Chapter 4: On the Simplicity, Infinity, and Intellectuality of the First Being

Chapter 4: On the Simplicity, Infinity, and Intellectuality of the First Being

Chapter 4 On the Simplicity, Infinity, and Intellectuality of the First Being1 49. (2) Lord our God, if you so grant, I would like in some way to show the perfections that I do not doubt belong to your unique and truly First Nature.

I believe that you are simple, infinite, wise, and an agent who wills. Because I do not want to argue in a circular way, I will set forth some propositions about simplicity that can be proved here at the beginning. Other proposi tions about simplicity will be delayed until the proper place where they can be proved.

Simplicity 50. (3) Therefore, this is the first theorem to be shown in this fourth chapter:

Theorem 4.1: The First Nature in itself is simple.

(4) I have said 'in itself' because I am here thinking of essential simplicity, which completely excludes all composition in the essence.

Theorem 4.1 can be proved as follows: [First proof ] The First Nature is not caused (from Theorem 3.3); therefore it does not have matter and form as essential parts.

[Second proof ] Nor does that nature have diverse perfections really distinct in any way, from which could be taken concepts of genus and specific dif ference. This is proved from the first proof of Theorem 3.6: for either (i) one of those perfections according to its proper nature would be that whereby the whole primarily is necessary existence, and the other would exist neces sarily neither primarily nor through itself—and then, since it is essentially included in the whole, the whole will not be necessary existence since it includes formally something that is not necessary—or (ii) if each reality were that whereby the whole primarily is necessary existence, the First Nature would be necessary existence twice over, and it would have two primary

1. The heading of Chapter 4 belongs to the Latin text. It is numbered as paragraph 1 in Wolter's edition.

Translation existences, neither of which would essentially include the other. Similarly, one would not be the other, because something unified would not exist from them if each one primarily gives necessary existence. For each will be the ultimate actuality and so either nothing that has its own identity will be composed of them—or there will be no difference between them (and then they are not two realities after all).

(5) A corollary: the First Nature is not in a genus, which is clear from the argument just given. It is also proved in this way: the whole of a nature that is in a genus is expressed through a definition, where what is conveyed by the genus is not in any way the same as what is conveyed by the difference, lest there be vain repetition. But the opposite obtains in so simple a Nature.

51. (6) [First objection to the second proof ] There is an objection here: if, con cerning two perfections or realities existing in one and the same nature, only one can be necessary and the other non-necessary—since otherwise there would be two necessarily existing realities—it would follow that no realities that are distinct from each other by their formal natures could be granted necessary existence—not even the essence and a relation in a divine person.

But the consequent is false; therefore the first part of the argument [(i) in the second proof above] errs.

[Second objection to the second proof ] There is a similar argument against the second part [(ii) in the second proof, above], since either each would be a final actuality, or one of them would be non-necessary.

I respond. Concerning realities distinguished by their formal natures, if they can be composed as act and potency, or as two things by nature actual izing one and the same thing, then if one is infinite, it can include the other by identity, indeed it does include it by identity. Otherwise, the infinite could be composed, which is disproved by Theorem 4.9. But if instead it is finite, it does not include, by identity, that which by its formal nature is primarily diverse from it, because a finite reality either can be perfected by the other, or can compose something with it. Therefore, if it is granted that necessary existence has two realities, of which neither, by identity, contains the other— which is what is required for composition—it follows either that one will not be necessary existence, neither formally nor by identity, or that the whole will be necessary existence twice, and so the first and second parts of the proof

[(i) and (ii)] hold.

The objections about a divine person are to no avail, because those two realities do not make a composition; instead, because one is infinite, one is the other by identity. Suppose you object: "Then I say there is composition and two realities in the necessary being, but one is infinite"—you contradict yourself in two ways: first, because the infinite cannot be a part making a composition with another reality, since a part is less than the whole; second,

Chapter 4 because if you posit a composition, neither reality is the other through iden tity; and then the proofs go through.

Pure Perfections 52. (7) Theorem 4.2: Whatever is intrinsic to the highest nature is the highest such thing.

(8) Proof: By simplicity (see Theorem 4.1), any intrinsic perfection of the highest nature is entirely the same as that nature; therefore, just as that nature is the highest nature, so too any intrinsic perfection of that nature is the highest such perfection, because it is the same as that nature. Otherwise, if an intrinsic perfection of that nature could be understood to be excelled according to its own entity, then the nature itself, whose entity is the same as that perfection's entity, could be understood to be excelled according to its own entity.

53. (9) Theorem 4.3: Every pure perfection belongs to the highest nature necessarily and in the highest degree.

(10) That is called a pure perfection which is such that, in anything what soever, it is better than what is not it.2

But this description of pure perfection seems to be void, since if it is under stood to concern the affirmation in itself [e.g., wisdom] and the negation in itself [e.g., not-wisdom], the affirmation is not better than its negation; and the affirmation in anything compatible with the affirmation [e.g., wisdom in a man] is not better than the negation in it [e.g., not-wisdom in a man]. But if the description is understood not to concern the affirmation in itself and in whatever is compatible with it, but understood instead to concern the affir mation and negation in anything whatsoever, then the description is simply false: for wisdom is not better in a dog, since there is no perfection such that it is good in that which it contradicts.

I respond: this description of pure perfection is famous. It can be explained in this way: "better than what is not it," that is, better than any positive, incom possible thing that entails not being it. I say it is better, in the stated way, in everything—not for everything—insofar as it is in itself; for it is indeed bet ter than what is incompossible with it, due to which it cannot belong to such a subject. Briefly therefore it may be said that a pure perfection is that which is simply and absolutely better than anything incompossible with it. Thus,

2. Anselm, Monologion 15 (Williams, 21–23).

Translation "better than what is not it, in anything whatsoever" may be explained as "bet ter than anything that is not it." Other than this I am not worried about the description. I accept the first part of the description, which is plain enough.

But concerning the incompossibility, it ought to be understood according to denominative predication, because this is the way it is commonly used in discourse.

54. (11) Understanding Theorem 4.3 in this way, I prove it. [Proof ] A pure perfection has an order of nobility to everything that is incompossi ble with it—an order of excelling rather than being excelled (according to the description). Therefore, either it is incompossible with the Supreme

Nature and so excels it, or it is compossible with it and so can belong to it, even in the highest degree (for if it is compossible with anything, it is com possible in this way with the Supreme Nature). As it is compossible with it, so it belongs to it. But it does not belong to it as a contingent accident. Therefore either it is the same as it, or at least a necessary feature of it. Thus Theorem 4.3 is proved: pure perfections belong necessarily to the Supreme Nature.

That a pure perfection does not belong contingently to the Supreme Nature, as an accident, I prove. In every perfection with which necessity is not repugnant, something having that perfection necessarily has it more per fectly than something having it contingently. Necessity is not repugnant with a pure perfection as such, because otherwise something incompatible with it would excel it, such as that which is necessary or could be necessary. But nothing can have a pure perfection more perfectly than the First Nature (by Theorem 4.2); therefore, etc.

Intellect and Will 55. (12) I set forth intellect and will before infinity and the remainder of simplicity, because the former are assumed in what follows below. The first such theorem is this:

Theorem 4.4: The first efficient cause understands and wills.

(13) This is proved. [First proof ] The first is this. The first efficient cause is a per se agent, since something per se is prior to every per accidens cause

(according to Physics 2).3 Every per se agent acts for the sake of an end.

From this I draw two arguments. First, every natural agent, considered precisely as natural, acts by necessity and would act just as it does even if it were independently acting for the sake of no end at all. Therefore if it does

3. Aristotle, Physics 2.6198a7–9 (Barnes, 1:338).

Chapter 4 not act except for the sake of an end, this is because it is dependent on an agent loving that end. Hence, etc.

[Second proof ] The second argument goes like this. If the first efficient cause acts for the sake of an end, either the end moves it as something loved by an act of will (and so Theorem 4.4 is shown), or as loved only naturally.

But the second disjunct is false, because the first efficient cause does not naturally love an end other than itself, as a heavy thing loves the center of the earth or as matter loves form. Thus, if the first efficient cause loved an end naturally, it would exist in some sense for that end, because it would be inclined to it. But if it naturally loves only itself as an end, this means nothing more than that it is itself. But this cannot account for the fact that the First

Nature is both the first efficient and the first final cause.

(14) Again, the first efficient cause directs its effect to its end, and does this either naturally or by loving that end. But not naturally, because some thing without cognition directs nothing except in virtue of something else with cognition, for the primary ordering of things belongs to the wise.4 But the first efficient cause does not direct by anything else's power, just as it does not cause by anything else's power.

56. (15) [Third proof ] And a third argument: something is caused contin gently; therefore the first cause causes contingently; therefore it causes by willing. Here is the proof of the first consequence: every secondary cause causes insofar as it is moved by the first; therefore, if the first moves necessar ily, everything else is moved and caused necessarily. And here is the proof of the second consequence: the only principle of acting contingently is the will or something connected to will, since everything else acts by the necessity of nature, and so not contingently.

(16) There are objections to the first consequence [of the third proof].

