Part Four

Origin of Pure Ideas, which derive nothing
from Feeling

CHAPTER 1

Origin of elementary ideas or concepts of being presupposed in human reasoning

Article 1.

List of elementary ideas of being

575. The elementary concepts conditioning all human reasoning are principally the concepts of: 1. unity; 2. numbers; 3. possibility; 4. universality; 5. necessity; 6. immutability; 7. absoluteness.

 

Article 2.

Origin of these concepts

576. All these concepts, contained in ideal being, are its characteristics and natural qualities. As a result, they are given to our mind together with being itself. We simply have to note them one by one, distinguish them within being, and assign each a name. We do this through various uses of the idea of being, and of reflection.

577. This explains why such concepts, although so far removed by nature from material determinations that their formation would seem to require a long, difficult process of mental operation, are familiar to all human beings and presupposed by them. In fact, they are the most obvious, easily known and available of all human concepts.

 

Observation

578. Taken individually, these abstract concepts are an element of an idea rather than an idea itself. Of themselves, they provide no content to our knowledge. For this reason, I call them elementary concepts of ideal being. Generally speaking, abstract ideas are said to be elementary concepts of the idea from which they are abstracted.

 

Article 3.

St Augustine's arguments about the ideas of unity and number and similar things confirm the theory I have given

§1

579. Because these elementary concepts appertain to ideal being, we should not be surprised at the difficulty of knowing and explaining them through sensations.
Indeed, great thinkers were always struck by their appearance and extraordinary nature when they came upon any of them. Aware of the difficulty of explaining information which has nothing similar in the sensible world, they paid more attention to these concepts than people normally do when encountering problems. Each concept was used by some great philosopher to elevate his thought from nature and from the sphere of visible things to the infinite. However, because their meditation was limited to one concept, it did not lead them to the origin of all the elementary ideas in being. If they had grasped indeterminate, ideal being, they could have explained the great ideological problem in its entirety.

It will be helpful therefore, while discussing these concepts, to give an example of how any one of them could be sufficient to stimulate and guide great minds to rise above the highest peaks of human things and discover many of the truths I have explained. I choose the elementary concept of unity and numbers, and quote St. Augustine as the mind which reached such great height in these concepts.

580. He deals with this problem in his dialogue with a friend, Evodius. The dialogue, set in Rome (where it perhaps took place) is found in book 2 of his On Free Will. He begins by noting the difference between the individuality of our powers and the universality of truth shining equally in all human beings.

He writes:

 

