Fundamentals

The Categories

In The Categories, Aristotle lays out the fundamental categories into which beings fall. The first major dichotomy is between particulars and universals, which are related to one another by instantiation and abstraction. For example, the term "man" denotes a universal which is instatiated by particular men such as Teddy Roosevelt. Likewise, "white" denotes a universal, whereas the white you see on a particular T-shirt is a particular instance of whiteness. Conversely, "man" is a universal abstracted from Teddy Roosevelt, and "white" is a universal abstracted from a particular white T-shirt. Universals are also related to one another heirarchically. For example, Dogs are types of Animals, and animals are types of living things. In Aristotelian terms, "dog" denotes a species of the genus "animal," and "animal" denotes a species or subgenus of the genus "living things."

The second major dichotomy is between substance and accident. This terminology does not coincide with contemporary usage of these terms at all, and does not really come from Aristotle himself, but his subsequent Latin commentators. In modern usage, the "substance/accident" distinction is better thought of as the "object/attribute" distinction, but this is not entirely accurate, and in any event it is not the terminology that St. Thomas uses, so we will stick with "substance/accident." Aristotle defines an accident as something which exists "in" another thing, not as a part, and cannot exist independently of the thing it is in. So a toe is not an accident of a foot, but the length, color, hardness, location, and position of the foot are all accidents of the foot. He lists the highest genera of accidents as "quantity," "quality," "relation," "location," "temporality," "being-in-a-position," "having," "doing," or "being-affected."

Substances are then defined to be those things which do not exist in other things, except perhaps as parts. One can say they are the things which are bearers of attributes, but are not attributes of other things. He primarily has in mind particular substances here, which persist as the accidents they take on change over time. For example, Teddy Roosevelt's height, an accident in the genus of "quantity," changed throughout his life, but he remained Teddy Roosevelt. So Teddy Roosevelt was the fundamental, persistent substratum underlying the existence of all the various heights (3 feet, 4 feet, 5 feet, etc) that came to exist in him, that is, Teddy Roosevelt was a substance. Aristotle also considers universal terms abstracted from particular substances to count as a kind of substance, since, for example, the universal "man," which is abstracted from Teddy Roosevelt, has the differentiae "two-footedness" and "rationality" attributed to it, and is thus an underlying bearer of attributes in an analogous sense. Aristotle calls universal substances secondary substances, and does not really consider them to be true substances in the same way that particular substances are substances. However, there is a sense in which Aristotle considers universals to be real things, and therefore universal terms which refer to primary substances are better classified as substances than accidents.

It should be repeated that Aristotle's use of the word "substance" bears little relation to our contemporary usage of the word. In every day usage, a "substance" is the kind of thing whose parts are instances of the same kind of thing. For example, in the modern sense, dirt is a substance, because if you take a pile of dirt, and divide it into two piles, each of those piles is also dirt. On the other hand, an iguana is not a substance in the modern sense, because if you cut an iguana up, its parts are not iguanas. But to Aristotle, both count as substances. Etymologically, a substance is "that which stands under," it is a thing that bears properties, but retains its identity even as its properties change. Likewise, even "attribute" does not really capture the notion of what an "accident" is, because in modern usage "attribute" implies a kind of stability, but an "accident" can include things like "is running" in the statement "John is running."

It is helpful to be aware of some of the ways that the relations "instance of," "species/subgenus of," "part of", and "accident of," are all distinct from one another.

For the first pair of relations, note that if A is an instance of B, then A must be a particular, and B must be a universal, whereas if A is a species/subgenus of B, then both A and B must be universals. However, the notions are connected, because if A is an instance of B and B is a species/subgenus of C, then A is also an instance of C. There is close parallel here to the distinction between being a member of a set, and being a subset of a set, for those who are familiar with these modern concepts.

Likewise, the relation "part of" is formally similar, but also distinct, from the previous two relations mentioned. For if A is a part of B, then A and B are both particulars. Furthermore, if A is a part of B, there is no implied inheritance of properties between A and B. For example, I am six feet tall, but my parts, such as my hands and feet, are not all six feet tall. However, if A is an instance of B, then A inherits all the properties of B.