[First objection] Even if the first cause causes necessarily, our will can still cause something contingently. [Second objection] Also: the Philosopher con cedes the antecedent but denies the consequent in the case of God's will, positing contingency in lower things on account of a motion that, while caused necessarily insofar as it is uniform, produces diverse effects on account of its parts and so causes contingent things.5 And an objection to the sec ond consequence [of the third proof]: [Third objection] some motions can be impeded and so the opposite can come about contingently.

(17) In response to the first objection, if the first efficient cause is first with respect to our will, the same would follow for our will as for everything else.

4. Aristotle, Metaphysics 1.2.982a18–19 (Barnes, 2:1554).

5. Aristotle, Metaphysics 12.7.1072b3–8 (Barnes, 2:1694).

Translation This is because either it would move our will necessarily and immediately, or move something else necessarily to move our will necessarily and immedi ately—it moves because it is moved; ultimately some immediate cause will move the will necessarily, and so the will necessarily will will and its willing will be necessary. Moreover, something impossible follows, namely that the will causes necessarily what it causes by willing.

(18) In response to the second objection, I do not here call "contingent" whatever is not necessary or sempiternal, but rather something such that, when it comes about, its opposite could come about.6 This is why I said [in the third proof], "something is caused contingently" rather than "something is contingent." But I also say that the Philosopher could not, through his account of motion, deny the consequent while preserving the antecedent, for if that total motion exists necessarily by its cause, every part of it is caused necessarily when it is caused—that is to say, inevitably—so that the opposite could not then be caused. Moreover, what is caused by any part of a necessary motion is necessarily caused—that is, inevitably. Either therefore nothing comes about contingently (avoidably) or the first cause causes—even what it causes immediately—that which it need not cause.

(19) And in response to the third objection, if another cause can impede this cause, it can do so now by the power of a higher cause, and so on, up to the first cause. If the first cause necessarily moves the cause immediately below it, then there will be necessity throughout the whole order of causes, down to the impeding cause, and therefore it will impede necessarily. There fore no other cause could cause the effect contingently.

57. (20) [Fourth proof ] Here is a fourth argument. Something bad exists among beings; therefore the first efficient cause causes contingently; and then the argument continues as it does in the third proof just given. Proof of the consequence: an agent acting by the necessity of its nature acts to the full extent of its power, and so it will produce every perfection possible for it to produce. Therefore, if the first efficient cause acts necessarily (and con sequently, as has already been deduced, every other agent acts necessarily), it follows that the whole order of causes will cause in that order whatever it is possible for it to cause in that order. Therefore that order would lack no perfection that could be brought about in it by the activity of all the causes; therefore it would lack nothing that it could receive; and therefore there is no badness in it. The consequences are obvious, since every perfection that can be received in the total order of causes, is causable either by some cause or by all the ordered causes together. The last consequence is obvious given

6. Duns Scotus, Lectura 1.39.q.1–5.n.49–51 (Vatican 17:494–96).

Chapter 4 the nature of evil, and the proof works as much for moral viciousness as for natural evil.

You might say: "Matter does not obey." But this is nothing: a powerful agent would overcome disobedience.7

(21) [Fifth proof ] In a fifth way Theorem 4.4 is proved: a living thing is better than every non-living thing, and among living things, an intelligent thing is better than every non-intelligent thing.

58. (22) [Sixth proof ] Some argue for Theorem 4.4 in a sixth way, based on Theorem 4.3 above. They suppose it is obvious enough that understanding, willing, wisdom, and love are pure perfections.

[Objections to the sixth proof ] But it is not evident how it can be concluded that these perfections are pure perfections, while the nature of the first angel is not a pure perfection. For if you were to take wisdom denominatively, it is better than every denominative predicate incompatible with it, but you have not proved thereby that the First Nature is wise. I say you are begging the question. You can only maintain that it is better, in everything besides the First Nature, to be wise than not wise. In the same way the first angel— understood denominatively—is better than every being incompatible with it

(other than God). Indeed, the essence of the first angel, in the abstract, can be simply better than wisdom.

You might say, "An angel is repugnant with many things; thus, it is not better, taken denominatively, for everything than its opposite." I respond that neither is wisdom better denominatively for anything whatsoever; it too is repugnant with many things.

You might say, "On the contrary, it would be better for anything to which it could belong, since, for the dog, it would be better if it were wise." I respond: so too for the first angel: it would be better for it if it could be a dog, and for the dog it would be better if it could be the first angel.

You might say, "No indeed, for that would destroy the nature of dog; therefore it is not good for the dog." I respond: So too wisdom would destroy its nature. There is no difference here, except that the angel destroys as a nature of the same genus as the dog [i.e., substance], while wisdom destroys as a nature of a different genus from the dog [i.e., quality]—but wisdom is still incompatible with the dog because it demands for its subject a nature of the same genus as the dog but incompatible with it. And that which is primarily repugnant with a subject is also per se (but not primarily) repug nant with a property of that subject. The common way of talking about pure perfection is frequently weak.

7. Duns Scotus, Questions on the "Metaphysics" of Aristotle 9.q.12.n.11 (Etzkorn and Wolter, 2:552).

Translation Again: being intellectual seems to express a supreme degree of a determi nate category, such as substance. Should it for that reason be inferred that being intellectual is a pure perfection? With the properties of being as such it is different, because these follow from every being [not just substance], either as properties belonging to all, or as disjunctive properties. If a con tentious person were to say that every foremost denominative predicate of any most general genus is a pure perfection, how would you disprove it?

For such a person would say that any such perfection is better than any thing incompossible with it, if it is understood denominatively, because anything incompossible with it is a denominative predicate of its own genus, and it excels all of them. If this should be understood of denominated sub stances, insofar as they are denominated, such a person would likewise say that if such a perfection determines for itself a substance, it determines for itself what is noblest; or if not, it is at least the case that any subject, insofar as it is denominated by that perfection, is better than any other, insofar as the other is denominated by something else incompossible with it.

59. (23) Theorem 4.5: The first cause causes contingently whatever it causes.

(24) This is proved. [First proof ] That which the first cause causes imme diately, it contingently causes (from the third proof of Theorem 4.48); there fore it also causes everything else contingently, because the contingent does not naturally precede the necessary, nor does the necessary depend on the contingent.

(25) [Second proof ] Another proof comes from willing the end. Nothing is willed necessarily except that which is required for willing the end. God loves himself as the end, and whatever about himself he loves as an end, would remain even if nothing other than God exists, because what is nec essary from itself depends on nothing. Therefore, by willing himself as the end, he wills nothing else necessarily; neither, then, does he cause anything necessarily.

(26) [First objection] Against this. The First Nature itself is the same as its willing, even its willing something besides itself; therefore its willing some thing besides itself exists necessarily and therefore is not contingent.

[Second objection] Again: if the third proof of Theorem 4.4 holds up (on which the proofs for Theorem 4.5 rest), then there is no contingency in any secondary cause's causing unless there is contingency in the first cause's willing; just as necessity in the first cause's willing implies necessity in everything else's causing, so determination of its willing implies determination of everything else's causing. But the determination of its willing is eternal; therefore every

8. 4.56 above.

Chapter 4 secondary cause's causing is determined before it acts, such that it is not in its power to be determined to the opposite.

To explain further, if it is in a secondary cause's power to determine itself to the opposite, then this indeterminacy of its causing is consistent with determination in the first cause's willing, since it is not in a secondary cause's power to make the first cause indeterminate. And just as determination of the first cause is consistent with indeterminacy in the secondary cause, so also it would seem that the first cause's necessity is consistent with the sec ondary cause's possibility and non-necessity. Thus, either that third proof of Theorem 4.4 has no force, or it appears that our will is not of itself free with respect to opposites.

[Third objection] Again, if the first cause, itself determined, determines everything else, how could some secondary cause move toward something that is the opposite of that to which the first cause would move it, if it moved it—as happens in our will when sinning?

[Fourth objection] Again, a fourth objection. All effecting will be contin gent, since it depends on the efficient causality of the first cause, which is contingent.

These objections are difficult: a full and clear resolution of them requires that many things be described and explained. Let these be sought in the question I have discussed on God's foreknowledge of future contingents.9

60. (27) Theorem 4.6: The First Nature is the same as its love for itself.

(28) I prove the theorem in this way: [First proof ] the causality and causation of the final cause is simply first (from Theorem 2.4); thus the cau sality and causation of the first final cause is itself totally uncausable, by any causation whatsoever in any type of cause. But the causality of the first final cause is to move the first efficient as something loved, or (which is the same thing) for the first efficient to love the first end. Now, for the final cause to be an object loved by an act of willing is the same as for the will to love it as its object. Thus, the first efficient cause's love for the first final cause is totally uncausable, and so exists necessarily from itself (by Theorem 3.5). Thus, it will be the same as the First Nature (by Theorem 3.6); and the deduction is made clear in Theorem 3.15.

(29) [Second proof ] The theorem is deduced in another way, which amounts to the same: if the First Nature's love for itself is something different from the First Nature, it therefore can be caused (from Theorem 3.19), and there fore can be an effect (from Theorem 2.5), and therefore an effect of some

9. Duns Scotus, Lectura 1.d.39 (Vatican 17:481–510); Ordinatio 1.d.38–39 (Vatican

6:303–8 and 401–44); Reportatio 1-A.d.38–40 (Wolter and Bychkov, 2:448–91).

