ARTICLE IX

In the Ninth Article We Ask: DOES GOD KNOW INFINITES?

Difficulties:

It seems that He does not, for

1. Augustine says: "Whatever is known is made finite by the comprehension of the knower." But the infinite cannot be made finite. Therefore, the infinite is unknown to God.

2. But it was said that God knows infinite things by His knowledge of simple intelligence, not by His knowledge of vision.--On the contrary, all perfect knowledge comprehends and consequently limits that which it knows. But God's knowledge of simple intelligence is as perfect as His knowledge of vision; so, just as He does not know infinites by His knowledge of vision, neither does He know them by His knowledge of simple intelligence.

3. Whatever God knows He knows through His intellect. But intellectual cognition is called vision. Therefore, whatever He knows He knows by His knowledge of vision. But through His knowledge of vision He does not know infinites. Hence, He does not know infinites in any manner.

4. The natures of all the things known by God are in God, and are in Him actually. If, therefore, infinites were known by God, infinite natures would be in Him actually; but this is impossible.

5. Whatever God knows He knows perfectly. But nothing is known perfectly unless the knowledge of the knower penetrates to the heart of the thing. Therefore, whatever God knows, in some sense He passes through. But an infinite cannot in any way be passed through either by a finite or by an infinite being. Therefore, God does not know infinites in any way whatsoever.

6. Whoever sees something limits that thing by the very fact that he can see it. But whatever God knows He sees. Therefore, what is infinite cannot be known by Him.

7. If God knows infinite things, then His knowledge is infinite. But this cannot be, for whatever is infinite is imperfect, as is proved in the Physics. Consequently, God does not know infinite things.

8. Whatever is repugnant to the definition of an infinite can by no means be attributed to an infinite. But to be known is repugnant to the definition of an infinite; for "it is characteristic of an infinite," as is said in the Physics, "that whatever quantity one takes from it, there always remains more to be taken." However, that which is known must be taken or received by the knower; and a thing is not known fully if something of it remains beyond the knower. Consequently, it is clearly repugnant to the definition of an infinite that it be fully known by someone. Therefore, since whatever God knows He knows fully, He does not know infinite things.

9. God's knowledge is the measure of the thing He knows. But there cannot be any measure for an infinite. Hence, an infinite does not come within His knowledge.

10. Measuring is simply ascertaining the quantity of what is measured. Therefore, if God knew an infinite, and thus knew its quantity, He would measure it. But this is impossible, because an infinite, by its very nature, is immeasurable. Hence, God does not know an infinite.

To the Contrary:

1'. As Augustine says: "Although there is no number for an infinite number, yet an infinite is not incomprehensible to Him whose knowledge has no number."

2'. Since God makes nothing that is unknown to Him, He can know whatever He can make. But, since He can make infinite things, He can know them.

3'. In order to understand something, immateriality is required in the one who understands, in the thing understood, and in the conjunction of the two. But, since the divine intellect is infinitely more immaterial than any created intellect, it is infinitely more capable of understanding. Now, a created intellect can know what is potentially infinite. Therefore, the divine intellect can know what is actually infinite.

4'. God knows whatever is, will be, or has been. But, if the duration of the world were infinite, then generation would never end, and there would be an infinite number of singular things. This, moreover, would be possible for God. Therefore, it is not impossible for Him to know infinites.

5'. As the Commentator says, "All proportions and forms which are potentially in first matter exist actually in the first mover." Augustine agrees when he says that there are seminal principles of things in first matter, but that the causal principles are in God. Now, in first matter there are, potentially, an infinite number of forms, because its passive potency is infinite. Therefore, in God, the first mover, there are actual infinites. But God knows whatever is in Him actually. Hence, God knows infinites.

6'. In arguing against the Academics, who denied that anything was true, Augustine shows that there is not merely a multitude of true things but even an infinite multitude of them, resulting from a kind of intellectual reduplication or from the reduplication of a sentence. For example, if I tell the truth, it is true that I tell the truth, and it is true that I say that I tell the truth, and so on to infinity. But God knows all true things. Hence, He knows infinites.

7'. Whatever is in God is God. Therefore, God's knowledge is God Himself. But God is infinite, because He cannot be comprehended. Therefore, His knowledge is infinite, and He has knowledge of infinites.

REPLY:

As Augustine says, some, wishing to conceive of the divine intellect in terms of our own intellects, have said that God cannot know infinites, just as we cannot know them; and since they asserted both that God knows singulars and that the world is eternal, it followed that there would be a cycle of numerically the same things in different ages--an opinion which is utterly absurd.

It must accordingly be said that God knows infinites, as can be shown from the reasons given above. For, since He knows not only things which have been, are, or will be, but also all those which could participate in His goodness--and the number of these is infinite since His goodness is infinite--it follows that He knows infinites. How this takes place must now be considered.

Note, therefore, that cognition extends itself to many or to few things according to the force of the means of knowing. For example, a likeness received in the sense of sight has the same determinations as the particular conditions of the thing. Hence, it leads us to the knowledge of only one thing. But a likeness received in the intellect is freed from particular conditions; and since it is more elevated, it leads us to the knowledge of a number of things. Indeed, because one universal form, by its very nature, is such that it can be participated in by an infinite number of singulars, the intellect can in some way be said to know infinites. However, since that intellectual likeness does not lead to knowledge of a singular according to its distinctive features but only under the aspect of a common nature, our intellect, through the species which it has within it, knows infinites only potentially. But the medium by which God knows, namely, His own essence, is a likeness of the infinites capable of imitating that essence. It is a likeness not only of that which is common to them, but also of those features by which they are distinguished from one another, as is clear from what was said earlier. Hence, the divine cognition has the power to know infinites.

