by Dr. Anthony P. Andres
Thomas Aquinas College
January 17, 2014
Note: Dr. Andres is a tutor at Thomas Aquinas College. The following is the prepared text for a lecture he presented as part of the the St. Vincent de Paul Lecture and Concert Series, endowed by Barbara and Paul Henkels.
I need to begin by explaining the foolishly chosen title of my lecture, “Does God Play Dice With The World?” This lecture is not about predestination. It is not really about God, and it’s not on the evils of gambling. What it’s really about is the question of whether everything that happens in the natural world happens by necessity, or whether there is really chance in nature. The most famous physicists of the 18th and 19th centuries assumed that the workings of the natural world followed exact laws that could not be violated:, everything that happened had to happen, that is, was necessary, and everything that did not happen could not happen, that is, was impossible. According to these men, if I threw a log on a fire under the right conditions, it had to burn, but if I did so under the wrong conditions, it was impossible for it to burn. Pierre Laplace gave the most famous formulation of this opinion in:
We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.
But in the early decades of the 20th century a new theory in physics, quantum mechanics, upset the scientific consensus on this question. Quantum mechanics explains events on the atomic level using laws that are not determinist, but only probabilistic. For example, quantum mechanics explains the decay of radioactive atoms, that is, the fact that their nuclei split, but it only does this probabilistically. Quantum theory does not allow the scientist to say that, under the right conditions, this atom must decay at this particular time; it only allows him to say that, under the right conditions, this atom has a 50 percent chance of decaying within a particular amount of time. The atom could decay almost immediately or could resist decay for thousands of years without violating the theory. That is, the radioactive decay of an atom within a given time happens contingently, not by necessity.
Some of the scientists who developed quantum theory initially thought of it as a stopgap, as a stage on the way to a better theory which would show that phenomena like radioactive decay had necessary causes. But eventually many concluded that quantum mechanics could not be replaced by such a theory. The reason: they came to believe that events in the physical world were in themselves contingent, that they did not happen by necessity. Quantum theory was probabilistic because nature herself was probabilistic.
This opinion, that events in the physical world are not predetermined by necessary physical laws, shocked Albert Einstein and led him to say, “Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the “old one.” “I, at any rate, am convinced that He does not throw dice.” And the most eminent Thomist of that time, Jacques Maritain, agreed with Einstein. He argued that the principle of causality demands that in the natural world the future follows necessarily from the present. And many other Catholic philosophers followed his lead.
But Charles DeKoninck, a professor of philosophy at Laval University and himself a staunch disciple of St. Thomas, was astonished at their resistance to the new theory. In two papers published in the mid-1930s, “The Problem of Indeterminism” and “Reflections on the Problem of Indeterminism,” he vigorously argued that Aristotle and St. Thomas posit a degree of real contingency in the events of the natural world. He also pointed out that St. Thomas had refuted the very arguments used by Maritain and his followers in opposition to this conclusion. In these two papers, DeKoninck tackles both philosophical and scientific objections against indeterminism; he explains the nature of the relation between the philosophy of nature, the philosophy of science, and science itself; and he unfolds the true distinction between absolute and hypothetical necessity. The papers display both DeKoninck’s grasp of the philosophy of nature and his dialectical prowess. But because of the great number of issues that he discusses in these papers, the arguments he puts forward for particular conclusions are sometimes hard to understand.
In this lecture I intend to leave aside DeKoninck’s dialectical concerns with science, history, and method, and to focus entirely on the doctrine he proposes for the philosophy of nature. That is, I intend to present as clearly as I can his argument that contingency is a real feature of the natural world. Like DeKoninck himself, I will make use of the writings of Aristotle and St. Thomas. So my lecture has three main parts. First I will talk about how contingency in the natural world is rooted in the indetermination of matter and form. Second, I want to show that contingency is itself the root of the accidental in nature. Third, I will explain how DeKoninck answers the rejoinders of those scholastic philosophers who reject real contingency in nature.
But I have two preliminary matters to clear up. First, I need to review Aristotle’s basic doctrine on substantial change, and then I want to lay out what the words ‘necessary’ and ‘contingent’ mean.