Translation per se efficient cause (from the proof of Theorem 4.4), and therefore can be caused by something loving it as an end (by the same Theorem 4.4). There fore the First Nature's love of itself would be caused by some prior act of love of an end, which is impossible.

61. [Third proof ] Aristotle shows this in Metaphysics 12,10 concerning the activity of understanding. If the first cause is not the same as its act of under standing, it will not be the best substance, because it is honorable through its act of understanding.

[Fourth proof ] Also, according to Aristotle, it will be laborious to maintain continuous understanding, since, if it is not the same as its understanding but in a potency of contradiction to it, it must work for it.11

(30) These arguments, [i.e., the third and fourth proofs drawn from Aristotle], can be explained. First [concerning the third proof ], the ultimate perfection of every being in first act is a second act by which it is conjoined to the best. This is especially so for a being that is active and not just some thing that is productive. Now, every intellectual being is active, and the First

Nature is intellectual, from what has already been said [Theorem 4.4]. It follows that its ultimate perfection is in a second act. Therefore, if that second act is not its own substance, that substance is not the best, because something else is its ultimate perfection.

(31) Second [concerning the fourth proof ], only a receptive potency is a potency of contradiction; therefore, etc. But that second argument from Aristotle [i.e., the fourth proof ] is not a demonstration but only a probable argument; hence, he prefaces it by saying, "It is reasonable (etc.)."

[Fifth proof ] In another way the theorem is shown from the identity between power and object; therefore its act is the same as it—but the con sequence is not valid. Counterexample: an angel understands itself and loves itself, but its act is not the same as its substance.

62. (32) This theorem is fertile with corollaries. [First corollary] It follows first that the First Nature and its will are the same, since its willing is an act of the will; therefore its will is uncausable; therefore, etc. Similarly, an act of willing is understood as though it were posterior to the will, yet the First

Nature is the same as its act of willing; therefore, it is all the more the same as its will.

[Second corollary] It follows second that the First Nature is the same as its act of understanding itself, since nothing is loved unless it is cognized; therefore its act of understanding necessarily exists from itself. Likewise, its

10. Aristotle, Metaphysics 12.9.1074b18–21 (Barnes, 2:1698).

11. Aristotle, Metaphysics 12.9.1074b28–30 (Barnes, 2:1698).

Chapter 4 act of understanding is, as it were, even closer to the First Nature than its act of willing.

[Third corollary] It follows third that the First Nature is the same as its intellect, just as it was argued before about the will, from the act of willing.

[Fourth corollary] It also follows that the First Nature is the same as that by which it understands itself, since this necessarily exists from itself and the First Nature understands it, so to speak, before its act of understanding.

63. (33) Theorem 4.7: No act of understanding can be an accident of the First Nature.

(34) [First proof ] Proof. The First Nature has been shown to be in itself first in the order of efficient causality. Therefore by itself, excluding any other causes, it can cause whatever can be caused—or at the very least it is the first cause of anything that can be caused. But excluding knowledge of what can be caused, it could not cause from itself everything that can be caused. There fore its knowledge of whatever can be caused is not something different from its own nature. This last claim is proved in this way: nothing can cause except out of love for the end, by willing the end—otherwise it could not be a per se agent, because it could not act for the sake of an end. But willing anything for the sake of an end requires first that the thing willed is understood. There fore, prior to the first instant at which something causes A or wills A, it understands A; thus, without understanding, nothing can be a per se efficient cause of A (or anything else).

64. (35) [Second proof ] Again, all acts of understanding belonging to the same intellect have a similar relation to that intellect: either essential or acci dental identity with it. It is clear that all acts of understanding belonging to any created intellect have the latter sort of relation to it, since all created acts of understanding seem to be perfections within the same genus. Thus, if some acts of understanding are received by the intellect, all are; and if some acts of understanding are accidents of the intellect, all are. Now some acts of understanding of the First Nature cannot be accidental (by Theorem 4.6); therefore none is accidental.

(36) [Third proof ] Again, if an act of understanding can be an accident, it will be received in the intellect as in a subject. Therefore that act of under standing that is the same as the First Nature—and so more perfect than an accidental act of understanding—will be a receptive potency with respect to a less perfect act of understanding.

(37) [Fourth proof ] Again, one and the same act of understanding can be of several ordered objects simultaneously, and therefore the more per fect the act of understanding, the more objects it can understand simultane ously. Thus, the most perfect act of understanding, than which there cannot

Translation be a more perfect, will be the act of understanding everything that can be understood. The First Nature's act of understanding is the most perfect (from Theorem 4.2); therefore it is the act of understanding everything that can be understood. Now the First Nature and its act of self-understanding are the same, from what has been said above. Therefore, etc.

Understand this theorem to hold for willing as well as understanding.

65. (38) [First rejected proof ] Again, it is argued that the intellect of the First

Nature is nothing other than a certain act of understanding. But that intellect is the same for everything, such that it cannot be otherwise for one object than it is for another. Thus, neither can its act of understanding; indeed, with one and the same act of understanding it understands everything.

My response to this argument is that it is a fallacy of accident to infer from the identity of things with each other, to their identity with respect to a third thing distinct from them. For example, given that the understanding of the First Nature is its willing, it does not follow that if it understands a thing it also wills it. Rather, the understanding of that thing is a willing.

And that act of willing is indeed some act in regards to that same thing, because it is in fact an act of understanding that thing [rather than a will ing of it]. So one can make the inference in a divided sense, but not in a conjoined one.

(39) [Second rejected proof ] Again, it is argued that the intellect of the First Nature has one complete and coeternal act, because its understand ing is the same as itself; therefore, it cannot have an additional act. But the consequence is not valid. Someone blessed in heaven sees God, but also sees something else; even if he sees God to his fullest capacity, as is assumed of the soul of Christ, still, he can see another.

(40) [Third rejected proof ] Again it is argued that the intellect of the First Nature has, in itself, by identity, the maximum perfection of understanding; therefore it also understands everything besides itself. But I respond that this does not follow, since understanding of other, lesser, things can be causable and so would differ from what is uncausable. But maximal understanding is uncausable.

66. (41) Theorem 4.8: (i) The intellect of the First Nature actually under stands—always, necessarily, and distinctly—all in telligible things, and (ii) its understanding of these is naturally prior to their actual existence.

(42) [First proof of (i)] The first part of the theorem is proved in this way.

The First Nature can understand in this way whatever is intelligible, since it belongs to the perfection of intellect as such to be able to understand distinctly and actually; indeed, this is a necessary feature of intellect, since

Chapter 4 the object or goal of every intellect is the whole of being understood most generally, as I have elsewhere discussed.12 But the First Nature cannot have any act of understanding that is not the same as the First Nature itself—from Theorem 4.7; therefore it has an actual and distinct understanding of each and every intelligible thing. And the First Nature and this act of understand ing are the same.

(43) [Second proof of (i)] The first part of the theorem is also supported in this way: a perfect craftsman distinctly understands anything that is to be done before it comes about; otherwise, it would not act perfectly, since understanding is the measure by which the craftsman acts. Therefore God has distinct and actual—or at least habitual—knowledge of everything he can produce by himself, and this knowledge is prior to the existence of any thing he produces. An objection to this argument is that a general skill suf fices for the production of individual things.

(44) [First proof of (ii)] The second part of the theorem, about the priority of the First Nature's understanding, can be proved in this way: whatever is the same as the First Nature exists necessarily from itself (by Theorem 3.5 and 4.1). But the existence of other intelligible things is not necessary exis tence (by Theorem 3.6). Necessary existence from itself is naturally prior to everything that does not exist necessarily.

(45) [Second proof of (ii)] The second part of the theorem is proved in another way. The existence of everything other than the First Nature depends on the First Nature as on a cause (by Theorem 3.19); and since the cause is a cause of some particular thing, necessarily the cause has knowledge of it; therefore, that knowledge is naturally prior to the existence of the thing known.

Infinity 67. (46) O the depth of the riches of your wisdom and knowledge, God,13 by which you comprehend every intelligible thing! Will you please empower my small intellect to conclude that:

Theorem 4.9: You are infinite existence and are incomprehensible by what is finite?

(47) I will try to infer this most fertile conclusion which, if it had been proved of you in the beginning, would have made more evident much of 12. Duns Scotus, Ordinatio 1.d.3.q.2.n.137 (Van den Bercken, 92).

13. Romans 11:33.

Translation what has already been discussed. Therefore, if you are willing, I will seek to infer your infinity from what has already been said about your intellect. Then

I will present some additional arguments, inquiring whether or not they are cogent arguments for the theorem.

First proof of infinity: first proof from intellect 68. (48) Lord God, are there not infinitely many intelligible things, actually in the intellect that actually understands everything? Therefore the intel lect that actually and simultaneously understands all intelligible things is infinite. You are such an intellect, our God (from Theorem 4.7).14 Therefore the nature that is the same as this intellect is also infinite.

