De veritate EN 18
There have been many errors in connection will this problem. Some, as the Commentator mentions, have simply denied that God knows singulars, except, perhaps, in general. These persons will to confine the nature of the divine intellect within the limits of our own. But this error can be destroyed by the reasoning used by the Philosopher against Empedocles; for if—as would follow from what Empedocles had said—God were ignorant of that which others knew, God would be most stupid, although He Himself is most happy and, for this reason, most will. The same thing would be true if it were asserted that God did not know the singulars which all of us know.
Therefore, others, such as Avicenna and his followers, have said that God knows every singular, but universally, as it were, in knowing all the universal causes from which a singular is produced. An astronomer, for example, knowing all the motions of the heavens and the distances between the celestial bodies, would know every eclipse that will occur even for the next hundred years, yet he would not know any one eclipse as a distinct singular so as to have evidential knowledge that it actually exists or not—which a country bumpkin has when he sees an eclipse. It is in this manner, they say, that God knows singulars: He does not, as it were, see them in their singular nature but through knowledge of universal causes. But neither can this opinion stand; for from universal causes there follow only universal forms, un less something intervenes through which these forms are individuated. But from a number of universal forms gathered together—no matter how great this number may be—no singular can be constituted, because the collection of these forms can still be understood to be in many. Therefore, if one were to know an eclipse by means of universal causes in the manner described above, he would know, not a singular, but only a universal. For a universal cause has as proportionate to it a universal effect, and a particular cause, a particular effect. Hence, there would still remain the inadmissible consequence mentioned earlier, that God should be ignorant of singulars.
Therefore, we must simply admit that God knows all singulars, not only in their universal causes, but also each in its proper and singular nature. As proof of this, note that the divine knowledge which God has of things can be compared to the knowledge of an artist, since He is the cause of all things as art is the cause of all works of art. Now, an artist knows a product of his art by means of the form which he has in himself and upon which he models his product. However, he pro duces his work only will respect to its form—nature has prepared the matter for the works of art. Accordingly, by means of his art, an artist knows his works only under the aspect of the form. Now, every form is of itself universal; and, consequently, by means of his art, a builder knows, indeed, bouse in general, but not this house or that bouse, un less he acquires other knowledge of it through his senses. But if the artistic form produced matter as it produces form, then by its means the artist would know his work both under the aspect of its form and under that of its matter. Consequently, since matter is the principle of individuation, he would know it not only in its universal nature but also inasmuch as it is a definite singular. Therefore, since divine art produces not only the form but also the matter, it contains not only the likeness of form but also that of matter. Consequently, God knows things in regard to both their matter and their form; and, therefore, He knows not only universals but also singulars.
But a difficulty still remains. Since everything that is in something is in it according to the manner of that in which it is, and thus the like ness of a thing can be in God only immaterially, how is it that our intellect, because it receives the forms of things in an immaterial way, does not know singulars, yet God knows them?
The reason for this will be clear if we consider the difference between the relation to the thing had by its likeness in our intellect and that had by its likeness in the divine intellect. For the likeness in our intellect is received from a thing in so far as the thing acts upon our intellect by previously acting upon our senses. Now, matter, because of the feebleness of its existence (for it is being only potentially), can not be a principle of action; hence, a thing which acts upon our soul acts only through its form; consequently, the likeness of a thing which is impressed upon our sense and purified by several stages until it reaches the intellect is a likeness only of the form.
On the other hand, the likeness of things in the divine intellect is one which causes things; for, whether a thing has a vigorous or a feeble share in the act of being, it has this from God alone; and be cause each thing participates in an act of existence given by God, the likeness of each is found in Him. Consequently, the immaterial like ness in God is a likeness, not only of the form, but also of the matter. Now, in order that a thing be known, its likeness must be in the knower, though it need not be in him in the same manner as it is in reality. Hence, our intellect does not know singulars, because the knowledge of these depends upon matter, and the likeness of matter is not in our intellect. It is not because a likeness of the singular is in our intellect in an immaterial way. The divine intellect, however, can know singulars, since it possesses a likeness of matter, although in an immaterial way.