Let me assume for the moment that an acorn, and the oak tree which comes from it, are two distinct substances. It doesn’t matter to me right now if scientifically I’m mistaken here, because I’m just using this to make a philosophical point. We see that the acorn becomes an oak tree; the first substance, acorn, stops existing, corrupts, while the second, the oak tree, comes into existence or is generated. The first thing we can say is that something must survive the change from acorn to oak tree; if not, there would be no need for an acorn, since the oak tree could just pop into existence out of nothing. But we know by experience that we can’t get something from nothing, that the oak tree comes from the acorn.
On the other hand, we can also argue that nothing actually can survive the change, since if an actual substance survived the change, the oak tree would not really be a new substance, distinct from the acorn. The oak tree would only be the acorn with a new shape. So, we seem to be at an impasse; on the one hand, we know that something must survive the change from acorn to oak tree; on the other, we know that nothing actual can survive the change from acorn to oak tree. So we can ask, how does Aristotle solve this kind of problem?
Aristotle uses the notion of the potential to solve the problem. What survives the change from acorn to oak tree is the potential to be a substance. The potential is first present in the acorn, and the substantial form of the acorn makes it actual. That same potential survives the change and is then present in the oak tree, and the substantial form of the oak tree makes it actual again. Because this potential survives the change of substance, and because substance is the most fundamental kind of being, Aristotle calls this potential “prime matter.” Prime matter is real, but not anything actual: it is the potential to be a substance.
And really, it is the potential to be any substance. An acorn is designed to become an oak tree, but most acorns never make it. Squirrels and pigs and other animals usually eat them before they germinate. If the pig eats the acorn, the acorn still undergoes a substantial change, but this time a change into being part of a pig: the acorn becomes pig flesh. When I eat bacon, the pig in turn undergoes a substantial change, becoming part of me. But through every change the prime matter survives; first it is an acorn, then a pig, and finally me. So prime matter is not a determinate potential to be some determinate substance, but a potential to be any changeable substance.
Let me sum up: the acorn is a changeable substance, and prime matter, the potential to be a substance, is present in it. At first, that prime matter is actually an acorn because it has the substantial form of an acorn; but when water and sunlight act upon it, the matter loses that substantial form and gains another, the form of an oak tree. Now it is actually an oak tree. In general, every changeable substance has two principles, prime matter, the ability to be any substance, and substantial form, what makes it actually be this particular substance. I hope that this review of the doctrine of Aristotle on substantial change has not been burdensome, but I think it is necessary for understanding the doctrine of contingency in nature.
Now we can tackle something much more straightforward, the clarification of the meanings of the words ‘necessary’ and ‘contingent.’ As St. Thomas says in many places, the word ‘necessary’ simply names ‘that which cannot not be,’ or ‘that which cannot fail to be.’1 He also says that the word ‘contingent’ in its broader meaning names ‘that which might or might not be,’ or ‘that which can be, but can also fail to be.’ We see right away that necessity and contingency concern being and existence immediately, and that beings can be distinguished as beings by whether they are necessary or contingent.
Let’s give a couple of examples. God, whose very essence is existence, is the complete example of a necessary being. He cannot not-be simply because of what He is. DeKoninck points out that, compared to God, everything else is contingent: “All finite beings are equally contingent insofar as they are finite.”2 But he qualifies this assertion: “Compared to one another, some are less so than others according to the perfection of the essence which receives more or less intimately the proportioned existence.”3 That is, the more perfect created thing receives existence more intimately than the less perfect. The angels share this property, that their natures receive existence so intimately that their existence always remains secure: they do not have prime matter, they do not have any principle within their nature by which they might become something else, and so cease to exist. Angels do not die. In this way, angels are also necessary beings.
This is not the case with the substances of the material world, with dogs, pigs, or oak trees. The complexity of their natures entails a complexity of existence, which he notes, “makes a totally assured existence impossible.”4 That is, the existence of the physical substance is not the simple actuality of its nature, as an angel’s is; rather, its existence is its substantial form actually being in its prime matter, a matter that in itself is not only able to have its present substantial form, but is always capable of receiving another. For this reason, the continued existence of the material substance is not assured, and such a being is essentially contingent. Acorns are contingent beings: pigs eat them. And since we eat the pigs, the pigs are contingent as well.