Augustine: I first ask whether the feeling of my body is the same as yours or whether mine is only mine, and yours only yours.
Evodius: I fully grant that each of us has particular senses of seeing, hearing and other sensible operations, although they are of the same kind.
Augustine: Would you say the same about the internal sense?
Evodius: I would.
Augustine: But what about reason? Don't we each have our own? Certainly, I can understand something which you don't. And you cannot know whether I understand or not, although I myself certainly know whether I understand.
Evodius: Yes, we have our own particular mind.
Augustine: But can you say perhaps that we also have our own particular visible sun, our own particular light, star and such things, although we each see them with our own sense?
Evodius: No, I wouldn't say that.
Augustine: A group of us therefore can see one, single thing, although each of us has our own particular sense with which we all sense that thing and simultaneously see it. Although my sense is not yours, I see the same thing as you; the same thing is present to and seen simultaneously by both of us.
Evodius: Yes, that's clear.
Augustine: We can also hear the same voice, although my sense is not yours. But my hearing does not receive one part and yours another; we both hear the total sound whatever it is.
Evodius: Right.(58)
Augustine: Now, tell me, do all who reason (each of course with his own reason) see anything in common? What is seen by the eye is, as we said, present to all; it is not changed in use by those to whom it is present for their use, like food and drink; it remains entire and incorrupt whether seen or not. Or do you think that nothing of this sort exists?
Evodius: On the contrary, I see there are many things like this. It is sufficient to recall one: the explanation and truth of number. Number is present to all who can count.(59) in such a way that each strives to apprehend it with his own reason and intelligence. Some do this easily, others with more difficulty, and some not at all. Nevertheless it presents itself equally to all who can understand it. Moreover, when understood, it is not changed into food, as it were, for its perceiver, nor altered.(60)
Even when someone makes a mistake in calculation, the explanation and truth of number remains true and complete although the person making the calculation is more involved in error the less he sees the truth.
Augustine: Quite right. I see you have some experience of these matters and can reply immediately. But what would you say if someone claimed that numbers were not impressed in the spirit in virtue of their nature, but by the things we perceive with our corporeal sense, as if numbers were images of visible things? Do you think this could be the case?
Evodius: No, I don't. Even if I perceived numbers with my corporeal sense,(61) this could not explain how they can be subtracted or added. Only through this light of my mind do I correct a person who makes a mistake in adding or subtracting. I may not know the duration of everything I perceive with my bodily sense, like the sky, earth and everything in them, but I do know that seven and three make ten, and that this is true now and for ever; there never was and never will be a time when seven and three do not make ten.(62)
Augustine: I agree entirely; there is no doubt about that. But note, not even the ideas of numbers are abstracted from corporeal senses. You will see this easily if you consider that every number is a composite of unity. For example, the number which is twice one unity is called two; that which is three times one unity, is three, and that which is ten times, ten. In other words, each number receives its name according to the number of times it has one. Now, anyone who truthfully thinks what one is finds that it certainly cannot be felt by the corporeal senses. Everything perceived by bodily sense shows itself as many, not one, because it is a body, which has innumerable parts. But without getting involved in such small, inarticulate parts of bodies, I say that whatever the size of a body, it certainly has left, right, higher and lower parts, or sides and an end and a middle part. Such things are clearly present in every size of body, no matter how small. We must grant therefore that no body is truly and purely one, although in order to number all the things in it we would have to distinguish them by means of our knowledge of unity. When I look for unity in a body and certainly know I cannot find it, I nevertheless know beyond all doubt what I'm looking for, although I do not and cannot find it, or rather it is not there to be found. Thus knowing that one is not body presupposes that I have the idea 'one'. If I do not know what one is, I could not number the many things of the body. Furthermore, whenever I know one, I certainly do not know it through bodily sense. This gives me knowledge only of body, which never shows itself as truly and purely one.(63)
If however we do not know unity through bodily sense, we cannot know any number with that sense - I mean numbers seen with our understanding.(64)
In fact, all numbers are named by the quantity of unity within them - unity which is not perceived by bodily sense. -

St. Augustine goes on to discuss the properties and relationships of numbers, and shows them to be eternal and independent of anything temporal.

581. He says:

 

Moreover, if we look at the order of numbers, we see that two comes after one and is the double of one. But the double of two does not come immediately after two. To obtain this double, which is four, we have to place another number, three, between two and four. This fact, which applies to all numbers, is governed by the following most certain, immutable law: the quantity of a given number must be repeated in order to find its double. This characteristic, which we see to be immutable, firm and incorrupt and valid for all numbers, does not come from our senses, because nobody can perceive with his bodily sense all numbers, which are innumerable.(65) How then do we know that this law is valid for all numbers? What phantasy or phantasm enables us to see a totally reliable truth about numbers applicable with complete certainty to an innumerable series of things, if we do not see this truth in interior light, a light unknown to bodily sense?

He concludes:

 

These and many other teachings constrain those whom God has gifted with skill in argument and whose minds are not darkened with prejudice, to confess that the explanation and truth of numbers does not pertain to the bodily senses, that this truth is inflexible and always clear, and a common object given to be seen by all who reason.(66)

§2

582. St. Augustine now introduces similar arguments for all unassailable truths whatsoever. He shows how they are completely alien to the senses, like the truths concerning numbers, and how they must proceed from a source higher than sensible, temporary natures. I will make use of one passage from these arguments to reveal more clearly the mind of such an authority, and to confirm more securely the truth discussed in the whole of this work, namely, that the formal part of knowledge cannot come from the senses. I shall continue his discussion with Evodius at the point where he moves from numbers to other truths.

