Question 1
QUESTION I. Whether the knowledge of Christ, insofar as He is the Word, actually extends to infinite things.
It is asked concerning the knowledge of Christ, insofar as He is the Word, whether it actually extends to infinite things. And that it does is shown:
1. First, by the authority of Augustine, in the twelfth book of the City of God, chapter eighteen: "The infinity of number, although there is no number of infinite numbers, is nevertheless not incomprehensible to Him whose understanding is without number ."
2. Likewise, the same author in the eleventh book of the City of God, chapter ten, speaking of the wisdom of God, says thus: "Nor are there many, but there is one wisdom, in which there are certain infinite, and to it finite, treasures of intelligible things," etc.
3. Likewise, it is shown by reason thus. The simpler a substance is, the more things it can know: therefore a substance that is infinitely more simple than any created substance knows infinitely more than any creature: therefore, etc.
4. Likewise, God actually comprehends both His own essence and His own power; but God can do infinite things: therefore if He actually knows His entire power, He actually comprehends infinite things: therefore, etc.
5. Likewise, it is a mark of nobility in a creature to know many things, and of greater nobility still to know more: therefore knowledge that is of infinite nobility extends to infinite things: therefore, etc.
6. Likewise, God knows more things than He can do, because He knows the evils of sin, which He cannot do; but He can do infinite things: therefore He also knows more than infinite things.
7. Likewise, whoever knows a point according to its substance and power knows it not only in itself, but also those things that can emanate from it; but infinite lines can emanate from one point: therefore if in any line there are infinite points, and from any point infinite lines can proceed, and God comprehends the power of every creature; therefore He knows not only infinite things, but also infinitely times infinite things.
8. Likewise, whatever the human intellect understands in potency or has in potency, the divine intellect has in act and more, because the created can be equaled to the uncreated neither in act nor in potency: but the human possible intellect extends to infinite things, because it never knows so many that it cannot know more: therefore if the divine intellect is actually directed to more than the human intellect, it actually extends to more than infinite things.
9. Likewise, by impossibility: because if God knew only finite things, since for every finite thing something greater can be devised, something could be conceived greater than divine knowledge; but this is impossible: therefore, etc.
10. Likewise, if He knew finite things, either He could know something beyond them, or not. If not, then His knowledge would be limited: if so, but whoever can know something that he does not know can learn: which is impious to say of God: therefore, etc.
11. Likewise, if He knew only those things that are, and not those that can come to be; since a created artisan knows many things that he can make and never will make, a man would know something that would be hidden from God: but this is false and impossible: therefore, etc.
Contra: 1. Everything known is true, and everything true is a being: therefore if infinite things are known, there are infinite beings: but the consequent is impossible: therefore so is the antecedent.
2. Likewise, whatever God knows he judges; but whatever he judges is such as he judges it to be, and so many: but whatever God judges he apprehends as finite: therefore whatever he knows is finite.
If you say that it does not follow—because it is finite to God, therefore it is finite—on the contrary: each thing is such in itself as it is according to the judgment of truth: therefore if something is finite to God, it is necessary that it be finite absolutely.
3. Likewise, everything infinite is untraversable both by the infinite and by the finite, because by whatever it were traversed it would receive a terminus: therefore it would be finite: but whatever the divine intellect knows it comprehends and traverses: therefore if infinite things are untraversable, infinite things are unknowable.
4. Likewise, whatever God knows he knows distinctly: but whatever he distinguishes he numbers, and whatever is numbered is measured, and all such things are finite: therefore whatever is known by God is finite.
5. Likewise, every number is either even or odd: therefore whatever is numbered by God is numbered by an even or an odd number: but every even number is divisible into two equals, and likewise every odd number when the unit is removed: but every such number is finite: therefore if God numbers whatever he knows, it is necessary that he numbers them by a finite number: therefore they are finite: therefore etc.
6. Likewise, whatever God knows he knows in an ordered manner: but wherever there is order, there is the notion of a first and a last, which is the notion of the finite: if therefore wherever there is the notion of order there is the notion of finitude, and God knows nothing without order, because he knows nothing in a disordered manner: it is impossible for God to know infinite things.
7. Likewise, if God knows infinite things, they are either infinite to him, or to us, or in themselves. If infinite to us, this is not a great thing to say, because those things are finite absolutely. If to him: but whatever things are infinite to someone are not knowable by him nor comprehended by him: therefore if God knows infinite things, he does not comprehend infinite things. If infinite in themselves: but a thing other than God, by the very fact that it is other, is a creature, and by the very fact that it is a creature, is limited: therefore to know other things as infinite is to know finite things as infinite: which is false and unintelligible, because it implies a contradiction in itself.