I show the antecedent and consequence of this enthymeme. The anteced ent: things that are potentially infinite—that is, taking one after another they cannot come to an end—all those things, if they are simultaneously actual, are actually infinite. Intelligible things are potentially infinite with respect to created intellect, as is clear; but in your intellect all the things that can be understood only successively by the created intellect, are actually and simultaneously understood. Therefore in your intellect the intelligible things are actually infinite.

I prove the major premise of this syllogism [i.e., the syllogism offered for the antecedent above], although it appears to be sufficiently obvious. Tak ing all these intelligible things, if they are simultaneously existing, they are either actually infinite or actually finite. If actually finite, then by taking one after another eventually all could be grasped. Thus, if they cannot all be grasped and if they actually exist simultaneously, then they are actually infinite.

I prove the consequence of the enthymeme. When a plurality of things requires or implies a greater perfection than a paucity of things, a numer ical infinity of things implies infinite perfection. For example, to be able to carry ten things requires a greater perfection of motive power than to be able to carry five things; thus, to be able to carry an infinity of things implies an infinite motive power. Therefore, regarding this consequence to be proved, since to be able to understand two things simultaneously and distinctly implies a greater perfection of understanding than to be able to understand one thing, the consequence follows. This last claim I in turn prove: understanding an intelligible thing distinctly requires the attention and determinate turning of the intellect toward the intelligible thing; there fore, if an intellect can attend to several, it is not limited by any one of these; and thus, if it can attend to infinitely many intelligible things, it is altogether unlimited.

14. Scotus must have meant Theorem 4.8.

Chapter 4 (49) I prove the consequence in a similar way, at least concerning the act of understanding, from which the consequence concerning the intellect fol lows. Since to understand A is some perfection, and likewise to understand

B is a different perfection, it will never turn out that one and the same act understands A and B equally and as two distinct things, unless that act of understanding includes the perfections of the pair; the same goes for three things, and so on.

69. (50) [First objection] It will be said that when many things are under stood through one and the same concept, a greater perfection of understand ing does not follow from the plurality of things understood.

[Second objection] Or else it will be said that the argument goes through when applied to the act of understanding, but only when those several acts of understanding naturally have distinct formal perfections and are therefore acts of understanding diverse species—of which there is not an infinite num ber, as there is of individuals. But acts of understanding several individuals of the same species do not express different formal perfections, and so do not imply that an act of understanding more such things has a greater perfection.

Against the first [objection]: the same argument applies to the concept as applies to the intellect and its act. For a greater perfection in the concept follows from the plurality of those things of which it is the concept, because it must include eminently the perfections of all the specific concepts [of the different things of which it is the concept], where each concept posits a cer tain perfection of its own. Therefore an infinite [number of things under stood] implies an infinite [concept by which they are understood].

Against the second objection: individuals are understood imperfectly in a universal concept, because they are not understood according to every positive entity in them, as I have shown in the question on individuation.15

Therefore an intellect that understands every intelligible whatsoever, accord ing to every aspect of positive intelligibility, understands the distinct positive entities of many individuals, which posit a greater perfection in the act of understanding than does the understanding of just one of those individu als. For the understanding of any one of the absolute positive entities—for example, this individual's—is a certain perfection. Otherwise, if it were not present in the intellect, then neither the intellect nor the act of understand ing would be less perfect. Then it would not be necessary to posit such an understanding of the individual in the divine intellect, but this conclusion is ruled out by Theorem 4.8.

15. Duns Scotus, Ordinatio 2.d.3.p.1.q.1–6 (Spade, 57–113).

Translation Again: numbers and shapes show that there is an infinity of intelligibles in one species, as attested by Augustine in City of God 12, chapter 18.16

Second proof of infinity: second proof from intellect 70. (51) I show Theorem 4.9 in a second way. A first cause acting with the full extent of its causality, to which a secondary cause adds some perfection to its causing, does not seem to be able to cause its effect as perfectly by itself alone as it could with the secondary cause, because the causality of the first cause alone would be weaker than the causality of both together. Therefore if that which comes to be from a secondary cause and a first cause together would be more perfect if it came to be only from a first cause, the secondary cause adds no perfection to the first. But for every finite thing, something added to it adds some perfection to it. Therefore a first cause, to which a secondary cause adds no perfection to its causing, is infinite.

Regarding the claim to be proved, then: knowledge of any object is gen erated by the object known as by a proximate cause—most especially that knowledge that comes from vision.17 Therefore if knowledge belongs to some intellect without the action of any such object, but instead only by the power of another, prior, object whose nature it is to be a higher cause of such know ing, it follows that that higher object is infinite in its power to generate knowledge, since a lower object adds nothing to its power to generate knowl edge. The First Nature is such a higher object, because solely by its presence to the First Intellect—with no other object causing along with it—there is in that intellect knowledge of every object whatsoever (from Theorem 4.7),18 and most perfect knowledge of every object whatsoever (from Theorem 4.2).

Therefore no other intelligible thing adds anything to the First Nature with respect to the First Nature's power to generate knowledge. Therefore the First Nature is infinite; so also therefore it is infinite in being, since a thing can generate knowledge only proportionate to its existence.

71. (52) [First objection to the second proof ] Here it is objected that, from what has just been said, it follows that no secondary cause (each of which 16. Augustine, City of God 12.18 (Dyson, 523–26).

17. Duns Scotus, Quodlibet 6.19 (Alluntis and Wolter, 136–37). By "vision," here and following, Scotus means not the sensory power of sight but a type of cognition he calls intuitive cognition and describes as "knowledge precisely of a present object as present and of an existing object as existing," and also as "an intuition of a thing as existing and present." With respect to the present context, the intuitively cognized object is a proximate cause of the intellect's intuitive cognition.

18. As in his last reference to Theorem 4.7, Scotus must have meant Theorem 4.8.

Chapter 4 is finite) could produce knowledge of the thing caused that is as perfect as that knowledge produced by the caused thing itself. But this is false, since knowing a thing through a cause is more perfect than knowing it from itself without its cause.

[Second objection to the second proof ] Again, from the claim that the primary cause causes equally perfectly without a secondary cause as with a secondary cause, it seems to follow only that the primary cause has the perfection of the secondary cause more perfectly than the secondary cause has it. But this does not seem to imply infinity, since there could be a perfection that is finite yet more eminent in the perfection of the secondary cause.

[Third objection to the second proof ] Again, granting that nothing adds to the primary cause's causing when it causes with the full extent of its power, how is it proved that nothing adds to its being? For in causing light in a medium, if the sun were to cause as much as the medium could receive, another sun would add no more light to the medium. Nevertheless, there would be addition in being. So too, let it be granted that in the intellect of the First Nature there is as much knowledge as it can have, due to the pres ence of the First Nature as its object, and therefore a secondary cause adds nothing to the causing of knowledge in that intellect, since it cannot do any thing in that already fully actualized intellect—just as the other sun cannot produce any light in the medium. But if this proves that nothing is added in being, it seems that it could be argued likewise that the earth adds nothing to the sun in being, since it adds nothing to the causing of light in the medium.

72. (53) I reply to these objections. To the first objection: since nothing is established scientifically about a thing unless it is first conceived as it is in itself, so in our science, when we know a caused thing through its cause, the cause does not produce the kind of simple knowledge of the caused thing that the caused thing itself would naturally produce. As Augustine says in the last chapter of On the Trinity 9: "from the one knowing and the thing known, knowledge is born."19 Or if the cause could produce simple knowl edge of the caused thing, still it could not produce intuitive knowledge of it, about which I have written much elsewhere.20 Hence, beyond all knowing through a cause, something is still longed for, something caused in us only by the object itself. Therefore, if God has intuitive understanding of a stone, in no way caused by the stone, it must be that the stone, with regard to the power to generate knowledge, adds nothing to the First Nature's own power to generate knowledge, through which God intuitively knows the stone.

19. Augustine, On the Trinity 9.12.18 (McKenna, 287).

20. Duns Scotus, Quodlibet 6:18–21 (Alluntis and Wolter, 135–37); Quodlibet 13.27–47

(Alluntis and Wolter, 290–96).

Translation Therefore, when you insist that no finite cause produces perfect knowl edge of the thing caused, I concede that none can produce the most perfect knowledge possible for us. When you say that knowing through a cause is more perfect, I say that such knowledge includes the simple knowledge of the effect caused by the effect itself. Complex knowing is caused simulta neously by knowing the cause and the thing caused, and it is true that what comes from a primary and secondary cause together is something more per fect than what comes from a secondary cause alone. Now it may be said against this that that which is from a primary finite cause alone can be more perfect than that which is from a secondary cause alone, meaning by "that which is from a secondary cause alone" the vision of it. To this I reply that what is from a primary finite cause alone—such as a vision of the primary cause—can indeed be something more perfect than what is from a secondary cause alone; but the primary cause cannot produce the effect naturally caused by that thing which is the secondary cause, considering it either as a second ary cause or even as a primary cause relative to other finite causes—for with respect to causing this particular knowing, the thing that happens to be the secondary cause is only accidentally ordered to its prior finite cause, since a vision of that thing which is the secondary cause does not by its nature exist due to a prior finite cause. That vision would exist even if the thing seen were uncaused by such a prior cause, or were without every other prior finite cause, provided the intellect exists.