The manner in which God knows actual infinites must now be considered. There is no reason why something cannot be infinite in one respect and finite in another. For example, a body can be infinite in length but finite in width. The same can be true of forms. For example, let us suppose some infinite body that is white. The extensive quantity of the whiteness (in so far as whiteness can be said to have quantity accidentally) will be infinite; but its intensive or essential quantity will nevertheless be finite. The same is true of any other form of an infinite body; for every form received in matter is limited according to the nature of the recipient and so does not have infinite intensity. It is possible neither to know nor to traverse an infinite. Both are repugnant to the idea of infinite. Nevertheless, if something were to be moved across an infinite, not in the direction of its infinity, it could be traversed. For example, what is infinite in length but finite in width could be traversed across its width but not along its length. Similarly, if an infinite were known in the respect in which it is infinite, it could by no means be known perfectly; but, if it were known in a respect which is not that of the infinite, it could be perfectly known. For, since "the character of infinity fits quantity," as the Philosopher says, and quantity of its very nature has an order of parts, an infinite would be known by way of its infinity if it were known part by part.

If our intellect had to know a white body in this manner, it would never be able to know either it or its whiteness perfectly. If, however, it knew the nature of whiteness or of corporeity which is found in an infinite body, then it would know the infinite perfectly with respect to all its parts--not, however, according to its infinity. Thus it is possible for our intellect in some manner to know an infinite continuum perfectly; but it cannot know an infinite number of things taken one by one, since it cannot know many things by means of one species. Hence, if our intellect has to consider a number of things, it has to know them one after another. Consequently, it knows discontinuous quantity only through continuous quantity. Therefore, if it were to know a multitude that is actually infinite, our intellect would be knowing an infinite according to its infinity, but that is impossible.

The divine intellect, however, knows all things through one species. Hence, simultaneously and with one intuition, God has knowledge of all things. Consequently, He does not know a multitude according to the order of its parts, and He can know an infinite multitude, but not according to its infinity; for, if He were to know it according to its infinity so that He would be grasping part after part of the multitude, He would never come to its end and never know it perfectly. I simply concede, therefore, that God actually knows infinites absolutely. These infinites, however, are not equal to His intellect in the way in which He Himself as known equals His intellect; for the essences of created infinites are, as it were, intensively finite as whiteness is in an infinite body. God's essence, however, is infinite in all respects; and because of this all infinites are finite to Him and can be comprehended by Him.

Answers to Difficulties:

1. A thing is said to be made finite by a knower in the sense that it is known to such an extent that it does not exceed the intellect of the knower; in other words, some part of it does not remain outside the knower's intellect. In this way, the thing known stands as something finite to the intellect. There is no reason why this cannot happen to an infinite which is known in a way other than according to its infinity.

2. Knowledge of simple intelligence and that of vision imply no difference on the part of the knower but only on the part of the things known. Knowledge of vision is said to be in God because of its resemblance to bodily sight which looks upon things outside of itself. Hence, God is said to know by His knowledge of vision only those things that are outside of Him, whether they are present, past, or future. But, as was proved above, God knows by His knowledge of simple intelligence things that neither are, will be, nor ever have been. There is no other way by which God knows these and those things. Hence, the fact that God does not see infinites is not due to His knowledge of vision but rather to the non-existence of the things that would be the objects of His knowledge of vision. For if it were held that these were infinite, either actually or successively, no doubt God would know them by His knowledge of vision.

3. Properly speaking, sight is a bodily sense. Hence, if the word vision is transferred to immaterial cognition, its use will be merely metaphorical. In metaphors, however, there is a different basis of truth according to the different points of likeness found in things. Hence, nothing prevents our sometimes calling all divine knowledge vision and at other times reserving the name to that which is about things present, past, and future.

4. By His essence God Himself is a likeness of all things and a proper likeness of each one of them. Hence, there cannot be said to be many intelligible characters of things in God except in regard to His various relations to various creatures. These relations, however, are merely rational relations. Moreover, as Avicenna says, there is no reason why rational relations cannot be multiplied to infinity.

5. Passing through implies a motion from one thing to another. Since God knows all the parts of an infinite, continuous or discontinuous, not by a progression of His thought, but in one simple intuition, He therefore knows an infinite perfectly. He does not, however, pass through an infinite in understanding it.

6. See the reply to the first difficulty.

7. This argument is based on what is infinite in a privative sense--a type of infinity peculiar to quantity. Whatever is spoken of privatively is imperfect. The argument does not touch what is infinite in the negative sense in which God is said to be infinite. It is more perfect for a thing not to be limited at all.

8. The argument proves that an infinite cannot be known according to its infinity; for whatever part of its infinity you take, no matter how big it is, something further will always remain to be taken. God, however, does not know an infinite by passing from part to part.

9. That which is infinite in quantity has a finite act of existence, as has been said.* Accordingly, God's knowledge can be the measure of an infinite.

10. The nature of measuring consists in this, that from it certainty results about the determinate quantity of a thing. God, however, does not know an infinite in such a way that He knows its determinate quantity, for an infinite does not have determinate quantity. Hence, it is not repugnant to the nature of an infinite that God should know it.