Answers to Difficulties:
1. Besides being separated from matter, our intellect receives its knowledge from things. Consequently, because it does not receive forms materially and, because matter can have no likeness, our intellect does not know singulars. The case is otherwise will the divine intellect, as has been said.
2. Sense and imagination are powers attached to bodily organs. Consequently, likenesses of things are received in them in a material manner, that is, will material conditions, although without matter. For this reason, they know singulars. The case is otherwise will the intellect. Hence, the argument does not follow.
3. Because of the terminus of the purifying process, it happens that the form is received immaterially; but this alone does not explain why the singular is not known. It is rather because of the very beginning of this process that the likeness of matter is not received into the intellect, but only that of the form. Hence, the argument does not follow.
4. All knowledge, taken in itself, belongs to the class of good things; but it may happen accidentally that the knowledge of certain despicable things is bad, either because it is the occasion of some base action (and for this reason certain knowledge is forbidden) or because some individual might be kept from better things because of certain knowledge; consequently, what is good in itself may harm certain people. This, however, cannot happen to God.
5. For knowledge a likeness of conformity in nature is not required, but only a representative likeness. For example, we are reminded of a certain man merely by a golden statue of him. This argument, how ever, proceeds on the assumption that knowledge requires a likeness consisting in conformity in nature.
6. The perfection of knowledge consists in knowing the thing to be as it is, not in having the same mode of existence as the thing known in the knower—as we have said repeatedly above.
7. That application of the known to the knower, which causes knowledge, should not be understood by way of identity but rather by way of representation. Therefore, it is not necessary that the mode of the knower and of what is known be the same.
8. That argument would hold if the likeness by which God knows were common in such a way that it could not be proper to each individual thing. That the contrary is true we have shown earlier.
9. The same thing in the same aspect cannot be both common and proper. But how the divine essence, through which God knows all things, is a common likeness of all, yet a proper likeness of each, has been explained above.
10. There are two mediums for physical sight. First, there is the medium under which it knows. This is light, which does not determine sight to any particular object. Second, there is the medium by which it knows, namely, the likeness of the thing known. By this medium, sight is determined to a special object. In divine knowledge, however, the divine essence takes the place of both. Hence, it can cause proper knowledge of individual things.
11. Divine knowledge is in no way changed by a change in the objects of its knowledge. Our knowledge varies when the objects change because it knows will separate conceptions things present, past, and future. Consequently, when Socrates is not sitting, the cognition had of him when he was sitting becomes false. God, however, sees things as present, past, or future in a single intuition. Therefore, no matter how a thing may change, the truth in His intellect remains the same.
12. Those things which possess a defective act of existence fall short of knowability for our intellect for the very reason that they fail short of the ability to act. But this does not affect the divine intellect, which, as we have said, does not receive its knowledge from things.
13. In the divine intellect, which is the cause of matter, there can exist a likeness of matter which, as it were, leaves its impression upon the matter. In our intellect, however, a likeness cannot exist that is capable of making us know matter. This is clear from what has been said.’
14. Although a singular as such cannot be separated from matter, it can be known by means of a likeness separated from matter, namely, the likeness of matter itself. Consequently, even if it be separated from matter physically, it is not separated from matter representatively.
15. An act of divine knowledge is not something other than God’s essence, for in God intellect and intellectual operation are one and the same, because His action is His essence. His knowledge, therefore, cannot be said to pass outside of Him simply because He knows some
thing other than Himself. Moreover, no action of a cognitive power can be said to pass outside in the way in which acts of physical powers do, which go from the agent into the patient. For knowledge does not mean something flowing from the knower to a thing known, as hap pens in physical actions. It means, rather, the existence of the thing known in the knower.
i6. An act of divine knowledge has no dependence upon the thing known; for the relation implied in divine knowledge does not involve dependence of the knowledge upon the things known, but, rather, the dependence of the thing known upon the knowledge. The opposite is true of us, for the relation implied by the word knowledge when used of us is one that indicates a dependence of our knowledge upon its object. Moreover, the relation of an act of knowledge to its object is not the same as its relation to the power of knowing; for it is supported in its act of existence by the knowing power, not by its object, because the act is in the power but not in the object.