Finally, the relation "accident of" is distinct from all that came before. For one thing, generally speaking if A is an accident of B, then B should be a substance, although we have to be careful about this point. When we say "The dog runs swiftly," it seems that "runs" is an attribute of the dog, and "swiftly" is an attribute of the dog's running, but "swiftly" is not an attribute of the dog itself. In a sense this is true, and scholastics would describe "swiftly" as a secondary accident, that is, an accident of an accident. However, with respect to being, the swiftness of the running ultimately inheres in the dog itself. That is, the attributes or modifiers of an accident ultimately exist within the underlying substance in which the "primary" accident (in this case "running") inheres. In this sense they can be thought of as accidents of the substance itself. Properly understood, the question about whether something is an accident of something else is not meant to be a semantic question, but an ontological one.

Mathematical reasoning provides a clear illustration of the difference between a merely semantic view of the subtance/accident distinction, and an ontological one. A mathematician reasons about numbers, shapes, and so forth as though they are substances with accidents. For example, a mathematician would say that the number 7 is prime, where here "primeness" can be thought of as a kind of accident, and 7 is the substance in which the "primeness" inheres. However, Aristotle would not consider the number 7 as a substance, but as an accident inhering in substances. Similarly, a logician might say that an argument is valid. In this case he speaks of the argument as though it were a substance, and validity as an accident. But insofar as arguments are things pronounced or thought of by a person, they would count as accidents in Aristotle's scheme.

Based on what Aristotle writes in the Categories, one might be inclined to think that primary substances must be material entities, especially since the categories of accidents all seem to be attributes of material things, but in his other works he makes it clear that this is not what he thought about substances. For example he considers the unmoved mover, which is pure, immaterial actuality, to be a substance. St. Thomas also considers human souls and angelic beings to be immaterial substances, although the case of the human soul is complex.

The question naturally arises as to why something like the number 7 cannot be thought of as a primary substance. The difference is that things like the unmoved mover, angelic beings, and human souls all act as external agents upon other things in the world. Whereas universals or mathematical entities like the number 7 consistute intelligible notes of substances which allow us to make inferences about substances, but they do not act on substances. Even the Platonists, who regarded the abstract number 7 as more fundamentally real than its various instantiations in physical reality, considered it (and all universals) to exist separately and independently from the realm of material beings, which merely participate in the being of forms, but are not directly affected by them as one entity affects another in the world.

Matter and Form

The distinction between matter and form is another fundamental part of Aristotelian and Thomistic philosophy. On the surface the distinction is clear; taking the example of a bronze statue, the matter is bronze, the form is the geometric shape that it has been molded into.

More generally, if X is a part of Y, and X is made of matter M, then Y should also have M as part of its matter. It follows that matter should always be some kind of substance in the modern sense of the word discussed above, that is, matter should be a kind of stuff which, when divided into parts, is the same kind of stuff. So, for example, the matter of a man does not consist of the parts of him like his heart, liver, and lungs, but rather of the stuff of which he is made, for example, flesh and bone, or if one wants to be more fine-grained, the various tissues of which he is made. It is important to be aware here that Aristotle did not think the world was made up of atomic (or subatomic) particles. Instead, he thought the world was made of stuff like air, earth, water, and fire, that had form imprinted upon it.

Similarly, form does not merely amount to the shape of a substance, but also the various powers and attributes that are active within it. For example, the form of the eye does not just include its roundess, but also its ability to see. Aristotle famously describes souls as the form of living bodies. For example, when a plant is living, it's form is that of a "vegetative soul." It has the power to feed itself, to grow, and to reproduce, but once it dies and loses these powers, its form changes even though its shape and the underlying matter are still the same. The matter in the plant is no longer "ensouled." Similarly, animals have a more advanced soul, the "sensitive" soul, which is capable of locomotion and sense-perception, and finally man has a "rational" soul, which is capable of all the above plus reasoning. The ability to perceive and, in part, even to think, are qualities actualized in the matter, and which disappear from the matter when a person dies, even though all aspects of its sensible form remain the same. Thus form does not consist only of what is externally sensible.