73. (54) In reply to the second objection: even if a prior finite cause essen tially contained, in its causing, the complete perfection of the secondary cause, and in this way excelled the secondary cause, which has that perfection only formally, still, that perfection possessed both eminently and formally excels—even in causing—that same perfection possessed only eminently. To generalize the point: when a perfection possessed formally adds perfection to that same perfection possessed eminently, then both together excel either on its own. There is such addition when the eminent is finite, since a finite added to a finite makes the latter greater. Otherwise the universe would not be more perfect than the first caused nature alone, postulated by some to con tain eminently every inferior perfection (which I denied in Theorem 2.16).21

74. (55) In reply to the third objection: that perfection which, where it is causable, either can only be caused by something that has that perfection formally and is a sort of first cause of it, only accidentally ordered to prior finite causes, or is causable only by other finite things causing together with something that has that perfection formally—such a perfection could never

21. Avicenna, The Metaphysics of "The Healing" 9.4.5–6, 11 (Marmura, 328, 330).

Chapter 4 exist anywhere except by virtue of something infinite. Something formally having that perfection, if added to this infinite thing, adds nothing to the infinite thing's causing. Therefore the argument offered above [i.e., the sec ond proof for infinity] stands, because if [what has a perfection formally] did add something [to the infinite thing's causing], then its own proper causal character, insofar as it is formally such, would be missing. And the effect ible perfection depends either on something else formally possessing that perfection or on that to which something formally such adds nothing to its causation.

Furthermore, neither would what is formally such add anything to its being, because that causation belongs to it according to its formal being.

Thus if something were added thereby to the being of the First Nature, without the other the First Nature would lack that proper causality which belongs to the other insofar as it is formally such, and thus the First Nature would not of itself more eminently possess that perfection which by its nature is [only] caused by that which formally has that perfection, insofar as it formally has it.

It is clear therefore that there is nothing in the objection about the sun, for if it pertains to this sun, insofar as it is this sun, to cause something, then the other sun would neither cause it nor have it in itself without the first sun.

If the second adds anything to the first—I do not care what recipient you refer to—I say briefly that it adds nothing of the same character as what is causable, and is necessarily from something, and is formally such as it is—

"necessarily," I say, in such a way that it cannot otherwise exist, either caused or uncaused, more perfectly than it does in the causable effect, except in the power of something to which what is formally such adds nothing either in causing or in being.

It is clear therefore that there is no merit in that objection about the earth, for light does not by nature depend on it as an effect depends on a cause.

Third proof of infinity: third proof from intellect 75. (56) I show Theorem 4.9 in a third way, thus. No finite perfection that has the same nature as an accidental perfection is a substance. Our act of understanding is an accident, since it is essentially a quality; therefore no finite act of understanding is a substance. But the First Nature's act of under standing is a substance (from Theorems 4.5, 4.6,22 and 4.7).

The proof of the major premise: things that agree in the formal nature from which their specific difference is received, agree also in genus, if each formal perfection is finite. This is because such a finite difference contracts

22. The second, third, and fourth corollaries.

Translation the same genus, in anything that has that perfection. But it is otherwise when the difference in one is finite, but infinite in the other. In this case, they are of the same nature in some respect, namely, in their formal nature.

But where that difference is finite, it contracts a genus, and therefore a thing belongs to a genus through that difference. Where the difference is infinite, it cannot contract anything; thus, a thing with an infinite difference does not belong to a genus.

(57) It is in this way, then, that I understand the claim that species but not genus can be applied to God, since species expresses perfection, but not genus. This claim includes a contradiction if it is understood to be about a whole species, since the essential understanding of species includes its genus.

Therefore it ought to be understood instead to be about the difference: it expresses perfection while the genus does not. Understanding it in this way really is possible, for neither difference nor genus as such includes the other.

But neither can the difference as difference be applied to God, because as difference it is finite and belongs to a genus necessarily. What can be applied to God is the absolute nature of the difference, which is, absolutely under stood, a perfection that is indifferent between finite and infinite; these are modes of perfection of that entity, just as the modes of more and less are modes of perfections of whiteness.

(58) I am aware that some of what is here set forth contradicts others' opinions, but I have not set out here to disprove various opinions; there will be another place for doing that.23

76. (59) An argument similar to this third argument can be made, reasoning from the converse. No finite substance is the same as a perfection that by nature is such that if it were finite, it would be accidental. The first substance is the same as its act of understanding. Therefore, etc. Thus the major prem ise of the third argument can be added: no perfection of the same nature as something accidental is substantial, or the same as a substance, since genera are primarily diverse, and what is an accident in one thing is a substance in nothing. Therefore an act of understanding is not the same as any substance that is in the genus of substance; so if the first substance is finite, it is not the same as its act of understanding; but if it is not finite, the conclusion follows.

23. Duns Scotus, Ordinatio 1.d.8.p.1.q.3.n.100–109 (Vatican 4:199–203); Lectura 1.d.8.p.1.q.3.n.99–105 (Vatican 17:33–36); Questions on the "Metaphysics" of Aristotle

7.q.19.n.51–53 (Etzkorn and Wolter, 2:322–23).

Chapter 4 Fourth proof of infinity: from simplicity 77. (60) I offer a fourth argument, similar to the previous. Every finite sub stance belongs to a genus. The First Nature does not belong to a genus (from Theorem 4.1). Therefore, etc. The major premise is clear, because a finite sub stance shares the same feature of being a substance with other finite sub stances, and yet is formally distinguished from them, as is clear. Therefore that distinguishing feature, which makes a substance distinct, is in some way the same as the entity of substance, but not by complete identity, since their natures are primarily diverse and neither is infinite, and thus neither com pletely includes the other by identity. Therefore a substance is one thing from these as from a contracting thing and a contracted thing, act and potency

[respectively], and so genus and difference [respectively], and therefore a species.

(61) The same thing is argued briefly in this way: everything really agree ing and really differing, agrees and differs by a reality not formally the same.

But no reality by which something agrees is identical with a reality by which it differs, unless one of the two is infinite, and then the thing including both will be infinite. But if neither is the other by identity, it follows that they make a composition. Thus, everything agreeing essentially and differ ing essentially either is composed of formally distinct realities, or is infinite.

Everything existing per se agrees and differs in this way. Therefore, if a thing is in itself totally simple, it follows that it will also be infinite.

(62) In these four ways it appears that God's infinity can be proved, three from premises about the nature of understanding, and a fourth, just given, from simplicity in essence.

Fifth proof of infinity: from eminence 78. (63) It seems there is a fifth way, from eminence, and I argue accord ingly in this way: it is impossible for something more perfect than the most eminent being to exist (from the corollary of Theorem 3.4).24 But no finite being is such that it is impossible that something more perfect than it exists.

Therefore, etc. The minor premise is proved: the infinite is not repugnant to being; the infinite is greater than any finite thing. The same thing is argued in a different way: that to which intensive infinity is not repugnant is most perfect only if it is infinite; if it is finite, it can be excelled, since infinity is not repugnant to it. Infinity is not repugnant to being; therefore the most perfect being is infinite.

24. 3.33(20) above.

Translation (64) It seems that the minor premise, assumed in the preceding argu ment,25 cannot be shown from anything prior to it. For just as a pair of contradictories contradict each other by their own natures, nor can their contradiction be proved through something more manifest than these, so too non-repugnant things are non-repugnant by their own natures, nor it seems can their non-repugnance be shown except with reference to these. Being cannot be explained through anything better known than it. We under stand the infinite through the finite, and I gloss this in the common way: the infinite is that which excels any finite thing, not just in a limited way by some finite measure, but excels it in a way that is beyond any condition a finite thing could have.

Nevertheless, the minor premise can be defended in this way: just as any thing should be held to be possible that is not found to be impossible, so also two or more things should be held to be compossible that are not found to be incompossible. Here nothing incompossible is found, since being finite is not part of the nature of being, nor is it clear from the nature of being that the finite is a property convertible with being—yet one of these must be true for there to be the aforementioned repugnance between being and infinite.

It seems clear enough which primary and convertible properties belong to being.

It can be defended in a third way, thus: the infinite is not repugnant with quantity in its own way, that is, taking part after part. Therefore, neither is the infinite repugnant to entity taken in its own way, that is, in perfectly existing all at once.

A fourth way: if a quantity of power is simply more perfect than a quan tity of mass, how will it be possible for there to be an infinity in mass, but not in power? Such a power, if it is possible, is actual (from Theorem 3.4).

A fifth way, thus: intellect, the object of which is being, encounters no repugnance when thinking of infinite being; indeed, it seems to be the most perfect intelligible. But it would be strange if no intellect could detect a con tradiction in something pertaining to the intellect's first object, when discord in sound so easily offends hearing. If, I say, what is unfitting is immedi ately perceived and offends, why does no intellect naturally flee from infinite being, as from something not fitting with, and so destructive of, the intellect's first object?