17. A thing is known because it is represented in the knower, not because it exists in him; for the likeness existing in a knowing power is a principle by which a thing is known, not under the aspect of the act of being it has in the knowing power, but under the aspect of the relation it has to the thing known. Consequently, a thing is not known according to the mode of existence which the likeness of the thing has in the knower, but rather according to the manner in which the like ness existing in the intellect represents the thing. Therefore, although the likeness in the divine intellect has an immaterial act of existence, nevertheless, since it is a likeness of matter, it is also a principle of knowing material things and, therefore, singulars.
Parallel readings: Summa Theol., I, 86, 1; II Sentences 3, 3, 3, ad 1; IV Sentences 50, 1, 3; Contra Gentiles 1,65; III De anima, lectura 8, n. 710 seq.; Q. D. De anima, aa. 5, 20; Quodibet VII, I, 3 Quodibet XII, 8, li; De prin. individ. (Perr. i:nn. I-4).
It seems that it does, for
1. The human intellect knows by abstracting the form from matter. Now, the abstraction of a form from matter does not destroy its particularity, for mathematics, which abstracts from matter, considers particular limes. Consequently, the fact that our intellect is immaterial does not prevent it from knowing singulars.
2. Singulars are not distinct according to their participation in a common nature, for the fact that many men participate in the species of man makes them one man. Therefore, if our intellect knows only universals, it does not know one singular as distinct from another. Consequently, our intellect would not direct us to those objects of operations in regard to which we are guided by choice; for choice pre supposes the distinction of one thing from another.
3. But it was said that our intellect knows singulars inasmuch as it applies the universal form to some particulars.—On the contrary, our intellect cannot apply one thing to another unless it already knows each. Consequently, knowledge of the singular precedes the application of the universal to the singular. Therefore, the above-mentioned application cannot be the reason why our intellect knows the singular.
4. According to Boethius, whatever a lower power can do a higher power can do. Now, as he says in the same place, the intellect is superior to imagination and the imagination is superior to sense. There fore, since sense knows the singular, our intellect should also know it.
To the Contrary:
Boethius says: "What is sensed is singular, what is understood is universal."
All action is determined by the condition of the form of the agent, the principle of action, just as the process of heating is measured by the amount of heat. Now, the likeness of the thing known, by which the knowing power is informed, is the principle of actual knowledge, just as heat is of heating. Hence, all cognition is necessarily determined by the limitations of the form in the knower. Consequently, since the likeness of a thing existing in our intellect is received as separated from matter and all the conditions of matter, which are the principles of individuation, it follows that our intellect, of itself, does not know singulars but only universals. For every form as such is universal, un less it happens to be a subsistent form, which, from the very fact of its being subsistent, is incommunicable.
It happens, however, that our intellect knows the singular indirectly. For, as the Philosopher says, phantasms are related to our intellect as sensible objects are related to sense and as colors outside the soul are related to sight. Therefore, just as the species in the sense is abstracted from things themselves and by its means the cognition of the sense is extended to the sensible things themselves, so also our intellect abstracts the species from the phantasms, and, by means of this species, its cognition is extended, in a certain sense, to the phantasms.
There is, however, this difference: The likeness in sense is abstracted from the thing as from an object of knowledge, and, consequently, the thing itself is directly known by means of this likeness. The like ness in the intellect, however, is not abstracted from the phantasm as from an object of knowledge but as from a medium of knowledge after the manner in which our sense receives the likeness of a thing which is in a mirror; it is directed to it not as to a thing but rather as to a likeness of a thing. Consequently, from the species which it receives, our intellect is not applied directly to knowing the phantasm but rather the thing whose phantasm is presented. Nevertheless, by a certain reflection our intellect also returns to a knowledge of the phantasm itself when it considers the nature of its act, the nature of the species by which it knows, and, finally, the nature of that from which it has abstracted the species, namely, the phantasm. It is like the case of sight, which is brought through a likeness received from a mirror directly to a knowledge of the thing reflected, but by a sort of reflection to the image itself in the mirror. Therefore, inasmuch as our intellect, through the likeness which it receives from the phantasm, turns back upon the phantasm from which it abstracts the species, the phantasm being a particular likeness, our intellect gets some kind of knowledge of the singular because of its dynamic union will the imagination.
