[The contents of this chapter are discussed in Modes of the Finite, Part 1, Section 2, Chapters 5-10.]

3.1. Aristotle's "four causes"

The definitions of "effect," "affected object," "cause" and "causer" are not in the tradition of what is called Scholastic philosophy, which is basically what this book is a modern version of. To relate what I am saying here to the tradition, let me mention first Aristotle's notion that there are four types of causes (his "four causes"): efficient, material, formal, and final.

As I noted in the preceding chapter, Aristotle held basically that effects were "why"-type questions, and the cause (aitia, from which we get our word "etiology") was "what was demanded (aite)" or in other words the "reason" for something.

Now if you ask, say, of a wooden chair, "Why is this object what it is?" you can give four possible answers: "Because the carpenter made it," (the efficient cause, the thing that produced it, what we normally mean by "cause"); "because it's made of wood" (the material cause, the "stuff" out of which the thing came to be what it is); "because it has this shape," (the formal cause, the particular configuration of the matter); or "because it's to sit in," (the final cause or purpose for which it came to be). Aristotle thought that these four types of answers summed up all the different kinds of causes there could be.

I'm not a hundred per cent sure that he was right, and my definition makes the whole question, it seems to me, moot. It isn't (for me) a question of when we can ask and answer the question "Why?" but when we are confronted with something that doesn't make sense.

True, "Why?" is the question we ask when something doesn't make sense to us, and so I am probably saying pretty much the same thing as Aristotle--except that I am, I think, spelling out a little more clearly what is behind our asking the question: that we have evidence on both sides of a contradiction, and so need further information.

Of course, if you wanted to classify different kinds of causes, then you would do so by trying to find the different sorts of ways in which you could make sense out of what doesn't make sense by itself. But why bother with how many different kinds there are?

In later Scholastic tradition, the "cause" was defined as "that which influences the existence of something else," and it was related to the "four causes" of Aristotle in this way: (1) by acting on it (efficient), (2) by being the material it was made of (material), (3) by being the form the material takes (formal), or (4) by being the goal the thing is headed toward (final). You'll notice that there has been a subtle shift here; the emphasis now goes from cause to effect rather than from effect to cause, and this has caused a number of problems in the history of philosophy.

This view related to my own, however, in that the "existence of something" is known "to be influenced" if the object can't exist in the way in question by itself; or, in other words, if by itself it is a contradiction. The cause, therefore (what does the "influencing") removes its in-itself-contradictoriness.

My difficulty with this traditional view is twofold: (1) it confuses the effect with the affected object and the cause with the causer, creating the temptation to ascribe non-necessary properties to the cause; and (2), the notion of "influencing" (in-fluere in Latin, to "pour in") creates the false impression that the cause "gives something of itself" to the effect, which seems to imply that the cause(r) loses what the effect (i.e. the affected object) gains. But this is not always the case. When I tell you a fact that you didn't know before, your knowledge is greater than it was a moment ago, and this increase in knowledge makes no sense without someone informing you; and so my statement to you is the cause of this effect. But clearly my statement is not "lessened" or altered in any way because you gained knowledge from it--nor is my knowledge any less because I have "imparted" it to you. No, the cause just removes the contradiction from the effect.

So that's why I think my definition is an improvement on the traditional view.

3.2. Causality and condition

Let me now make some other distinctions we will need later on. It is one thing to know what the cause is and distinguish it from the causer; but there is more to the situation than just this. The cause is what is doing the causing; but this says nothing about how the cause is saving the effect from being a contradiction.

DEFINITION: The causality of the cause is the way in which it removes the contradictoriness from the effect.

DEFINITION: The being-affected is the way in which the effect is made sense out of by the cause.

The cause, then, is what makes sense out of the effect. The causality is the relation between the cause and the effect, looked at from the point of view of the cause (what, in ordinary terms, it "is doing" to the effect), while the being affected is the same relation, looked at from the point of view of the effect (what "is being done to it" by the cause).

So, for instance, if we notice that the earth is warmer on its light side than on its dark side, then earth, of course, is the affected object, and the difference in temperatures is the effect. the cause of this is the heat of the sun; the causer is the sun. The causality is the heating of the earth by the sun, and the being-affected is the being-warmed of the earth by the sun.