79. (65) In this way, Anselm's reasoning about the highest thinkable thing can be enhanced. His description should be understood in this way: God is that thing, thought without contradiction, a greater than which cannot be

25. That is, "the infinite is not repugnant to being," the minor premise of the argument offered in support of the minor premise of the fifth proof.

Chapter 4 thought without contradiction.26 Something the thought of which includes a contradiction is said to be unthinkable, and so it is, for in such a case there are two thinkable but opposed things, which cannot in any way make up one thinkable thing, since neither determines the other. It follows that the aforementioned highest thinkable thing, which is as God is described to be, exists in reality. First, concerning the being of its essence, since the intellect finally comes to rest in such a highest thinkable thing, therefore in it, in the highest way, is the nature of the first object of the intellect, that is, of being.

Next, concerning its actual existence: the highest thinkable thing is not only in the thinking intellect, for otherwise it could exist (because it is thinkable), and it could not exist (because it is repugnant with its nature for it to exist by another) (from Theorems 3.3 and 3.4). Therefore that which exists in reality rather than the intellect alone is a greater thinkable thing—not understand ing this to mean that the same thing, if thought, would be a greater thinkable thing were it to exist; but rather that, for anything that is in the intellect only, there is something else that exists and is a greater thinkable thing than it.

Or Anselm's reasoning can be enhanced in this way: something is more thinkable if it exists, that is, it is more perfectly thinkable because it is visible.

What does not exist, either in itself or in something nobler than it to which it adds nothing, is not visible. What is visible [by intuitive cognition] is more per fectly knowable than what is not visible [by intuitive cognition], that is, intelligi ble only through abstraction. Therefore the most perfectly knowable thing exists.

Sixth proof of infinity: from finality 80. (66) The sixth way to Theorem 4.9, taken from the nature of an end, goes like this: for every finite end, our will can desire and love something greater than it, just as the intellect can understand something greater than it. And it seems there is a natural inclination for loving the infinite good supremely; for it is argued on the following basis that there is a natural inclination in the will toward something: namely, that the free will, from itself and without a habit, wills it promptly and with delight. It seems that we experience just this in loving the infinite good; it seems that in nothing else is the will perfectly at rest. If this infinite good were opposed to the will's object, how would the will not naturally hate it, just as it naturally hates non-existence?

26. Anselm, Proslogion 2 (Williams, 81–82).

Translation Seventh proof of infinity: from efficiency 81. (67) The seventh way is from the nature of the efficient cause, on which Aristotle touches in Physics 827 and Metaphysics 12:28 the first efficient cause moves with infinite motion; therefore it has infinite power.

The reasoning can be enhanced, as far as the antecedent is concerned, in this way: the conclusion is equally well established if the efficient cause can move through an infinite motion, as it is if the efficient cause does in fact so move, since it is equally in act either way. And as far as the consequence is concerned the reasoning can be enhanced in this way: if it moves with an infinite motion from itself, and not by another's power, then it does not receive from another its moving in this way; rather, in its active power it has the total effect all at once, because it moves independently. What virtually has an infinite effect all at once, is infinite; therefore, etc.

The reasoning can be enhanced in another way. The first mover has, all at once, in its active power, all possible effects producible through motion.

These are infinite, if motion is infinite; therefore, etc.

82. (68) [Objection to the first enhancement] It does not seem that the con sequence is proved well. Not the first way, because greater duration adds no perfection: whiteness is no more perfect if it lasts one year rather than one day; therefore motion of however long a duration is not a more perfect effect than the motion of one day. Therefore from the fact that an agent has in its active power an infinite effect all at once, it cannot be established that there is greater perfection here than elsewhere, except that the agent moves for a longer time and from itself. Thus, it remains to be shown that the eternity of an agent establishes its infinity; otherwise its infinity cannot be established from the infinity of its motion. Then the last premise of the first enhance ment is rejected, unless it is understood to concern infinity of duration only.

[Objection to the second enhancement] The second enhancement, too, is blot ted out, because a greater intensive perfection is not established from the fact that any agent can produce successively any number of individuals of the same species as long as it endures, since that which can produce one indi vidual at one time, can produce a thousand by the same power, if it should last for a thousand times. But according to the philosophers, an infinity is not possible except in the number of effects producible through motion— that is, generable and corruptible things—because the philosophers posited only a finite number of species. Should someone else prove that an infinite number of species is possible, by proving that some celestial motions are

27. Aristotle, Physics 8.10.266a10–24 (Barnes, 1:444).

28. Aristotle, Metaphysics 12.7.1073a3–13 (Barnes, 2:1695).

Chapter 4 incommensurable, and so never can return to uniformity even if they endured infinitely, and that an infinite number of celestial conjunctions different in kind from each other would produce an infinite number of generable things different in species from one another—whatever may be said about this view on its own terms—this has nothing to do with the thought of Aristotle, who denied an infinite number of species.

83. (69) [First objection to the objections] On the other hand, it is here objected by asking how it is that in the first proof of infinity29 you labored to estab lish infinity from the fact that the divine essence is the cause of the being known of an infinite number of things, but you here deny that infinity can be inferred from the fact that the divine essence is the cause of the existence of an infinite number of things, as though it were greater to make something to be known than to be a true being?

[Second objection to the objections] Again, how is it that in the second argu ment for infinity30 you wanted to establish infinity from this fact alone: that the First Nature is the total explanation of some other nature's being seen, but infinity is not established here, where the First Nature is the total explana tion of another nature's existence? For it is the total cause of existence, at least of the nature proximate to it.

84. (70) [Reply to the first objection to the objections] In response to the first objection, whatever can do many things at once, the doing of each of which requires some distinct perfection, that thing is confirmed as more perfect due to the plurality of its perfections. So it is with understanding an infinite number of things simultaneously. So if you should prove that it can cause an infinite number of things simultaneously—not just successively—I would concede that there would be an infinite power.

[Objection to the reply] Against this, it does have the power to cause an infinite number of things simultaneously, and as far as itself is concerned, it can cause an infinite number of things simultaneously. But the nature of the effect does not permit it, just as a power to cause white and black is no less perfect because these cannot be caused simultaneously; for this is due to their repugnance, and not the defect of the agent.

[Reply to the objection] I reply that it has not been proved that the First is the total cause of these infinite things and that it has them all in its power at once, since it has not been proved from its efficient causality that it does not need a secondary cause for some causality corresponding to the secondary cause's own nature.

29. 4.68(48)–69(50) above.

30. 4.70(51)–74(55) above.

Translation [Objection to the reply] Against this, it has been well proved that the First

Nature has eminently every causality of a secondary cause, even the causality belonging to a secondary cause by its nature, although it has not been proved that that causality as formally possessed adds nothing to it as eminently possessed. The First Nature, therefore, has eminently and all at once every causality in relation to everything that can be effected, even to an infinite number of these—though they can only come about successively.

[Scotus's own solution, in support of the seventh proof ] I reply that as I see it, this is what finally and truly enhances Aristotle's aforementioned conse quence, and from it I prove infinity in this way: if the First Nature were to have every causality formally and simultaneously, although not every caus able thing could be granted existence simultaneously, yet it would be infinite because as far as it itself is concerned, it can grant existence to an infinite number of things simultaneously. And power to do a great many things at once establishes a greater intensive power. Therefore, if it has this power even more perfectly than it would have it by possessing every causality formally, so much the more its intensive infinity follows. But it has every causality, as a whole that is in it, in a higher way than would be in it formally. Therefore it is a nature of intensively infinite power.

85. (71) Thus, although I have so far reserved discussion of omnipotence properly speaking (as it is understood by Catholics) for a treatise on the articles of faith, and although omnipotence has not been proved here, still, it has been proved that there is an infinite power that all at once, from itself, has every causality eminently, and that in its own right would be capable of pro ducing simultaneously an infinite number of effects if it did have the same causality formally and if such effects were capable of being produced at the same time. If it is objected that the First Nature cannot, from itself, cause an infinite number of things simultaneously, since it has not been proved that it is in fact the total cause of an infinite number of things, this is of no concern.

For if it had all at once what was required to be a total cause, it would be no more perfect than it now is when it has what is required to be the first cause.

There are two reasons for this. First, if the first cause were simply the first cause and not the total cause, secondary causes would not be needed in order to supplement the first cause's perfection in causing; otherwise a more remote effect would be more perfect, because it would require, for its causing, a more perfect cause; but (according to the philosophers) if the first cause does require, for its causing, a secondary cause, this is due to imperfection in the effect, for the first cause together with an imperfect cause can cause a yet more imperfect thing that, according to them, it could not cause immediately by itself alone. Second, because according to Aristotle, the first cause has the totality of perfections more eminently than it would have these perfections if

Chapter 4 it had the formalities of these perfections—if it could have them. So it seems

Aristotle's argument about infinite power can reach its conclusion.

(72) [Reply to the second objection to the objections] To the second objection, above, I say that since the divine essence alone is the reason for its seeing the stone perfectly, it follows that the stone adds no perfection to that essence.