8. Likewise, if God knows infinite things, they are either infinite in their cause, or in their proper genus. If infinite in their cause: but everything that is in its cause is one: therefore whatever he knows as in its cause he knows by way of unity, not therefore by way of infinite things. If infinite in act and in their proper genus: but for infinite things to exist in act in their proper genus is false and impossible: therefore it is false and impossible for God to know infinite things.
9. Again, let every knowable thing known by God be called A: then I inquire thus: A is either God or something other than God. If it is God: then what is known by God is God: therefore a donkey is God. If something other than God: every such thing is actually finite: therefore A is actually finite; and A designates all knowable things: therefore all knowable things are finite: therefore etc.
10. Again, A is either equal to God, or less, or greater. If less than God: therefore finite: if equal, or greater: therefore it is God: therefore if God knows infinite things, God knows nothing but God: and if He knows nothing but God, He does not know infinitely: therefore if He knows infinite things, He does not know infinite things.
11. Again, since there is in God a power of making and a power of knowing, and each is infinite, and the power of making always makes finitely: it seems that the power of knowing always knows things finite in act; or if not, why not? This is to ask, since in God there is willing, knowing, and making, and willing and making do not extend to infinite things: how does knowing extend to infinite things, since the middle does not exceed the extremes.
CONCLUSION.
God by the knowledge of simple intelligence knows and comprehends infinite things.
I respond: For the understanding of the foregoing, it must be noted that according to the ancient doctors we are compelled to hold that God knows infinite things, as the Prophet David says in the Psalm: Great is our Lord and great is his power, and of his wisdom there is no number; and as Augustine not only asserts this but also proves it in the twelfth book of the City of God, the eighteenth chapter, where he speaks thus: "Therefore, as for that which certain ones, namely the philosophers, say—that not even by God's knowledge can infinite things be comprehended—it remains for them to dare to say, and to plunge themselves into this abyss of impiety, that God does not know all numbers. For it is most certain that they are infinite, since in whatever number you may think the end should be placed, that same number—I do not say can be increased by adding one—but however great it may be and however vast a multitude it may contain, it can by the very theory and science of numbers not only be doubled but even multiplied. Indeed, each number is so bounded by its own properties that none of them can be equal to any other: therefore they are both unequal among themselves and diverse, and each one individually is finite, and all together are infinite. Does God then not know all numbers on account of their infinity, and does the knowledge of God reach up to a certain sum of numbers and remain ignorant of the rest? Who, even the most demented, would say this?" And a little further on: "The infinity of number, therefore, although there is no number of infinite numbers, is nevertheless not incomprehensible to him whose understanding has no number. Wherefore, if whatever is comprehended by knowledge is made finite by the comprehension of the knower, then assuredly all infinity is in some ineffable manner made finite to God, because it is not incomprehensible to his knowledge. Therefore, if the infinity of numbers cannot be infinite to the knowledge of God by which it is comprehended, who are we, mere little men, to presume to fix a limit to his knowledge?"
By these testimonies, therefore, as by the most certain witnesses, we are compelled to say or to hold that God knows infinite things.
The manner of this position, however, is assigned by the more modern doctors, who have said that there is a threefold mode of divine cognition, not on account of a diversity of divine knowledge in itself, but in its connotation. For in God there is a knowledge of approbation, of vision, and of intelligence. The knowledge of approbation is of good things only, and of finite things. The knowledge of vision is of evil things and good things, but of finite things, inasmuch as it concerns time: for it is only of those things which were, are, and will be. But the knowledge of intelligence is of infinite things, inasmuch as God understands not only future things but also possible things: and the things possible to God are not finite but infinite.
The reason for this position, namely why we hold that God knows infinite things and does not make or will or dispose them, is that the divine knowing according to the third mode of understanding is an intrinsic act of God. By intrinsic I mean not only because it proceeds from what is intrinsic, but also because it is toward what is intrinsic and through what is intrinsic and according to an intrinsic mode. Toward what is intrinsic, I say, because the divine gaze in knowing does not leap outside itself, but by beholding itself as truth knows every truth.
Through what is intrinsic, because through the eternal reasons, which are identical with himself, he knows whatever he knows.