Now in general, you don't know how the cause manages to make sense out of the effect, even when you know what the cause is, and can separate it out from the causer. How did the rubbing of your hands together manage to raise their temperature? We know that it's the friction that did it, but how does friction create heat out of mechanical energy? Even the physicists throw up their hands at this, and say, "Well, we don't know; but it does it somehow." So they know that there is a causality here (how could there not be?), but they don't know what it actually is.

That is, just as we can't account for the particle-wave compatibility of the photon, but we know that the photon combines the characteristics of a particle and a wave (or light doesn't make sense), similarly the fact that we are ignorant of what the causality actually is does not mean that we don't know what the cause is.

Notice, by the way, that the causality of the cause is in the effect (because it's the way in which the effect is made sense out of by the cause). The heating of the earth is in the earth, (it is its change of temperature), not in the sun or even in the heat of the sun; it is the action of the sun on the earth.

Aristotle noticed this type of thing, but not strictly when he was talking about cause and effect. He spoke of it in discussing "action and being acted on." He mentioned that just as the road from Athens to Thebes was the same road as the road from Thebes to Athens, so acting-on something was the same relation as being-acted-on-by something, except that you were looking at the relation from opposite ends. But it's the same relation. He also was the one to point out that the "action" of the "agent" was actually in the effect (i.e. the affected object), as the teaching of a teacher (what the teacher is doing to the student) occurs in the student, because it's the learning of the student because of what the teacher is doing. If the student isn't learning, the teacher is just talking, not teaching.

All I did here was generalize "action" to "causality" and so take it from the realm solely of efficient causality. In general, then, the cause is what removes the contradictoriness from the effect, and its causality is how it does so (if you will "what it does" to the effect); and the being-affected is the same as the causality, only it is how the effect is made sense out of by the cause (or "what is done to it" by the cause to make sense out of it).

One other term:

DEFINITION: The condition is the cause of the cause.

The cause itself, while it makes sense out of the effect, might also contain self-contradictory aspects, which means that it can't make sense out of itself (it's not self-evident, or "self-sufficient"). In this case, it has a cause. That means, of course, that if the cause of the cause weren't there, there wouldn't be a cause, and so there wouldn't be an effect either.

Thus, your hands getting hot wouldn't be happening if you weren't rubbing them together. But if your parents didn't exist, then you would have any hands to rub together, and so your hands wouldn't be getting hot.

Hence, your parents' activity that produced you is the condition for your hands' becoming hot. Similarly, whatever it was that produced the sun in the first place is the condition for the fact that the earth gets warm on the sunny side.

Note that the condition is not the same as the causer. The sun is the causer of the warming of the earth; the cause of the sun is the condition.

One thing to note is that you don't have to know the condition in order to make sense out of the effect. The cause is a fact, whether it is self-explanatory or not; and, given this fact, the effect makes sense. So, for instance, the cause of your hands getting hot is the energy produced by rubbing them. Add this to the affected object and the effect makes sense. Perhaps the whole situation (cause + effect) doesn't make sense, but you were only trying to make sense out of the effect.

This notion of condition, however, is really put here for completeness, because there are some people who seem to want to go through the whole series of conditions right up to the "first uncaused cause" in order to explain anything. That is, for them nothing makes sense unless total intelligibility is reached.

But there's even a question of whether you can find all the conditions for a given effect; it looks on the face of it as if there were an infinity of them, since effects and causes are just abstract aspects of a concrete situation. So it not only might be a waste of time to try to resolve all possible difficulties connected with a given effect, it might even be impossible to do so.

And the point is that you don't need to do so. A fact, in itself, makes sense somehow: either by itself or by its cause. So as a fact, it can make sense out of the particular effect you are interested in, and so you don't have to go chasing conditions until you drop from exhaustion.

3.3. Theorems about effect and cause

Now then, since effect and cause are defined so abstractly, it turns out that there are some statements we can make about them that are necessarily true just by definition. Statements like this are called theorems.

THEOREM I: The cause is never contained within the effect.