 

Augustine: We maintain that wisdom exists, and everyone wishes to be wise and happy. How do we see this? I am sure you see it, and see that it is true. But do you see this truth in the same way as you see your thought of which I am ignorant, unless you tell me what it is? Or rather, do you see the truth and are at the same time aware that I also can see it, even if you do not reveal it to me?(67)
Evodius: I am certain that you can yourself see the truth, even if I do not want you to.
Augustine: Well, if we both see the same truth with our own individual minds, it must be common to us.
Evodius: I agree.
Augustine: Now let's take another, similar proposition. I think you will accept as true the proposition that human beings must apply themselves to the study and love of wisdom.
Evodius: Certainly.
Augustine: Can we deny that this truth is one, and is commonly visible to all who know it, even though each person sees it with his own mind and not mine or yours or anybody else's?
Evodius: We certainly cannot deny it.
Augustine: Would you not agree that we must live justly, that inferior things take second place to better things, that equal things must be considered equally, and that every ens must be given what is due to it? And if you agree, are not all these opinions true and present in common to me, yourself and all who see them?
Evodius: I fully agree.
Augustine: You will also not deny, I am sure, that what is incorrupt is more valuable than what is corrupt, and what is eternal, more than what is temporary, and what is inviolable, more than what is violable?
Evodius: No doubt about it.
Augustine: Can anyone call this truth his own when it is there to be contemplated, resplendent in an unchangeable light, by all who are capable of doing so?
Evodius: No one would truly say it is their own; it is as much one and common to all as it is true.
Augustine: Right. You agree with me and grant as certain that these rules and lights of virtue, as we may call them, are both true and immutable and, whether taken singularly or all together, are present in common ready to be intuited by those able to intuit them, each with his own reason and mind. In your opinion therefore, do these things appertain to wisdom?
Evodius: Certainly.
Augustine: Well then, the rules of wisdom are just as true and unchangeable as those of numbers, whose explanation and truth are present unchangeably and in common to all who gaze upon them. I have taken a few of the rules of wisdom and questioned you about them individually. You replied that they are true and clear, and granted that they are contemplated in common by all who are capable of doing so.(68)
Evodius: I certainly did.
Augustine: You conclude that you cannot deny that there is an unchangeable truth which contains all these things that are immutably true, a truth that you cannot call your own or mine or anybody else's. You say in fact that it is ready to offer itself to be seen in common by all who can see immutable truths; it is, in a wonderful way, a kind of hidden and simultaneously public light.
Evodius: Everything you say is very true and clear.
Augustine: Let me ask you something. This truth we have been discussing for a long time and in which we see so many things, do you think it is more excellent than our mind, or equal or inferior to it?
Evodius: Perhaps inferior.(69)
Augustine: If it were inferior, we would judge it just as we judge inferior bodies rather than judge by it; we often say not only that they are this or that, but that they ought to be different in this way or that. We say the same about our spirit: not only do we know what it is, we often know what it ought to be. In the case of bodies, for example, we judge, 'It is not as white as it should be', or 'It is not truly square', and so on. In the case of a spirit, 'It is not disposed as it should be', or 'It is not gentle enough', or 'It is far too listless', according to the demands of custom. We judge these things according to the internal rules of the truth we all see in common. But no one judges the internal rules in any way. If someone says that eternal things are more valuable than temporal, and that seven and three make ten, no one will say it has to be like that. Instead, knowing that the thing is like that, he does not correct it as though he were inspecting it, but delights in it as though he had discovered it.
Evodius: Well, if the truth is not inferior to the mind, I presume it is equal to it.
Augustine: If that were the case, the truth would be changeable, just as our mind is.(70)
Our minds, which sometimes see more, sometimes less, must be accepted as changeable. When the truth is constant in itself, it does not develop because we see it better, nor regress because we see it less. Complete and incorrupt, it satisfies with its light those who turn to it and punishes with blindness those who withdraw from it. This is so true that we judge even our minds according to it, although we cannot judge it in any way. We quite rightly say a person does not understand, or understands sufficiently. The mind is governed by this law: it understands in exact proportion to its nearness and attachment to immutable truth. We must conclude therefore that the truth is neither inferior nor equal but superior to the mind and of a more excellent nature.(71)

