Analogy
But there is another corollary that leads to something interesting: Suppose two effects (as effects, now, as problems, not as concrete situations) are not absolutely identical and not absolutely different from one another, but are similar: they have some respects in common, but others in which they differ.
For instance, suppose the branch outside your window moves on two different occasions, but the amplitude of the movement is different each time. These are not exactly different effects, because the movement itself of a non-animal is an effect, and in both cases there was movement; but the movement is greater in one case than the other (and hence as an effect it is different from the other one). So here we have an example of similar but not identical effects or problems.
Obviously, each of the two effects will have two aspects or "parts": one aspect (set of facts) which is identical with the other effect, and another aspect which is different. In the case above, the mere fact of the movement of a non-initiator of movement is identical in both cases; in the other case, the total energy of the moving branch over what it has at rest (and which it can't give itself) is different each time.
Once, then, you have separated the two into two different pairs of effects, you can say (a) that in the respect in which the effects are identical, their causes are identical; and (b) in the respect in which the effects are different, the causes are different.
Hence, the causes of the two similar effects are also partly identical with each other and partly different from each other; or they too are similar.
In the case of the movements of the branch, the cause is force (assuming the mass of the branch the same both times), and the fact that there is a force applied is identical, while the magnitude of the force is what is different. The two forces are similar, not identical.
Before stating this as a corollary and giving a formal proof, let me make a definition, and after I give the proof I will explain why I want a term defined in this way:
Two things are analogous if it is (a) known that they are identical or similar, but (b) the respects in which they are identical or similar cannot be directly pointed out. That is, if you know the fact that two things are the same (either totally or partially), but you can't point out where the sameness lies in them (obviously, because you can't observe them directly), then they are analogous.
Analogy, then, is a type of similarity, and it would pass over into similarity if you could actually see the points of similarity. But when all you know is that the two things in question are somehow similar, then this weakly known kind of similarity is not called "similarity" but "analogy."
With that said, then, let me state the following as a corollary to what we have so far seen, and give a formal proof of it:
Corollary III: Similar effects have analogous causes.
Two effects can only be known as similar effects if they are in some respect identical as effects and in some other respect different as effects. But this always allows them to be split into two pairs of effects, one pair of which is identical (having identical causes) and the other different (having different causes).
But since the causes as known from the effects are not observed in themselves, then all that is known from this corollary is the fact that the causes are somehow similar to each other, but not what it is about them that is partly identical and partly different.
Therefore, similar effects have similar causes, but all that can be known about the causes as similar is the fact that they are (somehow) similar. Therefore, the causes are analogous. Q. E. D.
It would seem that we can know more than this; in the case of the movements of the branch, we said that the respect in which the two causes were identical was the energy, and the respect in which they were different was the magnitude. But if you consider this carefully, you don't know what exactly you mean by "greater or lesser magnitude" except "whatever it is about some energy that causes a greater or lesser movement." But what is it that is its "magnitudeness"? Who knows?
In fact, we don't even know what the "energeticness" of the energy is either, as can be shown from the fact that if you light a firecracker in the branch, you can also make it move; but here we have energy that is a chemical reaction, while the energy in the squirrel's paw is different in kind. There are different kinds of energies (electrical, mechanical, chemical, thermal, etc.), in other words, and what do they all have in common? They "have what it takes" to cause movement--and sometimes these different kinds not only have "energeticness" in common, but the same magnitude of "energeticness," when they cause the same degree of movement. But what is that "common element"? Who knows?
So once again, in order to follow what is being said here, you must learn to think abstractly, and not try to "put your finger on" what you are talking about, and be content with the fact that you know it exists. If not, you will be totally lost in what follows.
But now, to redeem my promise of saying why I call that similarity-when-only-the-fact-of-being-similar-is-known "analogy," it turns out that historically, "analogy" was used to refer to this kind of similarity, but all kinds of explanations were given of why we could say "A is a sort of B" when it was clear that we didn't know what we were talking about.
Aristotle talked about two kinds of analogy: what was later called the "analogy of attribution," where something was given an attribute that it didn't actually have as such, but which it was connected with in some way: as we say that a complexion is "healthy," not because the complexion isn't sick (color can't be sick), but because it is a sign that the person who has it is healthy.
Of course, what this amounts to is that this particular skin color is an effect whose cause is the health of the person; and hence, while it doesn't exactly fit the meaning I gave above, it still deals with effect and cause.
Similarly, going the other way, you can call a fire "comfortable," not because it feels good, but because it is the causer of your comfort (and its "comfortableness," of course, would be the cause).
In any case, the "analogy of attribution" uses a term belonging to a cause and applies it to its effect or vice versa.
But the more interesting use of analogy is what Aristotle thought of as resulting from a proportion, which he thought explained metaphor; as, for example, the "evening of life" which is old age. He looked at these things this way:
evening : the day :: old age : life
What you do to form the analogy is replace one term with the corresponding one on the other side of the proportion, and you get "old age is the evening of life," or alternatively, "evening is the old age of the day." The idea is that neither term itself (old age or evening) is really like the other one; but the relation between evening and the day is like the relation between old age and life (they're both the ending of the period); and so the terms can be connected now with each other through this relationship.