This does not follow if the divine essence is merely the reason for its causing the stone immediately, even as its total cause; for with respect to the highest created nature, the first cause is the total cause, but since this [highest created nature] is finite, it cannot establish the infinity of its first cause; but it has not been proved that it is the total cause of other things; therefore etc.

Eighth proof of infinity (rejected): from creation 86. (73) In line with the above argument for infinity from the nature of efficient causality it is argued that the First Nature creates, and between the extremes between which creation occurs there is an infinite distance.

The antecedent of this argument may be granted as a matter of faith, and it is true that non-existence precedes existence by duration, in a manner of speaking. But if the antecedent is taken in the sense that non-existence pre cedes existence only, so to speak, by nature, then it is true in the way proposed by the philosopher Avicenna.31 The antecedent is shown by Theorem 3.19, since at least the first nature after God is from God and not from itself, nor does it receive existence in a subject that already exists. And, as has already been said, being effected does not imply being changed. But if non-existence is understood in this way to be prior in nature to existence, there are not present there the kinds of extremes that would require an infinite power.

[Rejection of the eighth proof ] But however it may be with the antecedent, the consequence is not proved, since when there is no real distance between extremes, where instead these are said to be distant merely due to the natures of the extremes in themselves, then the distance is only as great as the greater extreme. For example: God is infinitely distant from a creature.

Ninth proof of infinity (rejected): from the lack of intrinsic causes 87. (74) The theorem about divine infinity is shown in a final way, namely, from the denial of an intrinsic cause in the First Nature. Since form is lim ited by matter, therefore that which by its nature does not exist in matter, is infinite.

[Rejection of the ninth proof ] This argument, in my opinion, is totally weak.

According to the very people who support it, an angel is immaterial but is 31. Avicenna, The Metaphysics of "The Healing" 6.2.9 (Marmura, 203).

Translation not infinite. The same people think that existence is posterior to essence, so existence will never limit essence. Hence, any entity has a grade of perfection intrinsic to it and not through another being. And if they argue that form is limited by matter, therefore if it is not limited by matter, it is not limited at all, well then, they commit a fallacy of the consequent. Consider: a body is limited by another body, therefore, if it is not limited by another body, it is infinite—so the highest heaven will be infinite. This sophism is in Physics 3.32

A body is limited in itself; likewise a finite form is limited in itself prior to being limited by matter, because prior to being so limited it just is that kind of thing among beings. The second limiting by matter presupposes the first limiting; it does not cause it. Therefore, in some instant of nature there is the finite essence; therefore existence cannot limit it, and therefore in a second instant of nature it is not limited by existence.

Proving Simplicity from Infinity 88. (75) Theorem 4.10: Every kind of simplicity follows from infinity.

First type of simplicity: no parts (76) [Proof of the first type of simplicity] First is a simplicity intrinsic to the essence, since, supposing the essence is composed of parts, either it is com posed from parts finite in themselves or from parts infinite in themselves. If the former, therefore the essence is finite; if the latter, then a part would turn out to be not less than the whole.

Second type of simplicity: no quantitative parts (77) [Proof of the second type of simplicity] Second, the essence is not com posed of quantitative parts. This is because infinite perfection does not exist in a magnitude, since, on the one hand, if the magnitude is finite, a greater magnitude would have a greater perfection; and, on the other hand, infinite magnitude cannot exist. This is Aristotle's reasoning in Physics 833 and Meta physics 12.34

(78) [Objection] But it is objected that infinite perfection in magnitude would be of the same nature in the whole as in a part and so would not be greater in a greater magnitude, in just the way the intellective soul is the most

32. Aristotle, Physics 3.4.203b20–22 (Barnes, 1:347).

33. Aristotle, Physics 8.10.266a25–266b24 (Barnes, 1:444–45).

34. Aristotle, Metaphysics 12.7.1073a3–11 (Barnes, 2:1695).

Chapter 4 perfect form, and so is as perfect in a small body as it is in a large body, and as perfect in a part of the body as it is in the whole body. If an intellective soul had infinite power, such as the power of understanding infinite intelligible things, it would have it even in a small body, and if the body were bigger the soul's power would not be greater. Therefore, according to this objection, it is denied that every power in a magnitude is greater in a greater magnitude.

[Reply to the objection] But Aristotle's reasoning, here enhanced, proves that infinite perfection does not exist in a magnitude so as to be extended per accidens, that is, in such a way that a part [of the perfection] is in a part [of the magnitude]. If an infinite perfection were so extended, a greater power of efficiency in acting would be in the whole than in a part—though not in a greater intensity in itself—just as it is with a great fire and one of its parts.

So it follows that in a finite magnitude [i] there is not a power infinite in efficiency or extension; therefore, [ii] neither is there a power infinite in itself intensively in such a magnitude.

This second consequence [ii] is clear, since it cannot be inferred that a power is infinite in itself except from the infinity of its efficiency. That the first consequence [i] also follows is shown in two ways. First, there is only a power finite in efficiency in each indivisible part of a finite magnitude; otherwise a part would not have less than the whole. Therefore there is only a power finite in efficiency in the whole, since what is composed of finite parts, finite in number, is itself finite. Second, as magnitude is understood to increase, so increases the power according to its efficiency; therefore, the power was finite before and always will be finite, as long as it is understood to be capable of increasing—and if it is in a finite magnitude, it always can be understood to be capable of increasing. Therefore the power can never be understood to be incapable of increasing, unless it should be in an infinite magnitude—and thus it cannot in any other way be infinite in efficiency, and so neither in intensity.

[Objection to the reply] But how is it relevant to the argument that an intensively infinite power is not accidentally extended such that each part of it is in a separate part of a magnitude? How does it follow from this fact that such a power in no way exists in a magnitude?

[Reply to the objection to the reply] The ultimate reason is supplied thus: extension extends something that is a subject, and in this case neither that infinite perfection, nor a matter of which it is the form as the intellective soul is of the body, can be a subject for extension, since that perfection is not in matter (by Theorem 4.1); therefore, etc. And so the Philosopher, before this argument, proved that this thing does not exist in matter in Metaphysics 12;35

35. Aristotle, Metaphysics 12.6.1071b19–22 (Barnes, 2:1693).

Translation and in virtue of the conclusions of both arguments the proposed conclusion follows well enough.

(79) The same is proved more briefly in this way: understanding is not a subject of extension; the First Nature is understanding (from Theorem 4.6), and (from Theorem 4.1) is not received in matter (which can be expressed in terms of quantity and so magnitude).

Third type of simplicity: no accidents 89. (80) [First proof of the third type of simplicity] Third, it is established that the First Nature cannot make a composition with any accident, since any thing that can be perfected lacks in itself its perfecting entity—otherwise it would not be in potency to it. Thus the perfection is added to the perfectible, and the whole is something more perfect than either of the two things so united. But the infinite lacks nothing—that is, there is nothing such that it would add perfection to the infinite, were it united with the infinite— otherwise the infinite could be something greater than it is.

[Second proof ] Second, material accidents cannot belong to the First Nature, because the infinite is not subject to quantity. And immaterial acci dents pertaining to intellect and will are not in the First Nature, either, because acts of understanding and willing—which seem most of all to be accidents—are in fact the same as it, as Theorem 4.6 shows.

(81) In three other ways it is argued that nothing is accidental to the First Nature:

[Third proof ] what is essential is prior to everything accidental.

[Fourth proof ] Also, in the First Nature nothing is caused.

[Fifth proof ] Also, in the First Nature there is no potentiality.

[Objections to the third, fourth, and fifth proofs] This trio shows that an acci dent does not belong to the essence of the First Nature, but it does not show that an accident does not accidentally belong to it. Not the third because while nothing in the essence of the First Nature is accidental, something other than the essence could belong to it accidentally; and thus, in that First

Nature there would be something essential prior to what is accidental to it, because the first essence would be prior to that union between it and its accident. Not the fourth because while the first essence would be uncaused, something caused might accidentally inform it; for while no essence of a caused substance is a cause of itself, some such essence might be a cause of its accident. Not the fifth because potentiality to an accident is a potentiality in a qualified way; but how is it shown from this that an accident cannot be in something that in its essence is only act?

Chapter 4 90. (82) [Sixth proof ] It is argued in another way that nothing is in the First

Nature except pure perfections (from Theorem 4.2); each of these is the same as that nature, otherwise none would be the best from itself (or else there would be several unqualifiedly best things).

[First objection to the sixth proof ] This argument does not go through, since (as is clear from what was said in the sixth proof of Theorem 4.4)36 it is not repugnant to the nature of pure perfections that there should be several pure perfections, each one highest in its own grade, in such a way that neverthe less one highest perfection is better than another—better even than all the others—but the essence of the First Nature is better than any of them, and none is the same as it, but all inhere in it. The reason these are not repugnant is that it does not follow from "there is a denominative perfection better than anything incompossible with it, and it exists in the highest degree to which a perfection of its nature can exist," that "therefore it is unqualifiedly the best nature"; instead, it only follows that "therefore it is the best of the totality of things in the genus that includes both it and the denominative perfections incompossible with it."

[Reply to the first objection to the sixth proof ] But someone might reply that if all pure perfections include each other by identity, then whatever would have one in some more perfect way, would have the others in the same way.