This is obviously true because the effect is only the facts that don't make sense by themselves, and the cause is the fact that makes sense out of the whole situation. If the cause were part of the effect, then the effect would make sense, and so wouldn't be an effect. Q. E. D. (1)

The cause, as I said, can be part of the affected object, but it can't be part of the effect as I defined it.

For the same reason:

THEOREM II: Nothing can be the cause of itself.

If something were the cause of itself, then it would be simultaneously effect and cause. But if it is an effect, it is not self-explanatory, and if it is the cause, it is self-explanatory--which is clearly a contradiction. Q. E. D.

So when Gottfried Leibniz and others call God "The cause of himself," they are not using "cause" in the sense I am using it. Insofar as what they say makes sense, they presumably are saying either that God is self-sufficient (i.e. not an effect, and needing no cause), or that God is some kind of causer, part of which is the cause of some other part of himself.

Here is a theorem that isn't immediately obvious, but is also true by definition:

THEOREM III: The cause is not affected by the fact that it is a cause.

This particular theorem seems in fact counter-intuitive, and seems to be going against Newton's Third Law: "For every action, there is an equal and opposite reaction." But Newton was talking about causers and affected objects, and in the world of physical motion; and even in the world of causers this is not always the case.

For instance, suppose you have your radio on and you hear that a nuclear weapon has just destroyed the whole of New York, where your brother is living. Obviously, the consternation you feel now as opposed to the euphoria you had a minute before is explained by the words you heard the announcer say. So those words are the cause. But if you didn't have the radio on, the announcer would have said exactly the same words, except that they couldn't be called the cause of this change of mood in you. So the only "difference" in the cause by its having an effect is the fact that the exact same reality is either called a "cause" when something happens to be explainable by it, or not, if nothing is explained by it.

And this is true even in the realm of Newton's physics. The earth is warmed by the heat of the sun. But the sun is producing this particular amount of heat all over a sphere at the distance the earth happens to be at (obviously; the heat is radiating out in all directions). That amount of heat--which is the cause of the warming of the earth--is no different at this point in the sphere just because the earth happens to be in the way of it; it's no greater or less than it is anywhere else on the surface of that sphere.

True--and here's where Newton's law comes in--the fact that the earth gets warmed makes it radiate out heat, and a little bit of that heat hits the sun, and makes the sun slightly (infinitesimally) hotter than it would have been if the earth hadn't been warmed by it's (the sun's) heat. But the sun is the causer, not the cause; and all this says is that one aspect of this being is the effect of its temperature as greater than it would be if the earth (the original affected object) had not been radiating out heat (the aspect of this affected object by which it is the cause of the new effect in the sun). So it might be true in the realm of physics that every causer containing energy is affected by the affected object it transmits the energy to; but it doesn't mean that the cause is affected by the effect, as we have defined them. You see why I said that it was important to make the distinction?

And of course, it couldn't be. The cause is just the abstract fact that makes sense out of the effect; as such, it is simply a fact, and by the Principle of Identity, it is the fact which it is. So it is not altered by the additional fact that this particular fact happens to be the one which makes sense out of some other fact.

COROLLARY I: The cause is always independent of the effect.

A corollary is something that is really just another way of stating the theorem it's a corollary to.

In this case, the cause is neither (by Theorem I) part of the effect, nor (by Theorem III) altered by the fact that it has an effect; and so it is not dependent on the effect in any way.

The effect is dependent on the cause, since the effect without the cause is a contradiction, and so doesn't exist (because contradictions can't exist). But the cause is not dependent on the effect (except in the trivial sense that you then can't call it a "cause"). This is actually an implication of what Aristotle was saying when he said that "the action is in the object acted on" (like the teaching as such in the learner). The effect is the difference in the affected object that can't be explained without the cause; but the cause isn't unintelligible by itself; by itself it's just a fact. So the cause doesn't depend on the effect; the effect depends on the cause.

THEOREM IV: The cause is not the same as nor similar to its effect.

The cause will be completely different from the effect, because it is a different fact which is left out of the effect. This is perfectly obvious if you understand "cause" and "effect" abstractly, the way I have defined them. It couldn't be the same fact(s) as the effect, because then the effect would make sense by itself, violating the definition of an effect. Q. E. D.