Answers to Difficulties:
1. There are two kinds of matter from which abstraction is made: intelligible matter and sensible matter—as is clear from the Meta physics. I call that matter intelligible which is considered in the nature of a continuum, and sensible, that which is physical matter. Each, however, can be taken in two ways: as designated and as not designated. I call matter designated if it is considered together will the determination of its dimensions, that is, will these or those dimensions. I call it not designated, however, if it is considered without the determination of its dimensions. In this connection, it must be noted that designated matter is the principle of individuation, from which every intellect abstracts inasmuch as it is said to abstract from the here and now. The intellect of the natural philosopher, however, does not abstract from non-designated sensible matter; for it considers man, flesh, and bone, in whose definitions non-designated sensible matter is included. The intellect of the mathematician, however, abstracts entirely from sensible matter, though not from non-designated intelligible matter. Hence, it is clear that abstraction, which is common to all intellects, makes a form universal.
2. According to the Philosopher, in us the intellect is not the only motive principle. The imagination is also such, and, by its means, the universal knowledge of the intellect is applied to some particular thing to be done. For this reason, the intellect is, as it were, a remote mover; but particular reason and the imagination are proximate movers.
3. Man has prior knowledge of singulars through imagination and sense. Consequently, he can apply his universal intellectual knowledge to a particular; for, properly speaking, it is neither the intellect nor the sense that knows, but man that knows through both—as is clear from The Soul.
4. What a lower power can do a higher power can do; not in the same, but in a more noble, way. Consequently, the intellect knows the same thing that sense knows, but in a more noble, because a more immaterial, way. Hence, it does not follow that the intellect knows the singular if the senses know it.
Parallel readings: Summa Theol., I, II Sentences 38, 3; 41, 5; Contra Gentiles I, cc. 58-59.
This inquiry is occasioned by the position of Avicenna mentioned above. We will to inquire whether God knows propositions, especially about singulars.
It seems that He does not, for
1. The divine intellect always remains in the same state; but a singular, inasmuch as now it exists and now it does not exist, has different states. Consequently, the divine intellect does not know whether or not a singular now exists.
2. Those powers of the soul which are indifferent to a thing’s presence or absence—as, for example, the imagination—do not know whether or not a thing exists; this is known only by those powers, such as sense, which do not know absent things as though they were present. Now, the divine intellect is disposed in the same way to things present or absent. Consequently, it does not know whether things exist now or not; it knows merely their natures.
3. According to the Philosopher, the composition signified when a thing is said to be or not to be is not in things but only in the intellect. Now, there can be no composition in the divine intellect. Therefore, God does not know whether or not a thing exists.
4. In the Gospel according to St. John (1:3-4) we read: "What was made, in Him was life." Now, in his explanation of this passage, Augustine says that created things are in God in the way in which a trunk is in the mind of the one who makes it. By means of the mental likeness of the trunk, however, a carpenter does not know whether the trunk exists or not. Consequently, neither does God know whether or not a singular now exists.
5. The more noble knowledge is, the more it resembles God’s knowledge. But the knowledge of an intellect comprehending the definitions of things is more noble than sense knowledge; for, when the intellect defines, it penetrates to the interior of a thing, but sense deals will externals. When the intellect defines, however, it does not know whether a thing exists or not, but simply the nature of the thing. Sense, however, does have such knowledge. It seems, therefore, that that type of knowledge by which only the nature of a thing is known, but not whether a thing exists or not, should be attributed to God.
6. God knows each and every thing by means of the idea He has of it. Now, that idea is indifferent to the existence or the non-existence of the thing. Otherwise, God could not know the future by means of it. God, therefore, does not know whether or not a thing exists.