DeKoninck uses the case of a dog being killed by a falling tree to exemplify the contingency of a natural substance. He notes that the dog’s substantial form is too imperfect to receive a simple, assured existence. It can only come to exist by being the determination of matter, which in itself is undetermined potency. But the matter also has an ability to be another substance; and when the dog is struck by the falling tree, his matter does actually become another substance. Thus, the complexity of the dog’s nature, his composition from form and matter, results in the contingency of his existence.
No doubt the ground we have covered so far is familiar to many of you. St. Thomas’s third way of proving the existence of God explains that some beings are contingent because they have a principle of non-being in their essences. Others, he notes, have no such essential principle, but neither do they have something in their essence by which they exist. The latter are necessary beings who must receive existence from another. Finally, there is the necessary being, God, who not only has an assured existence, but has not received that existence from another. Here again St. Thomas divides beings into kinds according to their necessity and contingency.
Prime matter is a principle of contingency in the physical substance, insofar as matter is an indeterminate potency, that is, a potency to be any material substance. Maritain and his disciples granted this. DeKoninck argued, however, that the indetermination of matter not only makes the existence of the physical substance contingent, it also makes its coming to be contingent; this they deny. If DeKoninck’s argument firmly establishes this conclusion, then he will have completed his case for real contingency in the natural world. Before we can understand his argument, however, we need to see a little more clearly what is meant by the word “indetermination.”
First, we should note that indetermination is the privation of determination. Now St. Thomas writes about determination in the Seventh Quodlibetal Question. An objection in that question argues that, since determination, according to its very etymology, implies boundaries, and God is infinite, that is, without boundaries, then God is indeterminate. This would make God be like prime matter, which is absurd. St. Thomas solves the problem by saying, “determination is twofold, either with respect to limitation or with respect to distinction.”5 As the objection points out, determination is first said with respect to a boundary, a terminus. But determination refers to a boundary, not insofar as the boundary encloses the bounded, but insofar as the boundary excludes anything other than the bounded. That is, determination refers to the boundary insofar as the boundary is a principle of distinguishing one thing from another. And so, determination is also said with respect to distinction. That is, something is determinate insofar as it is distinct from another. This is what enables us to say that God is determinate. His existence is not bounded or limited by being received into an essence, but this very fact distinguishes Him from all creatures and actually makes Him most highly determinate. And the Divine Persons are also determinate without being bounded, since they are distinct from each other through distinct relations of origin.6
As the angelic natures share in the necessary existence of God, they also share in his determinateness. Nothing can exist without being one individual thing, and so if an essence has the ability to receive determinate existence by itself, it must also have in itself a determination to being one individual. And so, the same determination that makes the angelic natures able to receive necessary existence also makes each nature’s existence the determinate existence of one individual.
In contrast, just as the natures of material substances lack necessary existence, so also do they lack determination. Their matter is indeterminate insofar as it is not the distinct potency to be one thing rather than another. In other words, the potency of prime matter is indifferent to the many kinds of substantial forms that it can receive. And since the potency of matter to have another form is the cause of contingency, then the indeterminacy of prime matter is one source of the contingency of existence for the material substance.
But DeKoninck argues that the more fundamental reason for the indeterminacy of prime matter is the indeterminacy of the substantial form. He writes:
Contingency touches even the structure of natural forms, which cannot be entirely determined “ad unum” [to one] like the angelic form. It is just this lack of determination and incapacity for individuating itself that calls for matter. This need for matter introduces into the form itself an irreducible obscurity.7
The forms of material substances require matter. They are unable to receive existence without matter because they are too indeterminate to constitute one existing individual on their own. They need the help of matter to determine them to an existing individual. But this need is a need for a matter which itself is indeterminate, able to take on many other possible substantial forms. And so the indetermination of prime matter is rooted in the indetermination of the substantial forms of material substances. Thus, the deeper reason for the contingency of natural things is the indetermination of their forms.