[Reply to the reply] The consequent is false; for matter is more necessary than form, but less actual; and accident depends on substance, but is simpler than it; likewise a celestial body is more incorruptible than a body mixed of the elements, but our animated body (insofar as it is animated) is nobler than a celestial body. So it follows that pure perfections—except those that are properties of being—differ both from each other and perhaps from their subject, while one belongs to its subject intensely, and another does not belong to it intensely or even does not belong to it at all.

[Second objection to the sixth proof ] The first claim of this argument has not been shown, either, for Theorem 4.2, which is alleged to support it, does not prove anything about inhering accidents, but only about what is intrinsic to the highest nature.

But if some impudent person were to posit an accident in the First Nature, it would be difficult to rebut his claim that such an accident is a pure perfection, since at times nobler natures are denominated by a less noble denominative perfection, and less noble natures denominated by a nobler denominative perfection that is a pure perfection. For example, prime matter is simple, but a man is not simple; simplicity here is just such a denominative perfection.

36. 4.58(22) above.

Translation (83) [The inconclusiveness of the third through sixth proofs] Indeed, it would be difficult, perhaps impossible, to prove from these last four arguments that there is no accident contingently and accidentally inhering in the First

Nature, on account of which that Nature can undergo accidental change either by itself or by something posterior to it; after all, it is posited that our will, in its willing, is changed by itself (though a first cause of our actions is also posited).

If it were well proved that in the First Nature simplicity is repugnant with being the subject of an accident, the conclusion would be very fruitful.

Should anyone be unpleased with the first two proofs of simplicity given here, let him come up with better.

In Praise of God 91. (84) Lord our God, from what has been said here, Catholics can infer the many perfections the philosophers have known about you. You are the first efficient cause; you are the ultimate end; you are supreme in perfection; you transcend everything else. You are altogether uncaused and so cannot come into existence or pass out of existence; indeed it is altogether impossi ble for you not to exist, because you exist necessarily, from yourself. So also you are eternal, possessing unending and simultaneous duration without the potential to exist successively; for there can be no succession where there is not something continuously caused, or at least dependent on another for being—a dependence alien to something existing necessarily from itself.

You live a most noble life, because you understand and you love. You are blessed, indeed you are in your essence blessedness itself, because you are the comprehension of yourself. You are a bright vision of yourself, and a love surpassingly delightful. And although you are blessed in yourself and fully suffice for yourself, yet you actually understand, all at once, everything that can be understood. Everything that can be caused to exist, you can, all at once, will it contingently and freely, and by willing it cause it to exist. There fore you are, most truly, infinite power. You are incomprehensible, infinite; for nothing omniscient is finite, no infinite power is finite, neither the most

Supreme Nature nor the ultimate end is finite, nor is the altogether simple, essentially existing nature.

You are simplicity in the extreme, having no really distinct parts, hav ing no realities in your essence that are not really the same. In you there is no quantity; no accident can reach you; thus you cannot suffer accidental change; you are in fact immutable, as I have declared above.

You alone are unqualifiedly perfect: not a perfect angel, or a perfect body, but perfect being; of the being possible for anything whatsoever to have, you

Chapter 4 lack nothing. It is not possible to have formally all the being possible for any thing whatsoever to have; but it can be had formally or eminently, in just the way you have it, God, who are the highest of beings—indeed, among beings, the only infinite.

92. You are good without limit, communicating the rays of your goodness most liberally; to you, the most lovable, each individual thing in its own way returns, as to its final end.

(85) You only are the first truth. Now the false is what is not as it appears to be. But if the nature of the false thing itself were the only cause of its appearing as it does, it would appear as it really is. Therefore, there is some thing besides the false thing itself, which explains why it appears as it does.

But nothing besides yourself is a cause or explanation of how things appear to you, since your own essence is originally apparent to yourself, and for this reason, nothing posterior to your essence causes or explains how things appear to you.

In that essence, I say, every intelligible thing is present to your intellect in the most intelligible way possible. You are therefore the brightest intelligi ble truth, and infallible truth, and the one who comprehends with certitude every truth that can be understood. For other things that appear in you, do not for that reason appear to you in such a way as to deceive you, because this cause of how they appear does not prevent their proper nature from being revealed through it and appearing to your intellect. Our vision is deceived when an alien appearance prohibits something else from appearing as it is, but it is not like this in your intellect; rather, everything appearing in your essence, shining out from it with most perfect clarity, appears to you accord ing to its proper nature.

For what I have set out to accomplish, there is no need to write at greater length about your truth and your ideas. Many things may be said about the ideas, but if nothing at all were said, and the ideas not even named, no less of your perfection will be known. This remains, that your essence is the per fect object for knowing everything that can be known, in every way it can be known. Let whoever wants to do so call this "an idea," but here I do not intend to fixate on that Greek and Platonic word.

93. (86) Beyond all that has been said up to now, which concerns what the philosophers have said about you, Catholics often praise you as omnipo tent, immense, omnipresent, just and merciful, providing for all creatures and especially for intellectual creatures. All of these attributes are deferred for a subsequent treatise.37 Obviously, in this first treatise I have only attempted to see how metaphysical claims about you might in some way be established by 37. There is no such treatise.

Translation natural reason. In a following treatise will be set forth the claims believable by faith, in regard to which reason is held captive, but which, nonetheless, are more certain for Catholics because they firmly rest on your most solid truth and not on our blinded intellects, vacillating about so many things.

The Uniqueness of God 94. (87) Yet there is one more thing, which I place here and in which I will consummate this little book.

Theorem 4.11: You are one God, besides whom there is no other, as you have said through the Prophet.38

(88) I do not think that reason is inadequate to prove this theorem, so I propose five propositions, any of which, once it has been proved, yields the theorem.

First: There is only numerically one infinite intellect.

Second: There is only numerically one infinite will.

Third: There is only numerically one infinite power.

Fourth: There is only numerically one necessarily existing thing.

Fifth: There is only numerically one infinite goodness.

It is clear enough that the theorem follows from any of these. They are proved in order.

First proof of uniqueness: from infinite intellect 95. (89) First, the first: an infinite intellect most perfectly understands any thing to the extent that it is intelligible; and in so understanding depends on nothing else—otherwise it would not be infinite. If there were two infinite intellects—let them be A and B—both would fail to have perfect and inde pendent understanding. For A, if it understands B through B, depends for its understanding of B on B itself, just as an act depends on its object when these are not the same. But if A understands B through A itself and not through B, it does not understand B as perfectly as B can be understood, since nothing is most perfectly present except either in itself or in something containing it most eminently. But A does not contain B. If you say that it is just like B,

I answer to the contrary: knowing a thing through something like it is only knowing it under a universal, insofar as the two things are similar. The pecu liar properties of things, by which they are distinguished from one another, would not be known in this way. Also, this knowing under a universal is not 38. Isaiah 45:5.

Chapter 4 intuitive, but abstractive, and intuitive knowing is more perfect. Again, one and the same act does not have two adequate objects; A is its own adequate object; therefore it does not understand B [adequately].

Second proof of uniqueness: from infinite will 96. (90) Second, the proposition about infinite will is proved: an infinite will loves most what is most lovable; but A does not love B the most; first, because it naturally loves itself more, therefore likewise it loves itself more with a free and upright will; next because it would be blessed in B, but if B were destroyed, A would be no less blessed. Thus it is impossible for the same thing to be able to have blessedness in two things, but this follows given two infinite wills: for B is not used by A, therefore B is enjoyed by A; therefore

A is blessed in B.

Third proof of uniqueness: from infinite power 97. (91) Third, the proposition about infinite power is proved in this way. If there were two infinite powers, each would be first with respect to the same things, because essential dependence is dependence on the nature, and what depends essentially on it depends equally on anything having that nature.

But one and the same thing cannot depend on two firsts (from Theorem 3.16). A plurality of supremacy is therefore not good, since either it is impos sible or each ruler will be diminished and only partially foremost; and then it remains to ask: by whose power are they conjoined in their headship?

Fourth proof of uniqueness: from necessary existence (92) Fourth, the proposition about necessary existence is proved in this way.

A species that can be multiplied is, as far as its own nature is concerned, infinitely multipliable; therefore if necessary existence could be multiplied, there could be infinitely many necessarily existing things; therefore there are, since anything the nature of which includes necessity cannot exist at all if it does not exist in fact.

Fifth proof of uniqueness: from infinite goodness (93) Fifth, the proposition about the good is shown. Many goods are better than one, when one adds goodness to another; to an infinite good nothing better can be added. In the same vein it is argued in this way: any will is totally at rest in one infinite good; but if there were another, a will could rightly will for both to exist rather than just one; therefore it would not be totally at rest in the one highest good.

Other ways could be adduced, but the foregoing suffice for the present.

Translation Closing Prayer 98. (94) Lord our God, you are one in nature and one in number; truly you have said that besides you there is no god. For even if there were many puta tive gods or things called gods, yet you are unique in nature, the true God, from whom, in whom, and through whom are all things;39 you are blessed forever. Amen.

Here ends the treatise on the first principle by John Scotus.

39. Romans 11:36.

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