Aristotle linked the distinction between matter and form to the distinction between potentiality and actuality. Since the same matter is capable of taking on many different forms, matter possesses potency and it is actualized by form. This is not to say that all matter is devoid of form "in itself." For example, a lump of bronze has the potential to be "actualized" as many different statues, but they must all retain the same mass, they must all be hard like bronze, and they must all have the color and shine of bronze. Aristotle posited that the most elemental matter consisted of earth, air, water, fire, and, in the heavens, aether. These forms of matter have the most raw potential. Below that, there is only "prime matter," which, being pure unactualized potency, doesn't actually exist in pure form, but forms the interconvertable substratum of all material being.

On the other end of the spectrum are immaterial substances, which are pure form without matter. It would seem that such substances cannot change, having no matter and thus no potency, and St. Thomas does indeed assert that God is immutable. However, St. Thomas considers angels and the human soul to be immaterial, and does allow them to change insofar as there is potency in their very being. So at least on the Thomistic view, matter is not the only source of potency, and is therefore potency is not identical to matter.

This is a very different picture of reality than that painted by modern physics. In a nutshell, modern physics places subatomic particles (or perhaps "strings") as the fundamental substances underlying reality, and such particles are not "made" of anything, they are simply mathematical objects with quantitative attributes, forms without matter that interact with one another according to mathematical laws. In other words, the universe is effectively a large mathematical construct that we are a part of. Within this framework, it is difficult to identify what a candidate for Aristotelian matter even looks like. The "stuff" that was obviously matter to Aristotle is now understood to be collections of individual Aristotelian substances (atoms) which seem to be pure forms floating through space.

However, as noted by Werner Heisenberg, the understanding of matter as the "potency" of physical reality does correspond well with the quantum mechanical picture of reality. In quantum mechanics, a particle like an electron does not have a definite location or momentum until it is observed through a causal mechanism which forces the particle to assume definite classical properties in the observable world. Until such an observation occurs, the particle "exists" as essentially a probability function that assigns a probability to each potential quantitive attribute that its classical realization will possess upon observation. Moreover, this encoding of the "potentiality" of each particle in its unobserved state is affected by the fully actualized environment within which the particle exists, together with the other unobserved particles in its environment. This reopens the possibility that form can determine the actualization of matter in a more meaningful way, and that the soul can play a more active role than was previously thought. But these issues will have to await a more in-depth resolution as we proceed through the Summa.

Universals and Essences

The question about the nature of universals was a central concern in medieval philosophy, and St. Thomas's theory of universals and essences plays an important role throughout his work.

Consider the universal term "dog." We all know a dog when we see it, but it takes a specialist to define it in a way that distinguishes it from all other species of mammals. And even then, modern biologists do not provide a clean, Platonic definition of what a dog is in terms of its directly observable features, nor did Aristotle himself. Instead, they all recite its placement within a taxonomy of living things (they are the domesticated descendants of grey wolves), together with some common features (they are quadripedal, carniverous, and so on).

The curious thing about dogs is that all people agree that they are a four-legged creature, and yet there are many dogs which do not have four legs. They are creatures with a good sense of smell, and yet some dogs cannot smell at all. Dogs have sight, and yet some dogs are blind. And if we see a blind, three-legged dog that cannot smell, we still recognize it as a dog. The fact that it is a dog is simply "given" to us in a way that we cannot articulate in words.

Thus it is clear that when we say something like, "a dog is a four-legged creature" we implicitly understand by this that a normal dog has four legs, but it is possible for a dog to have more or fewer. But what exactly does "normal" mean here? Does it simply mean that the majority of dogs we have seen have had four legs? If that is the case, then it implies that there must be some other means by which we perceive that something is a dog in the first place. Whatever it is, it must be something perceivable through the senses, a tempo-morphological similarity (that is, a similarity in the way they look and act in space and time) that cannot be conceptually reduced to anything further than "dogness."

However, it does not seem accurate to say that "dogness," whatever it is, has nothing to do with having four legs, that we simply deduce that it is "normal" for dogs to have four legs because most dogs we have seen happen to have had four legs. Rather, I think that if somebody only saw three-legged dogs limping along for one's entire life, and then suddenly saw a four-legged dog running naturally along, he would not only recognize that dog as a dog because of its tempo-morphological dogness, he would recognize that the four-legged dog is more well-formed, more of a true dog, than all of the maimed three-legged dogs he had seen before. Indeed, even before seeing a four-legged dog at all, he would probably think that dogs should have four legs.