To the Contrary:
1’. The more perfect knowledge is, the more conditions it grasps in its object. Now, divine knowledge is most perfect; consequently, it knows a thing according to all its conditions. Therefore, God knows whether or not a thing exists.
2’. As we have said above, God has a proper and distinct knowledge of things. Now, He would not know things distinctly unless He could distinguish an existing thing from one which does not exist. There fore, He knows if a thing does or does not exist.
The relation of the universal essence of any species to the essential properties of that species is the same as that of a singular essence to all the proper accidents of that singular, that is, all the accidents found in the singular; for, in so far as they are individuated by the singular, they are made proper to it. Now, by knowing the essence of a species, the intellect comprehends all the essential properties of that species; for, as the Philosopher says, the definition is the principle of any demonstration that concludes to the proper accidents of a subject. Therefore, once the proper essence of any singular were known, all the accidents of that singular would also be known. Our intellect, however, cannot know the essence of a singular, because it abstracts from designated matter, which pertains to the essence of a singular and would be placed in its definition if the singular had one. The divine intellect, however, can comprehend not only the universal essence of a species, but, since it can apprehend matter, it can also comprehend the singular essence of each and every thing. Therefore, it knows all accidents, those common to the entire species or genus, as well as those proper to each individual. Among these latter is time, in which every concrete reality is found and according to which a thing is said to exist now or not. Consequently, God knows whether or not each and every thing exists; and He knows all other propositions that can be formed about universals or individuals.
In this respect, however, the divine intellect differs from ours. In order to know a subject and an accident and to know different accidents, our intellect forms separate concepts, and, consequently, passes from knowledge of a substance to knowledge of one of its accidents. Again, in order to know the inherence of one of its accidents, it joins one species will the other, and, in a certain manner, unites them. In this way, the intellect forms propositions in itself. But by one reality, namely, its own essence, the divine intellect knows all substances and all accidents. Consequently, it neither passes from substance to accident nor joins one will the other; but instead of the joining of species which takes place in our intellect, there is, in the divine intellect, complete unity; because of this, God, without complexity, knows what is complex, just as He knows many things simply and will unity, and material things immaterially.
Answers to Difficulties:
1. By means of one and the same reality, the divine intellect knows all the conditions in a thing that are subject to change; so, while remaining in one and the same state, it knows all the states of things, no matter how they change.
2. The likeness in the imagination is a likeness merely of the thing; it is not a likeness by which one can know the time in which a thing exists. This limitation is not found in the divine intellect, so the cases are not parallel.
3. In place of the composition found in our intellect, there is, in stead, a unity in the divine intellect. This composition, however, is a kind of imitation of unity, and for this reason it is said to be a union. Thus, it is clear that God knows enunciable truths by not composing more truly thafi an intellect that does compose and divide.
4. The trunk in the mind of its maker is not a likeness of everything which can belong to it. Consequently, a craftsman’s knowledge and God’s are not similar.
5. He who knows a definition knows potentially the truths demonstrable by the definition. But in the divine intellect, actually to be does not differ from to be able w be. Consequently, from the fact that it knows the essences of things, it immediately comprehends all the accidents that follow upon them.
6. That idea in the divine mind is related to a thing in the same way, no matter what its condition is, for it is a likeness of the thing according to all its states. Consequently, through it the divine mind knows that thing in any condition whatever.
Parallel readings: Summa Theol., I, 14, I Sentences 38, III Sentences 14, 2, sol. 2; Contra Gentiles I, 66.
It seems that He does not have such knowledge, for
1. Dionysius says that cognition is had only of existing things. But that which neither is nor will be nor has been does not exist in any way. Hence, God cannot have knowledge of such a thing.
2. All cognition takes place through an assimilation of the knower to the thing known. But the divine intellect cannot be assimilated to a non-being. Hence, it cannot know a non-being.
3. God’s knowledge of things is through ideas. But there is no idea of a non-being. Hence, God does not know a non-being.