Consider again the example of the acorn. The substantial form of an acorn is, of course, determinate to some degree: it places a limit on the perfection of the acorn and makes the acorn distinct from other substances. But that form is not entirely determinate. First, the form is indeterminate because it does not by itself constitute an individual acorn; it needs the help of prime matter to constitute this individual acorn. But the form is also indeterminate because it is a substantial form which exists in order to give way to another substantial form, that of the oak tree. An acorn is not just an acorn, it is something on its way to being an oak tree, and so its substantial form is not entirely distinct from that of an oak tree. Moreover, because it is on its way to being another substance, it needs to use a matter which is indeterminate, that is, at the very least able to be that other substance. And so, the indeterminacy of the prime matter of the acorn is rooted in the partial indeterminacy of the substantial form of an acorn.
Let us recall what we have seen so far. Beings are divided into the necessary and contingent, and matter is a principle of contingency in natural substances. But the indeterminacy of matter results from the indeterminacy of form in the material substance. Thus, the forms of those substances are also in some way indeterminate. In sum, DeKoninck has argued that both the matter and the form of a natural substance is indeterminate, and that this indeterminateness is the reason why they are contingent beings. What we now have to see is how he argues that, not only is the existence of a material substance contingent, so also is its coming to be. To understand why this is true, we need explain in more detail how coming to be occurs for a material substance.
Up to this point, we have been considering the contingency of the existence of a natural substance. Now we need to consider its generation, the process of its coming to be. As we saw before, the generation of a material substance presupposes a matter, already existing under the substantial form of a previous substance. The matter of the oak tree first exists in the acorn. But the matter does not acquire its new form by itself. There needs to be an agent in the process of generation. A natural agent, having a substantial form as the principle of its action, but using its accidental forms as instruments in that action, works to bring about a new substantial form in the old matter. These accidental forms, active qualities like heat and moisture, are instruments insofar as they alter the matter so that it is disposed to receive the new substantial form. The substantial change is the terminus of those alterations, a terminus that results in a new substance that resembles in some way the agent of its coming to be. An everyday example is a dog eating his food. The dog that eats his food brings about a substantial change. The food has a matter which the dog, using his digestive powers, alters more and more. The matter of the food becomes more and more disposed to be incorporated under the substantial form of the dog. The term of that alteration is dog-flesh; that is, the food becoming part of the dog. Thus, the dog uses his accidental forms as instruments to dispose the matter of food to receive the substantial form which the dog already possesses.
But according to DeKoninck, not only is the dog a contingent being, but the food that the dog eats becomes dog-flesh contingently; that is, because of the indetermination of form and matter, the food might or might not become dog-flesh. DeKoninck outlines three ways in which indetermination is responsible for the contingency of the coming to be of new substances: first, on the side of the material subject which comes to be; second, on the side of the agent which forms the matter; and third, on the side of the impeding agent cause.
Let us begin our examination of contingency in coming to be by looking at its subject. DeKoninck writes, “Matter is potency, and it is precisely its indetermination which is the cause of uncertainty.”8 That is, matter is the ability to have substantial form, not a distinct ability to have some particular kind of form, but an indeterminate ability to receive any form that it does not already have. The dispositions of the matter, the accidental forms which prepare the way for the reception and possession of the new substantial form in that matter, do make the ability more determinate, but they do not make that ability completely determinate. But any indetermination in the ability of a subject to receive a form is an impediment to the reception of that form, and what is impeded might not happen. Thus, the coming to be of a substance, which is the reception of this form in this matter, is uncertain; it might or might not happen. Matter is a principle only of a contingent coming to be.
But DeKoninck notes that indetermination also must also exist on the side of the natural agent of substantial change: “But matter can be the cause of contingency only because there is a defect of determination even on the side of the agent cause.”9 The natural agent acts in virtue of its accidental forms, which are ultimately rooted in its substantial form. But, as we saw before, the substantial form is in itself not entirely determined to one. Therefore its effects are not entirely determined to one: “The absence of necessity in form entails an absence of necessity in its effects.”10 Thus, the strength of the natural agent is always somewhat imperfect and indeterminate, and so the coming to be of the new substance which the agent attempts to bring about is contingent. That is, the agent might not have the strength to bring about a sufficient disposition in the matter for the new substantial form, or it might have strength to bring a barely sufficient disposition, but not one that guarantees the change.
As anyone who has owned a dog knows, this statement is clearly true in the case of canine digestion. Sometimes the dog digests his food, sometimes he does not. Since he sometimes does digest his food, his digestion clearly has sufficient strength to bring about the aimed at substantial change; but since he sometimes fails, its strength is not such that it guarantees success. The dog digests his food contingently.