It only seems counter-intuitive if you take "cause" in the usual sense, in the sense, for instance, that muskrats cause little muskrats (and not squirrels) to be born. But of course mommy and daddy muskrat are not the causes of little junior muskrat; they are the causers.

And little Junior isn't the effect; it's the affected object. The effect in question is the fact that a muskrat (and not a squirrel) began to exist, and the cause is the sexual activity of the two muskrats. And the last time I looked, sexual activity, even among muskrats, isn't anything like an actual muskrat.

In fact, the traditional notion of "cause," which is "that which influences the existence of something else," and which doesn't make the distinction between cause and causer, claims that there is a "self-evident first principle" to the effect that the cause has to have more of the "perfection" the effect "receives" than the effect does. The reason, of course, is that if the cause "pours perfection" (some quality) into the effect, then if it has the same amount of it, it vanishes, and if it has less, then it winds up with a negative amount of that perfection. St. Thomas used this idea in proving that God is the greatest of all beings and therefore the cause of the "being" of everything else; since every lesser being, which can't account for its own existence, has to receive the "perfection" of existence, and ultimately it has to receive it from God. Now it may be true that every finite being receives its existence from God (and in fact it is true), but this line of reasoning is a fallacy, as can be seen from St. Thomas's illustration of why it must be so, "just as fire, which is 'most' hot, is the cause of the heat of everything else."

This, of course, as we know from physics, is nonsense. You can get heat from friction, as by rubbing your hands together. These very words on the page are the cause of any new ideas you might be getting from reading them (they plus your mind which can understand English, of course); but neither the words themselves (marks on paper) nor the mind, which didn't have the ideas, is anything like the ideas which got produced (which is the effect).

So we'll just have to abandon the old notion of cause and effect, because it seems to imply as "self-evident" what not only isn't self-evident, but isn't even true.

But then, you can see why, if you're going to follow this book, you're going to have to learn to think abstractly. You will be horribly confused if you keep mixing up the abstract set of facts which is the effect with the concrete object which is the affected object.

3.3.1. Identical and different causes

Actually, "cause" and "effect" were defined in this extremely abstract way partly so that the following theorems would be true, because it turns out that, when the cause is unobservable, we can make statements showing that one cause is like another (perhaps observable) one based on the relation between the effects of each.

THEOREM V: Identical effects have identical causes.

First, let's be clear what we mean here. We do not mean that the effect is identical with its cause. That would violate Theorem IV above. What we mean is that if two effects are absolutely the same as each other, then the cause of one is absolutely the same fact as the cause of the other. Remember, effects (and causes) can be "absolutely identical" because they're just abstract facts. So, for instance, if Mommy bakes 24 cookies on Monday and puts them in the jar and finds 12 missing later on; and if she does this again on Tuesday, the fact that the batches contain different cookies and the days of the week are different is irrelevant: the effect in each case is (a) the fact that cookies don't walk out of jars, and (b) 12 cookies got removed from the jar. Both of these statements are true in both cases; so there's only one effect here, really.

There are two ways of proving this theorem: First, "effect" (in general) is defined as "that which does not make sense by itself" because something is missing from the situation. That "something," of course, is the cause.

Hence, this effect is defined as this one, not by the fact that something is missing from its intelligibility (that's what it has in common with other effects), but by what is missing (which makes it appear as a contradiction).

But that's another way of saying that one effect is distinguished from another as effect by precisely what specific cause it has (since the cause is the "missing element" without which it is a contradiction).

Hence, if two effects are identical as effects, their causes are just by definition identical. Q. E. D.

The second proof shows that if the theorem is not true, you get into a contradiction.

Suppose ("for the sake of the argument") that you have two identical effects and their causes are different. That means that Cause A and Cause B are not the same set of facts; but they cause the same effect (that is, you can replace Effect B with Effect A without changing anything at all--effects are abstractions, remember).