4. Whatever God knows is in His Word. But, as Anselm says: "There is no word for that which neither is, was, nor will be." Hence, God does not know non-beings.
5. God knows only the true. But the true and being are interchangeable. Hence, God does not know things that do not exist.
To the Contrary:
According to the Epistle to the Romans (4:17): "He calls things that are not as though they were." But God would not call non beings unless He knew them. Therefore, He knows non-beings.
God’s knowledge of created things may be compared to that which an artist has of his artistic products and which is their cause. Hence, the relation of God’s knowledge to things known is the opposite of the relation of our knowledge to them. Our knowledge is received from things, and, by its nature, comes after them. But the Creator’s knowledge of creatures, and the artist’s of his products, by its very nature, precedes the things known. Now, when what is antecedent is removed, what is subsequent is likewise removed; but the opposite is not true. Hence, our knowledge of natural things cannot be had unless these things previously exist; but the actual existence or non-existence of a thing is a matter of indifference to the intellect of God or that of an artist.
We must remark, however, that an artist has two kinds of knowledge about something that can be made: speculative and practical. He has speculative or theoretical knowledge when he knows the intimate nature of a work but does not have the intention of applying the principles to the production of the work. His knowledge is practical, properly speaking, when by his intention he ordains the principles of the work to operation as an end. In this way, as Avicenna says, medicine is divided into theoretical and practical.
It is clear that the practical knowledge of an artist follows his speculative knowledge, since it is made practical by applying the speculative to a work. But when the practical is absent, the speculative remains. Evidently, then, an artist can have knowledge of some work which he sometimes sets about making and sometimes does not, as when he thinks up the form of some piece of handicraft which he does not intend to make. Moreover, the artist does not always regard this work which he does not take steps to make as something within his power; for sometimes he visualizes a type of device entirely beyond his power of making. He regards it rather in the light of his own purposes, that is, he sees that he could attain such and such an end by means of such and such a device. For, as the Philosopher says, in the order of things to be done, ends are as principles are in the order of things to be studied; hence, as conclusions are known in their principles, products of art are known in the light of their purposes.
It is clear, therefore, that God eau know some non-beings of some He has, as it were, practical knowledge—that is, of those which are, have been, or will be; and these come forth from His knowledge as He decides. of those which neither have been, are, nor will be—which He has decreed never to make—He has a kind of speculative knowledge. And although one can say that He sees these things as within His power, since there is nothing He cannot do, it is more appropriate to say that He sees them in His goodness, the end of all that is made by Him; for He sees that there are many other ways of communicating His goodness, besides those He has already communicated to existing things, having existence, past, present, or future, because all created things cannot equal His goodness, no matter how much they seem to participate in it.
Answers to Difficulties:
1. Things which neither have been, are, nor will be, exist in some way in God’s power as in an active principle, or in His goodness as in a final cause.
2. Knowledge received from things known consists in a passive assimilation by which the knower is assimilated to objects of knowledge previously existing. But knowledge which is the cause of things known consists in an active assimilation by which the knower assimilates the thing known to himself. Since God can assimilate to Himself that Which has not yet been assimilated to Him, He can also have knowledge of non-being.
3. If, according to common usage, idea is taken as meaning the form of practical knowledge, then there is an idea only of those things which have been, are, or will be. If it be taken as also meaning the form of speculative knowledge, then there eau also be an idea of other things those things which neither are, have been, for will be.
4. The Word designates the operative power of the Father by which all His operations take place. Hence, the Word is extended only to those things to which the divine operation is extended. Consequently, we read in the Psalms (32:9): "He spoke and they were made." For, although the Word knows other beings, it is not the word of other beings.
5. Things which neither have been, are, nor will be possess truth in so far as they possess existence, namely, in so far as they are in their active principle or final cause. As such, they are also known by God.
Parallel readings: De veritate, 20,4, ad I; Summa Theol., I, 14, 12; III, 10, I Sentences 1, 2; Contra Gentiles 1,69; Quolibet III, 2, 3; Comp. Theol., I, C. 133.
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 in finites 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 in finites 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 in finite.
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.
De veritate EN 18