According to an intrinsic mode, because the divine knowing not only abstracts from the notion of actual cause, but also from that of cause absolutely. For he knows evils, of which he is not the cause; he also knows future things, which he does not yet bring about; he also knows possible things, which he will never bring about. And therefore, because knowing itself neither involves nor connotes anything actual outside, it signifies there an act in the mode of a habit, an act, I say, commensurate with the power itself — for whatever God can know, he knows — it also signifies an act in no way restricted, neither with respect to itself nor with respect to what is connoted, therefore universal with respect to places, with respect to times, and with respect to objects. For whatever he knew somewhere he knows everywhere, and whatever he knows once he knows always, and just as he knows one thing, so he knows all knowable things. Whence, because knowable things are not only beings in act, but also in potency: since it is not unfitting to hold that there are infinite things in potency, it is not unfitting to hold that infinite things are actually known by God.
And through this the response to the question and to the objections is clear.
1. To that which is objected, therefore: every known thing is true, etc.; it must be said that knowledge is twofold, namely that which causes things and that which is caused by things. What is known by knowledge caused by things is true in itself and in effect; but what is known by knowledge that causes things is true in its cause and in potency, and that truth does not entail a being in act, but a being in the potency of its cause; and therefore from this it does not follow that if God knows infinite things, infinite things are beings, but that infinite things are possible for God.
2. To that which is objected, that God judges whatever he knows, etc.; it must be said that God in knowing infinite things judges them to be infinite absolutely, but finite to himself; and this is not unfitting. For just as it does not follow that if something is infinite to the finite, it is infinite absolutely: so it does not follow that if something is finite to the infinite, it is finite absolutely: and this is what Augustine says in the aforementioned authority.
3. To that which is objected, that every infinite is untraversable, etc.: it must be said that traversable is said in two ways: in one way, through a discursive mode from one thing to another — and in this way the aforementioned statement is true, and so the Philosopher understands it in the sixth book of the Physics; in another way, through the universal and plenary intuition of that which is known by an intelligence — and in this way the infinite, since it is not incomprehensible to the infinite, is not untraversable to it, but only to the finite.
4. To that which is objected, that whatever He knows and cognizes, He cognizes distinctly, etc.: it must be said that that consequence fails in this respect, that it says: whatever He distinguishes, He numbers; because to distinguish extends further than to number.
Or say that whatever He distinguishes, He numbers by a finite or infinite number; but then it does not follow that He measures, because measure denotes something finite only.
5. To that which is objected: if He numbers, then either by an even or odd number, etc.: it must be said that that consequence does not hold, because an infinite number comprehends both. Whence, just as this consequence does not hold: man and donkey are animals, therefore rational or irrational — so neither does the aforesaid consequence.
6. To that which is objected, that whatever God knows, He knows in an ordered way, etc.: it must be said that divine cognition has a relation both to the knower and to the known: in relation to the knower, whatever He knows, He knows simultaneously, just as He simultaneously and at once says whatever He says; but in relation to the known, I say that He knows in an ordered way; but just as what is known by God is not only present but also future and possible, so also that order is not only an actual order but also a potential one, because He knows things in an ordered way not only by the order which has been made but also by the order which He can make.
Therefore, when it says that every order has a first and a last: this is true of actual order, not of potential order — as is evident in numbers, which have infinity and yet are ordered: for they have a possible order, just as they also have infinity.
7. To that which is objected: either He knows infinitely many things to us, etc.: it must be said that He knows infinitely many things in themselves, not indeed actually infinite, but in potency: and those things which are in potency are actually known by God. Whence potential infinity in the things known suffices for the actual infinity of divine comprehension; just as, therefore, infinity in potency does not conflict with actual finitude in a creature, so neither does the actual infinity of divine cognition conflict with the finitude of a creature.
8. To that which is objected: either He knows infinitely many things in their cause, etc.: it must be said: in both ways.
And if you object that in their cause they are one: this does not hold, because, although there is one art and one power, nevertheless the reasons of the things to be known are many.
If you object that in their own genus they are finite: this is true according to the being which they have; but nevertheless according to the being which they can have, they are at least infinite in potency, and thus infinite things known by God, because, as has often been said, those things which are in potency are actually known by God.
9. To that which is objected: A is either God or other than God, etc.: it must be said that known by God sometimes names the very principle of knowing, sometimes the thing known outside. In the first way it is God, because, as Anselm says in the Monologion, "the creature in the Creator is the creative essence." In the second way, however, it is other than God; but then it does not follow that it is actually infinite, because for infinitely many things to be actually known by God, it is not necessary that they be actually infinite, but it suffices that they be infinite in potency in their own genus.
10. To that which is objected: either A is equal to God, etc.: it must be said according to the aforementioned distinction that in the first way it is the same as God; in the second way it is other than God, for the reason that, although it has infinity in potency, it does not nevertheless have actual infinity; but God has actual infinity.
11. To that which is objected lastly concerning the power of making and knowing, and concerning willing just as making, the response is clear from the principal solution.