The indeterminacy of matter and form, however, brings into play a third factor in the contingent coming to be of natural things, the impeding agent cause. Since the coming to be of the natural substance is contingent, in the cases when it does come to be, the precise moment at which it comes to be is not predetermined in the agent and subject. That is, since there is indetermination on the side of both the agent and the subject, there is no set amount of time which guarantees that the change will take place in the subject. It might happen sooner, it might happen later. The dog might digest his food in thirty minutes or in forty-five minutes. Thus, the precise moment of the coming to be of a new material agent, or of a new state in the material agent, is not predetermined by the prior relation between the agent and the subject.
Thus, the contingency of the coming to be of a new substance, or even the contingency of the moment of its coming to be, inevitably brings about the existence of a third indeterminate factor in natural coming to be, the contrary cause impeding . We should contrast the cause to the cause. A cause brings about a particular kind of effect because of the kind of cause that it is. The dog digests food as he does because he is a dog; he is the cause of food becoming dog-flesh. Even the concurrence of two causes can be one cause if their concurrence is itself predetermined by prior causes; chewing and swallowing are one cause in digestion. There can be a concurrence of causes which is not a source of contingency.
But since the strength, and even the existence of natural agents is not entirely predetermined, then their concurrence is not always predetermined by the kind of agents that they are. Their concurrence just happens, is accidental or per accidens. Therefore, the contingency that comes from the indetermination of natural forms and matter is the source of the concurrence of agent causes in the natural world. And since this concurrence has its source in contingency, it itself is contingent and is even the reason for further contingency.
For even in cases when the agent is strong enough to bring about a more than sufficient disposition in the subject, its action may be frustrated by the concurrent action of a contrary agent. But the concurrence of contrary agents is , and therefore contingent. Consequently, the failure of the agent to bring about the change in the patient is itself contingent.
Let me explain what I mean using an example. A very healthy dog might find easily digestible food, but his eating could be frustrated by the untimely intrusion of a larger predator, say a lion. Thus, even a very strong agent beginning to act upon properly disposed matter can fail to bring about the intended result. Since the concurrence of the action of the lion and the dog is not predetermined, but , this case in which he fails to digest his food is contingent. And even when the lion does not interfere, and the dog actually succeeds in eating and digesting his food, his causality is still contingent because it has been impeded by another cause. Since the success or failure of the agent also hinges upon the contingent presence or absence of an impeding agent, success and failure are doubly contingent.
And so, we have detailed all of the aspects under which the coming to be of a natural, material substance is contingent. Coming to be might fail either because both the potency of matter and the strength of the agent is indeterminate or because of the concurrence of an impeding agent cause, which is itself rooted in some prior indetermination. The essential indetermination of form and matter, especially the former, is the ultimate root of real contingency with respect both to existence and to coming to be in the natural world.
This conclusion fits with our untutored experience of the world around us, but as we saw before Laplace, Einstein, and even the scholastics of the early 20th century rejected the objectivity of contingency in the natural world. They asserted that the appearance of contingency was the result of our ignorance of all of the causes. Maritain admitted an exception, the events influenced by the free choices of men, but all agreed that natural events uninfluenced by free will, including the comings to be of material substances, happen by necessity.
What rejoinder would the followers of Maritain make to DeKoninck’s account? They have invoked three principles for maintaining that the events of the natural world happen by necessity: first, the principle of sufficient reason, that everything that happens must have a sufficient cause for its happening; second, the principle that nature is determined to one, which requires that natural agents always act as they are inclined, and to the utmost of their strength; third, the presence of the impeding cause, that every instance in which the natural agent fails to achieve its effect can be attributed to the presence of an impediment.
Putting these principles together, they make the following argument. A natural agent always acts with its utmost strength to bring about its effect. And a sufficient cause being posited, the effect necessarily follows, unless there is an impediment. But the impediment itself is the result of a sufficient cause; therefore, the impediment, if present, is present necessarily. Thus, for a natural agent, if its effect comes to be, it does so necessarily, and if it fails, it was because its coming to be was made impossible by an impediment. Therefore, everything that happens happens by necessity; the contingency in the natural world is not a real contingency, but only our failure to foresee absence or presence of the impediment.