Thus, although the recognition of "dogness" is, at its root, based on tempo-morphological features that cannot be made entirely explicit, it brings with it a sense of what an ideal dog should be like, and allows us to start reasoning about the general nature of dogs. It's as though there is an abstract template, which does not look like any particular dog, but against which we compare sensible things, to discern whether or not they are dogs, or rather, how much of a dog they are.

This abstract, ideal template that underlies our use of universal terms is what Plato called a "form," or "idea," depending on how you translate him. He believed that forms are the most fundamental beings, having a timeless existence independent of the ever-changing, sensible world of appearances that we live in. Our ability to come to know the forms in a way that goes beyond what can be deduced from our experience, simply through appropriate questioning and limited experience with them, caused him to think that knowledge of the forms is really just a kind of recollection. That is, when we see a particular, imperfect dog in the world, it reminds us of what the true form "dog" is like. And if the forms are things that are remembered in this life, it follows that we must have somehow have known them before this life. From this, he deduces the pre-existence of the soul before it enters a body, and that, in its previous, bodiless state, it inhabited the world of forms, and understood them directly.

Aristotle rejected the elaborate metaphysics proposed by Plato regarding, universals, and instead simply asserted that the mind has the ability to abstract the "whatness" of a thing by looking at it. This "whatness," such as the "dogness" of a dog, was called by the scholastics the essence of the thing.

Today artificial neural networks can be trained to look at pictures and determine whether a dog is in the picture with high accuracy. This provides a clear proof that the essence of a thing is, somehow, present in the thing itself, without a need for pre-existence in a world of forms. One important point to note about artificial neural nets, however, is that they "learn" how to identify a dog when they "see" one only after an extended mathematical training regimen over a large set of images that have been labeled as dogs or non-dogs. Thus their "knowledge" is inherently dependent on human beings providing many examples of the right answer, they are not capable of generating such knowledge independently the way a child or even an animal can do. Furthermore, it is a well established fact of biology that, although the static structure of artificial neural nets resemble the static form of parts of the brain, the manner in which they function are very different. Thus it is not correct to claim that we now have proof that even this simple aspect of thinking--identifying that one thing is the same kind of thing as another-- is known to be carried out via a purely physical process.

Earlier I pointed out that our ability to identify different species of natural substances does not depend on explicitly rational criteria, as is clear both from our own experience and also from the fact that irrational creatures are able to identify different species to some extent. For example, a dog can tell the difference between a bear and a cow, and respond to the presence of each accordingly, without making recourse to formal definitions. Thus this ability is not the result of an act of the intellect. In animals, St. Thomas attributes this ability to the "estimative power," which not only identifies that something is the kind of thing it is, but associates things like danger, pleasure, and so forth, with the object identified. The human equivalent of the animal estimative power is the "cogitative power," which is different from the estimative power due to its interaction with the human intellect. If you think of the cogitative power as the source of our "gut instincts" about the objects of our perception, then it is evidently more refined than the gut instincts of animals. A human can perceive the deeper aspects of a thing, such as, for example, whether somebody is honest or not, or whether or not a given material will be suitable to make a tool, and so on. Moreover one's "gut instinct" about a person can be informed by knowledge of the history of that person, even if he never met the person before, but has only been told about him. People can likewise form an aversion to certain kinds of food which are pleasing to the tongue based on an awareness of its negative affect on their health, and conversely that which is naturally disgusting can come to bring delight. More generally, a human being can train his own cogititative power to associate pleasure or pain with things which his mind determines to be good or bad through repeated acts of the will informed by reason. This is a topic that I will discuss more while commenting on the Summa itself.