Now Effect A's cause has all the properties necessary and only the properties necessary to make sense out of it. So if Cause B contains a fact that is not part of Cause A, then Cause B has a property not necessary to make sense out of Effect A; but since Effect B and Effect A are absolutely identical, then Cause B has a property not necessary to explain Effect B--but by definition, this superfluous property is not part of the cause, but belongs to the causer.

Also, if Cause B lacks a property that Cause A has, then Cause B lacks something necessary to be the cause of Effect A, and so it can't cause Effect A. But since Effect B is identical with Effect A, it can't cause Effect B either.

So Cause B has to have exactly the same set of properties that Cause A has. Q. E. D.

But this doesn't mean, I stress, that the causers or the affected objects have to be identical to each other. For instance, if you look at two waves in the ocean (which is water raised above its normal level), and let us even suppose that they are the same height above sea level, then these two (one in the Atlantic and one in the Pacific Ocean) are identical as effects. Any differences are part of the affected object.

Let us now suppose that the moon's gravitation is what raised one of the waves, and an earthquake under the ocean is responsible for the other. Clearly, there are two different causers. But as causes these two are identical, since all that is needed to explain the raising of the water is energy of a certain quantity applied to the water. (If the energy were of a different quantity, the height of the waves would be different.) So as causes the moon as acting on the water and the earthquake as acting on the water are identical.

This is still another reason why I said that if you are going to understand this method, you have to learn to think abstractly. The actual, visible objects can be very different, but the precise aspect by which one is unintelligible might be identical in the abstract (i.e. the same set of abstract facts) as the other, in which case as effects the two are the same. But in that case, no matter how different the causers are from each other, the causes have to be the same as each other.

Not surprisingly, the following is also a theorem:

THEOREM VI: Different effects have different causes.

The first proof is parallel to that for the first proof of Theorem IV: Since a given effect is specified by the fact that a given fact (its particular cause) is missing from the situation as observed, then it automatically follows that two effects are different simply because their causes are different.

There's nothing mysterious here, as I mentioned; the terms "effect" and "cause" were defined in such a way that this would be true. This is not to say that the definitions aren't valid or are inapplicable to things; it's just that, since we can't observe the cause we're looking for, we want to refine the notion of "cause" so that we're not saying any more than we absolutely have to say; and it turns out that these theorems are a bonus we get when we define things in this way.

The second proof goes this way: If different effects were to have the same cause, then the difference between them is irrelevant to their unintelligibility (since they are made intelligible in exactly the same way--which is what "having the same cause" means). But what is "irrelevant to their unintelligibility" means "not part of them as effects, since the effect is nothing but the unintelligibility of the objects in question.

Therefore, in this case, the difference between the effects is irrelevant to their unintelligibility, which means that the effects are not different as effects, but only as affected objects. So if different effects have identical causes, they are not different as effects, which means that they aren't different effects. Therefore, different effects have to have different causes. Q. E. D.

Once having established both of these theorems, two corollaries automatically follow:

COROLLARY II: Identical causes have identical effects.

COROLLARY III: Different causes have different effects.

If Corollary II were not true, then you would have a case of identical causes with different effects, and hence different effects with identical causes, which contradicts Theorem VI; if Corollary III were not true, then you would have a case of identical effects with different causes, which contradicts Theorem V.

3.4. Similar effects and analogy

There is another corollary of these two theorems which is important enough to dignify with the name of a theorem in its own right. It happens to clear up a very mysterious aspect of metaphysics: that of analogy.

Since effects are more or less arbitrarily defined (by what is left out of the situation as you observe it), it's quite possible for two effects to have some facts in common and some facts that make them different.

For instance, if you looked at the two waves in the ocean (the one produced by the moon's gravity and the one produced by the earthquake), you might notice that the molecules of water were in the first case slightly farther apart than normal, and in the second, slightly closer together.(2) So, the two effects now are the same as each other in that they are water raised three feet above normal; but they are different from each other in that the water is expanded in the one case and compressed in the other.

DEFINITION: Two things are similar to each other when they are partly the same and partly different (and you can point out the respects in which they are the same and different).

Obviously, in the respect in which they are the same, the two causes will be the same as each other, and in the respect in which they are different, the causes will differ among themselves--so the causes will be similar among themselves if the effects are similar to each other. But the theorem I am going to state uses a different term, for reasons I will explain:

THEOREM VII: Similar effects have analogous causes.

