an exact knowledge of what we judge.