The point to be reiterated here is "abstracting the essence" does not amount merely to being able to identify whether or not two objects share a common essence and forming positive or negative associations with it, as animals are capable of doing. It means conceptualizing the essence, making it available to reason. This, according to St. Thomas, is accomplished by the "agent intellect," as I shall discuss elsewhere. While it is often difficult to define a species just by looking at it, the process of abstracting the essence allows us to answer, positively or negatively, whether a given property applies to an essence. For example, we all agree that dogs have four legs naturally, not three, and that they aren't made of metal. We are likewise able to abstract accidents like shape, and deduce general properties about such accidents. Thus, for example, the axioms of Euclid seem immediately true to one who has abstracted the essence of a straight line, even if he never would have thought of them himself.

More specifically, one who has understood the essence of a thing is capable of distinguishing the accidents of the thing that are essential to the thing and those which are not. For example, it is not essential to man that he have brown or grey hair; neither would be considered a defect in humanity. But that he is rational is essential. It is still possible for a man not to be rational, but this would be noted as a defect in the man.

Because the human mind is finite and imperfect, it cannot fully grasp the essences with the same fidelity that higher intelligences, such as angels, can grasp them. Thus we do not have a perfect ability to explicitly define essences, and it does not occur instantaneously by magic, but rather through repeated experience and observation. As modern scientists often remark, the more one knows, the more one realizes what one doesn't know.

All of this will be discussed in more depth as we go, but there is one final concept related to essence that I should touch on here: the being of a thing. In general, the essence of a thing is distinct from its being, for the essence only includes what the thing is, whereas its being consists in the fact that it exists. St. Thomas says this is true of all things except God, whose essence cannot be fully grasped in this life, and which is the same as His very being itself. The beatific vision consists in God impressing His essence upon the intellect, and every beautiful or interesting or good thing we have ever contemplated will be as nothing compared to it.

Science and the Four Causes

In the Physics, Aristotle states that there are four "causes" of a substance that one needs to know in order to know the substance. These are the material cause (its matter or substrate), the formal cause (its form), its efficient cause (the thing or act which brings it into existence), and its final cause (the ideal towards which it tends, the purpose for which it exists).

Aristotle gives letters in a syllable as an example of material causes, and parts as material causes of wholes. So although it is probably true in some sense to say that these "causes" are most properly attributed to primary substances, these concepts are applied both by St. Thomas and Aristotle in an analogical sense to many other entities.

The key point is that, in order to really know a thing, one should have a knowledge of these four causes; the essence of a thing includes all of them. One does not really understand the essence of a hammer if one does not know that it is a man-made (artificial) object, or that it is made of wood and steel, or its shape and hardness, or that it is meant to drive nails. Likewise in natural objects, it is not enough to only understand the efficient, material, and formal causes of a thing. To fully understand the essence of a thing is to understand the perfection of the thing. According to St. Thomas, this perfection or ideal is the same thing as God's purpose for the thing, since God is the author of all that is natural.

Modern science takes into consideration all of the above causes, including even final causes in living things, insofar as it assigns a purpose to the various parts of the animals. However, it reduces everything to forms in space-time. Properly speaking, modern science merely attaches a mathematical form to reality, and "causes" amount to a non-mathematical interpretation of these forms.

For example, the inverse-square law of gravity predicts the motion of the planets in our solar system. Now, it can predict that this motion would change dramatically if the sun were somehow deleted from the solar system, and so in this sense we can say that the sun is the "efficient" cause of the elliptic motion of the planets around the sun. However, the reality is that the elliptic motion of the planets is the result of the entire configuration of planets in the solar system. If, for example, Jupiter had substantially more mass, the motion of the planets would no longer be elliptic, and in truth, the motion of the planets around the sun is not perfectly elliptic due to the gravitational effects they have on one another. In other words, the question of whether, and in what sense, the sun is the efficient cause of the elliptic motion of the planets remains a philosophical question that Newtonian mechanics is not really concerned with. Likewise it is not concerned with the "material cause" underlying the planets of the solar system, it simply assigns a quantity called the "mass" of the object which is agnostic about what the thing is actually made of. That is, mass in Newtonian mechanics is reduced to what Aristotle would call an accident in the category of quantity. And a final cause, in the sense of an ideal, obviously cannot be extracted from Newtonian mechanics. One can determine the final state towards which the solar system is tending, and call that a "final cause" of the system, but that, again, is really a matter of philosophical interpretation. For it is possible for a philosopher or theologian to assign purposes to the current configuration of the solar system (say, it enables human flourishing) which is distinct from the final state it is approaching (complete dissolution).