The reason, then, why the causes are called "analogous" and not "similar" is that all that is known from the similarity of the effects is the mere fact that their causes are somehow similar among themselves, and not the respects in which they are identical and the respects in which they are different.

DEFINITION: Analogy is the term used for similarity when only the fact of similarity (not the points of similarity) is known.

If you take the waves in the ocean, you can see what I mean. The moon's gravitational attraction and the mechanical force of the earthquake are somehow or other similar, because both are capable of raising water above its normal level, though in different ways (since one is by expansion and the other by compression). But what are the respects in which they are the same, and what are the different respects?

We don't really know, because we can't actually observe directly either the moon's gravitational activity (indeed, if it is a "warping of space-time," it would be hard to see how you could), or what the actual energy transmitted from the earthquake is. How a warping of space-time could in any sense be the same as molecules of water bumping into each other is a little difficult to conceive; but they must be the same somehow, or they couldn't produce effects which are the same in some respect.

Now of course, we can put names on these in-themselves-unknown points of similarity if we want to. We can say that the moon's gravity and the earthquake's impulse have, say, the same amount of energy, but are different forms of energy. But when you unpack these two "characteristics," you find that "energy" just means "the capacity for doing work," which in turn means "that which can have an effect of a certain type," or in other words, "energy" as a common term means, "whatever it is that certain causes have in common because their effects are similar"--which is right back to where we were.

That is, we don't know what makes energy energy, or what makes all forms of energy the same insofar as they are all energy, except through the fact that they have similar effects. So "energy" is an analogous term, indicating an in-itself-unknown sameness among objects that you know is there, but you can't point out.

This shows, of course, that analogy has its place in science. Similarly, a photon is analogous to a wave and simultaneously analogous to a particle, but we don't know it is the same as each, or even (in this case) how it is possible for it to be similar to both at the same time. We know that it is, however.


Be careful not to be misled by analogous terms. The mere fact that a name can be placed on an in-itself-unknown point of similarity does not mean that we know what that point of similarity is in itself. The name still means "the respect in which this cause is similar to other causes of similar effects."

Now the reason why I called this "analogy" has to do with the philosophical tradition, of which I think I have to say a few words. Aristotle was the first to discuss the subject of using words "aside from" their "real" or primary meaning (ana, apart from, logos, word).

Not to make a historical treatise of this, the Scholastic tradition developed the notion in more or less this way: Terms could be used univocally (uni one voc- voice), in which the term has the same sense every time it is used (as "tree" means the same thing when applied to different trees), or equivocally (equi equal voc-), when the "term" is actually two different words with different meanings that have nothing to do with each other, but just happen to sound and spell the same (as a "pen" is something you write with or keep pigs in), or analogously, in which the meaning is partly the same and partly different.

There are two kinds of analogy in the tradition: The analogy of attribution in which the term doesn't mean what the primary term (the "prime analogate") means, but refers to that term somehow.

Thus, a "comfortable fire" is analogously "comfortable," not because it feels good (which is what you are when you're comfortable), but because it makes you feel comfortable. A "healthy" complexion is "healthy," not in itself (How can color feel healthy?), but because it's a sign that you are healthy (i.e. evidence of your health, or in other words an effect of it).

To relate this to my notion of analogy, the term is used analogously when it's either the effect of or the cause of the term used in the primary sense. The primary sense is "carried over" to the secondary use of the term in this way.

The other analogy, which is closer to what I was talking about, actually, is called the analogy of proportion or even refined into the analogy of proper proportionality.

The idea here is that a kind of proportion among four terms is made, and then one of the terms is substituted for the other in the proportion. Aristotle illustrates this by saying that as evening is to the day, so old age is to life (since both are the last part); thus, you can say that old age is (analogously) the "evening" of life (as if life were a kind of day). Or alternatively, evening is the old age of the day. He uses this analogy to say that the roots of a plant are analogously its mouth, for instance--and I think you can see how this applies.