The argument can be applied differently to each of the ways in which an effect can be contingent. We noted before that the coming to be of the effect is contingent because of the weakness of the agent. But those who argue for necessity insist that the agent which is so weak that he does not bring about his effect is not a sufficient agent, and so it is impossible for him to achieve his effect. If there is an impediment on the side of the disposition of matter, they reply that the disposition is of a certain degree, and that, taking into account the exact degree of the disposition and indisposition, we can determine the exact degree of strength necessary in the agent in order to bring about the effect. If the agent has that degree of strength, he will bring about the effect necessarily, but if not, he is again not a sufficient agent. Finally, if the agent is impeded by a concurrent agent cause, that cause comes to be in that place at that time by necessity, and so it makes the action of the agent impossible. In every case, necessity is preserved amid apparent contingency.
In reply to the main argument above, Cajetan notes that its use of the principle of sufficient reason commits the fallacy of the consequent.11 It is true that if an effect comes to be, there must be a sufficient cause, but it does not follow that, if there is a sufficient cause, then the effect must come to be. In fact, Cajetan argues that the effect might not come to be even if the cause is sufficient. So the main argument commits the fallacy of the consequent in its use of the principle of sufficient reason.
St. Thomas himself disputes the notion of necessity that is implicit in the main argument. The argument asserts that the effect is necessary because of the absence of an impediment. But just as the concurrence of the agent and the contrary agent is accidents, so the absence of an impediment is accidental to the coming to be of the effect. The fact that the lion fails to impede the feasting dog is accidental to the dog digesting his food. Thus, the objector has defined the necessary, not in relation to being per se, but to being per accidens. And this is a bad understanding of necessity, because it undermines necessity and contingency as distinctions between essentially different kinds of beings. St. Thomas argues that we should define necessity and contingency just in terms of being: the necessary is what cannot not-be and the contingent as what can be, but can also fail to be. The lack of an impediment is not the cause of necessity, as the opponents of contingency think; rather, necessity is the reason why some agents cannot be impeded.
And DeKoninck replies decisively to the subsequent application of this argument. The application assigns a precise degree of strength to the agent and a precise degree of disposition to the matter. For example, the argument assumes that my dog’s digestive powers have a precise degree of strength, and that the food has a precise degree of disposition to be digested. But to talk about a precise degree of strength or a precise degree of disposition is in fact to deny the indetermination of form and matter:
The margin of indetermination [of matter] which exceeds the form, and this form itself, are incommensurable, since matter is indetermination.... The margin of indetermination always remains indefinite, even if its range diminishes according to the perfection of the form. To say that “there is only a certain quantity of indetermination” is to suppress indetermination.12
DeKoninck is here appealing to the indetermination of the matter in the patient. It is true that, the more that the matter is altered, the more it is disposed to become this or that determinate kind of substance. And the more the matter is disposed, the more determinate it is. But disposed matter is still matter, and as matter it is still indeterminate. Making the matter more disposed can never entirely eliminate matter’s indetermination. Matter with “only a certain quantity of indetermination” is a contradiction in terms; it would be a completely determinate indetermination.
Let me sum up our consideration of this matter. Charles DeKoninck, following the doctrine of St. Thomas, argues that in the natural world neither being nor coming to be are necessary, but both are subject to contingency. Contingency in coming to be, which is caused by the weakness of the natural agent, the indisposition of matter, and the impediment of a contrary agent, is rooted in the indetermination both of natural form and of prime matter. If all of this is correct, no disciple of St. Thomas should be alarmed by quantum mechanics.
But DeKoninck did not argue for contingency in nature in order to update an obsolete natural philosophy; his respect for both St. Thomas and the physicists was far too great. DeKoninck wanted to show Thomists that contingency had always been part of the tradition, a part abandoned for insufficient reasons. I think that the recovery of a truly philosophical understanding of the natural world depends upon the wisdom of men like Charles DeKoninck. Thank you for your attention.
1. In Phys. II, lect. 8, n. 210
2. p. 405
4. p. 407
5. Quodlibetal VII, 1, ad i
6. Quodlibetal VII, 3
7. p. 408
8. p. 412
11. Commentary on ST I, q. 115, art. 6
12. p. 420
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