The modern updates of Newtonian mechanics all have essentially the same character. They are all focused on formal, quantifiable aspects of the objects under study, and predict how these quantities will change over time. In other words, they provide a more detailed description of the form, which perhaps enables a more precise and nuanced description of the other causes, but they do not directly provide such a description. That is the result of a different kind of thinking.

In the Aristotelian conception, science is an ordered body of knowledge about a class of objects through their causes, that is, the four causes described above. Modern science would count as a subset of this, restricted primarily to form. To achieve this fuller understanding, Aristotelian science requires a philosophical mode of reasoning in addition to the primarily mathematical reasoning that lies beyond the "hard" sciences of today. In truth, even modern scientists are forced to employ philosophical reasoning in their studies, they just tend not to acknowledge it. The Aristotelian conception is more complete. Indeed, without this additional philosophical mode of reasoning, it is simply not possible to pass from a detailed description of the form of reality to its underlying causes, which all men naturally want to know.

The primary mistake that modern science makes is in its attempt to reduce all four causes to mathematical form, and more specifically to the mathematical form that they currently ascribe to things. As a simple example, one who observes that Newton's theory of gravity works so well to predict the motion of the planets around the sun, might be inclined to explain the motion of entire cosmos in terms of the inverse square law of gravity. There is, of course, nothing wrong with attempting to explain this or that aspect of reality in terms of the inverse square law, but to assume that all physical phenomena can, in principle be explained in terms of the inverse square law would be an error. Leaving aside philosophy, Newtonian mechanics has subsequently been enhanced with the laws of electromagnetism, amended by Einstein's relativity, and is in outright contradiction with the laws of quantum mechanics at small scales.

Now, no scientist ever made the error of thinking that all physical phenomena could be reduced to Newtonian mechanics. However, most scientists and philosophers since Newton have believed that, in principle, all of physical reality should be reducible to a collection of mathematical entities governed by mathematical laws.

In response to this, one should first note that this belief has not been demonstrated. Modern theories are only verified in special experiments which are designed to observe various forces and physical properties in isolation. For example, to test Newton's law of gravity, one might observe the rate at which feathers and rocks fall in a vacuum near the earth. The purpose of doing the measurements in a vacuum is to eliminate the effects of other factors on the motion of the objects, such as the resistance of air or electromagnetic forces. So in this case, the experimental design has isolated the effect that the mass of the objects alone has on motion of the objects through space. By design, therefore, such physical experiments cannot eliminate the possibility that additional forces exert influence over objects in the world under normal circumstances. These could be hitherto unknown, mathematically describable forces that are poorly understood (like electromagnetic forces in Newton's time), but they could also be the acts of spiritual substances that do not satisfy any mathematical laws at all.

Indeed, one would have to attach some kind of apparatus which kept track of every particle in the body of a person, and verify that it acts in accordance with no law other than the known mathematical laws governing those entities, in order to eliminate the possibility that some spiritual substance like the soul is also playing a role in the motion of the body. This has not been done, nor can it even be done in principle, if quantum theory is correct about the nature of of physical reality at small scales.

Thus, even though modern science is capable of describing the effect of many forces on objects with fine-grained accuracy, it is incapable of eliminating the possibility that other entities might also be acting on substances in ways which modern science cannot detect. For that reason, if aliens came down to earth, and informed us that they are the creators of human souls, which are an invisible technology that they attach to every human body at conception, and which interacts with the neurons of human beings, people would be shocked for a variety of reasons, but scientists would not declare such a thing to be physically impossible. To the contrary, if the technology could be explained in more detail, it would seem like a marvelous addition to a hitherto woefully incomplete theory about how the human body and brain behave. Thus, there is simply no need to accept physical determinism and engage in Kantian acrobatics if one wishes to accept science while also preserving the reality of God, freedom, and immortality of the soul. Nor is this even possible within a Thomistic understanding of reality, which posits the existence of spiritual beings which have supernatural effects upon the natural world.