This kind of thing solved (or seemed to solve, at least) a serious problem in Christian medieval philosophy. God is infinite, and human beings are finite. Granted, God exists and so do humans. We know also from the Bible that God is good, that He is intelligent, merciful, etc., etc. But, for instance, a good man would not allow someone he loved to be injured if he could prevent it; and yet God clearly either causes or allows people to be injured from things like earthquakes or fires, which are nobody's fault. The answer given was that, we know from revelation that God is good, but since God is infinite and humans are finite, then "good" when applied to God what it means for humans. God can do to us what only an evil man would do, and yet still be (somehow) good.

But since we get the meaning of words from the way they are used to refer to finite things, and since "good" when applied to God seems to mean the opposite (at least in some cases) of what it means when applied to humans, why do we use the term at all? Because revelation says that it applies.

As I said, the "analogy of proportion" was used by St. Thomas and others to solve the problem. It isn't that goodness (which, as Aristotle showed, is another way of saying "existence"--as we will see a few chapters from now) is a univocal term when applied to humans and God, but it's not an equivocal term either. It's analogous, with the analogy of proportion. As human essence is to human existence, so God's essence is to God's existence. Human essence (what a human is) defines the human by limiting existence to being no more than human existence; God's essence defines God by not limiting existence at all (in other words, what God is is existence pure and simple).

Now it's the relation (the "defining the being") between the essence and the existence that's the same here, not either the essence or the existence itself. Hence, we can say of terms that describe God's essence, that as goodness is to God, so goodness is to humans. In God's case, this goodness sets no limitations, whereas human goodness is limited to being only human goodness. But since God's goodness imposes no limitations, then some of the things that would be bad for a human (such as killing a person) are not bad for God. (To make this a little more intelligible, the idea is that since it's not evil for a human to step on a cockroach or kill a weed, then it's not evil for God to kill a human.)

It's a solution, of sorts. The point is that you can legitimately say that the word does apply to God, and still say that you don't really know what it entails in practice.

Now then, to relate this to my view of analogy, the real problem the medievals had was how do you know that a given word is true of something if you can't observe it to see how it is true? What my notion of analogy accounts for is precisely this. We know that if the effects of two causes are similar, then the causes must in some unknown way be similar, just because identical effects must have identical causes, and different effects must have different ones. But these two theorems don't tell you how the two causes are similar; you just know that they are.

Thus we can call the moon's gravitation a "wave-maker" and the earth's earthquake a "wave-maker"; or we can call electricity "energy" and movement "energy," and gravitation "energy," and so on. We know that all of them are capable of having similar but not identical effects; and so they have something in common, even though we can't point to what it is.

Thus, if you can show that the effects God has on the world are similar to the effects a good man (as good) has on what he acts on, then God must be analogously "good." But you don't know exactly how God's goodness is similar to human goodness; and so when God seems to do bad things, it doesn't necessarily follow that He's not good; it's just as likely that "goodness" when applied to Him doesn't in this case resemble human goodness--just as electrical energy might not move you across the room, and might just give you a shock, even though mechanical energy will always give you a shove.


Note well: These summaries, particularly from now on, are not a substitute for reading the text itself, but just helps at remembering and organizing your studying. If you don't understand any of the brief statements below, be sure to go back and reread the pertinent section in the text until you grasp what is meant.

Aristotle's notion of "cause" as the answer to the question "why" led to his claim that there are four types of causes: efficient, which produces something, material, that out of which the thing is produced, formal the form that the efficient cause produces out of the material cause, and final, the goal the efficient cause had in mind. The relation to our theory is that "why" questions occur when you don't understand something, and that occurs when something you observe appears as a contradiction.

In the medieval tradition, the "cause" was "that which influences the existence of something else." The problem with this is that it seems to be "imparting" some of itself to the other thing, and that is not necessarily always true in causality, and never true if "cause" is distinguished from "causer," as the tradition did not do. The relation between the tradition and our view is that the existence of something is "influenced" when it can't exist by itself in the way in question, or when by itself it is a contradiction. So our notion is a clarification and refinement on the notion as developed through history.