Such is Augustine's teaching.

Notes

(58) In St. Augustine's time, the analysis of sensations was not as developed as it is now. We must not be surprised, therefore, if no distinction seems to be made here between the sun perceived by our senses and perceived by our understanding. Strictly speaking, our senses do not perceive the sun but only its partial action. The sun's action on different people, although similar and of the same kind, is numerically different. Thus, although we can say that different senses perceive different suns in a particular way, it would be more accurate to say that, strictly speaking, the sun as such is perceived only by the understanding, which perceives the sun-ens. Sense perceives only the agent in its various, separate actions.

(59) Note how carefully St. Augustine distinguishes between subject and object and between reasoning power and truth perceived by reason. The differences he notes are clear and undeniable. Nevertheless we still hear of people who claim to make knowledge and truth one with the human mind; for them, knowledge and truth are simply an effect or emanation of the mind.

(60) Note that subject who understands is varied, changeable and defective. Truth (object) does not suffer anything from the various conditions of the subject endeavouring to contemplate it. These last words of St. Augustine destroy every system which claims that knowledge is informed by the qualities of the subject. This cannot be true at all, because knowledge is by nature immutable.

(61) Although Evodius seems to grant here that numbers can be perceived by sense, St. Augustine immediately rejects this as impossible.

(62) These are the characteristics of immutability, necessity and eternity, noted by St. Augustine in the properties of numbers.

(63) Granted also that there is some kind of unity in the body, as in the case of extended continua, I must, in order to know the unity of a body, always perceive the body first as ens and then as one, that is, objectively. Sense itself, however, can receive only the action of things, and feels this action in its own feeling, not the things in themselves and outside its own feeling. Moreover, the unity of what is extended is not perfect because the possibility of division and multiplicity is never excluded.

(64) Shallow-thinking people are convinced that it is very easy to conceive multiplicity. Conceiving it is indeed easy, but explaining how it is conceived is difficult. They confuse the fact of the conception with its theory, the facility of the conception with the difficulty of its explanation. On the other hand, anyone who considers the matter deeply will see that 1. we cannot conceive the many unless the idea of the one is already in us, and 2. we cannot conceive the one unless the idea of ens is already in us.

(65) Here we see how St. Augustine realises that our reasoning about possible, necessary things exceeds all experience.

(66) His et talibus multis documentis coguntur fateri, quibus disputantibus Deus donavit ingenium et pertinacia caliginem non obducit, rationem veritatemque numerorum et ad sensus corporis non pertinere, et invertibilem sinceramque consistere, et omnibus ratiocinantibus ad videndum esse communem (De lib. Arbitrio, 2, 8).

(67) This is a very acute, accurate observation and greatly helps us to distinguish between knowledge of contingent and of necessary things.

(68) Note how St. Augustine proves that moral and metaphysical sciences are grounded on unshakeable foundations, just as much as those we call exact, rigorous sciences.

(69) To help the reader understand the argument better, I have interrupted Augustine's words here, and Evodius' reply further on, but the substance of the teaching is in no way disturbed.

(70) All these arguments are most effective in clearly demonstrating that the truth is not a product of the mind (of the subject) but an entity superior to the mind and to the human subject. It comes to the mind and to the human subject from a source infinitely superior to the human being. It is sad that Galluppi did not see this.

(71) De libero arbitrio, 2: 7-12.

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