The causality of the cause is the relation between the cause and the effect: how the cause removes the contradictoriness from the effect. Since it is a relation, it can be looked at backwards, which is the being-affected of the effect by the cause. These are the same thing, looked at from the different "ends" of the relation, so to speak. In general, even when the cause is known, the causality isn't; you don't know very often just how the cause does its job, even though you know it's doing it.

A condition is the cause of a cause. That is, if the cause of a given effect (call it A) is itself a contradiction-by-itself (an effect), then its cause is the condition for the effect in question (i.e. Effect A)--because, though the condition didn't cause it, it still couldn't have happened without it. But since the cause is what makes the effect reasonable, then you don't need to discover its causes (i.e. the conditions) in order to make sense out of the effect; all you need is to know that the cause is a fact.

There are various theorems (statements that necessarily are true by definition) based on these definitions of cause and effect. Theorem I: The cause is never contained within the effect, or the effect would be simultaneously unintelligible in itself and intelligible in itself, which is absurd. Theorem II: Nothing can be the cause of itself, since then it would be intelligible and not intelligible at the same time, which is absurd. Theorem III: The cause is not affected by the fact that it is a cause. The cause is simply the fact which is missing from what you know about the whole situation, and this fact is not altered by the fact that you are ignorant of it. Causers can be affected by affected objects, but the cause, as abstractly defined, can't be. Corollary I of this is that the cause is always independent of the effect. It makes no difference to the reality of what the cause is that it happens to be having an effect; it's just that you can't call it a cause unless it has an effect. The effect depends on the cause, not the other way round. Theorem IV: The cause is not the same as nor similar to its effect. The cause is simply an additional fact left out of the whole concrete situation, and has no resemblance to the situation with the fact missing (which is what the effect is). Causers can be similar to affected objects (as parents are similar to their children) but the cause is different from the effect.

Theorem V: Identical effects have identical causes (which means that if two effects are identical with each other, the cause of one is identical with the cause of the other) is proved in two ways: (1)The cause is defined as what is missing from the effect's intelligibility; hence, any definite effect has something definite missing from its intelligibility. (2) If the cause of Effect A had an additional property that the cause of B did not have, this property would be superfluous to it as cause of B and (since the two effects are identical) also as cause of A--which means that it's not part of the cause, but the causer. If it lacks a property that the cause of B has, it can't cause B (because it lacks what is necessary) and therefore can't cause A either, since the effects are identical.

Theorem VI: Different effects have different causes is also proved in two ways: (1) Since the cause is "the missing fact," then, as with identical effects, which fact is missing defines the particular effect; therefore different effects by definition have different causes. (2) If different effects had the same cause, then the difference between them would be irrelevant to them as effects (i.e. as needing explanation); and this by definition means that they are different effects, since "effect" is an abstraction.

Two corollaries follow: Corollary II: Identical causes have identical effects; and Corollary III: Different causes have different effects. If either of these were false, there would be either a case of identical effects with different causes, or different effects with identical causes, which violates the two theorems above.

Theorem VII: Similar effects have analogous causes. Two things are similar when they are partly the same and partly different and you know the respects in which they are identical and different; two things are analogous if you know the fact that they are (somehow) similar, but don't know the respects in which this is so. Note that in analogy, we sometimes put an abstract name to "whatever the two have in common," but the name means only this phrase and does not imply that we know what the respect actually is.

The theorem is actually a corollary of Theorems V and VI: Similar effects are as effects partly identical and partly different. As identical, their causes are identical to each other; as different, their causes are different from each other. But it is not known in what way the causes are actually identical and different, but only the fact that this must be the case if the effects are similar. Thus, the causes of similar effects are analogous to each other.

Historically, the notion of analogy has two functions: that of attribution, in which a word is transferred from the effect and applied to the cause (as a "comfortable" fire), or from the cause applied to its effect (as a "healthy" complexion). The other is that of proportionality in which it is the relation between the cause and the effect that is the same, and so the observable cause of an effect that is similar to some other effect with an unobservable cause is analogous to the unobservable cause.



1. Quod erat demonstrandum, Latin for "What was to be proved," a Latin translation of Euclid's conclusions in his proofs of theorems in geometry.

2. This actually would have to be very slight, since water doesn't compress or expand to amount to anything.