People like Thomas Aquinas used this to account for how we could use terms like "good" and "intelligent" and so on of God, when we knew (a) that God was totally different from us, and so goodness as it existed in God was utterly different from goodness as it exists in anything we can observe, and (b) Sacred Scripture shows that these terms actually do apply to God.
What his solution was was to set up the proportion
God's essence : God's existence :: creature's essence : creature's existence
and assert that the relation between God's essence (anything that could be said about him; his "whatness") and his existence (which relation in God's case is one of absolute identity) was similar to the relation between our essence and our existence (unification); and hence, God could be called "good" (because anything that exists is good insofar as it exists), but that, because the relation between essence and existence in the two cases was only similar, you couldn't specify how God was good, but only that (somehow) he must be.
I always found difficulty with this because in Thomism, creaturely essences were supposed to be really distinct from their existence while in God "essence" and "existence" are just two words that refer to absolutely the same aspect. I never could quite figure out how you could hold that the uniting of two really distinct "principles" was even similar to the absolute unity of what was in no sense distinct from itself--and of course, if you don't know how the relationship is similar, then how can you use the proportion Aristotle was talking about?
But after all, what Aquinas and the Christians who dealt with analogy seriously (for Aristotle it was more of a poetic or rhetorical device, though he did use it occasionally in a scientific context) wanted was the explanation of how it can be true that certain terms, derived from finite creatures, apply to God, who is not at all like his creatures. We know (from revelation) that it is true; but what we don't know is in what sense it is meaningful to call God "good," since "goodness" as we know it is shot through with the finiteness of the creatures we derived the concept from.
And I think it is precisely this sort of thing that my definition of "analogy" accounts for. For example, we call a finite causer a "good" one when what is affected is benefited rather than harmed by what it does. For instance, if you are starving and someone feeds you, you would call him a good man; and so his goodness is the cause of the benefit to you.
But God, in creating, makes something exist where there was nothing before (let us assume this for the sake of argument, taking the usual notion). But it is better to exist rather than be nothing; and so this is a sort of a benefit. Hence, God as Creator is somehow or other good. The "benefit" of coming into existence, however, is not identical with the benefit of improved existence; and so the effects are merely similar; and therefore, God's goodness is only analogous to human goodness.
Of course, what I have just said in this is to say (with Aquinas) that the relations are similar, and so we have a proportion and can do what Aristotle did with the terms. But what I have done that I think is an improvement is show how it is that the relation between the effects is one of similarity, and just why it can be said that from them the two unobserved causes must be similar. So I think this approach puts analogy on a rather more secure footing.
Let me make a brief remark here on the relation between analogy and metaphor, since we won't get to discussing metaphor for a long, long time, when we talk of aesthetics. In spite of what Aristotle thought, a metaphor is not really an analogy; it is a concept, but derived in a different way from what we might call "scientific" or "perception-based" concepts. A concept, as we will see, comes from comparing the sensations as effects of the reality outside us, and knowing that the relation between the sensations is the same relation as the relation between the realities (we just saw above, for instance, that identical effects have causes that are identical to each other). Thus, if I have the same sensation when looking at a traffic light as I do when looking at grass, then the traffic light must in some way be the same as grass (i.e. green). We don't call this "analogy," because the analogy does this at a further remove: if the realities have a relation, then the causes of these relations are related.
But metaphor is not at this extra remove; it is on the same level as other kinds of concepts. What metaphor does is compare emotional reactions to the world outside us, and on the basis of this relation we talk about "esthetic properties" of things. Thus, we feel happy when someone smiles at us, and we feel the same happiness when we go outside on a sunny day; and so the day "smiles" at us--meaning that it has in it "what it takes" to produce this emotional reaction.
Let this suffice for now. As I say, metaphor is not the same as analogy for two reasons: (a) metaphor is based on emotions, and analogy is based indirectly on perceptions; (b) metaphor uses the comparison of the conscious reaction as the basis of the knowledge of reality, and analogy uses the comparison of the causes of the conscious reactions (the realities) as the basis of its knowledge of this cause-of-the-cause.
Since we have been talking about identities and similarities and causes and effects, there is one thing that might cause confusion if it is not made explicit and emphasized. This is worth stating as another numbered conclusion:
Conclusion 3: The cause is not similar to its effect.
That is, the similarity between effects means that the causes of the effects have to be similar to each other, but it implies nothing at all about any similarity of the cause to its effect. And, if you think about it at all, you can see that the cause, as simply a fact missing from the effect, will in general have no similarity to the effect at all.
It was thought historically that the cause had to be similar to its effect (or actually, that the effect would be similar to the cause), since the "cause" (what I called the causer) was supposed to do its job by "giving something of its 'perfection'" (what would correspond, I suppose, to the "cause") to the effect (more or less the way we would think of an energetic object's giving up some of its energy to what is affected by it); and it would follow from this that the effect (the "perfection received") in what is affected would of course be like the cause (the "perfection imparted") in the causer. Further confusion came from the failure to distinguish clearly cause from causer and effect from what is affected.
The problem in this can be seen from the fact that logically you would now have to say that the beaver's dam was somehow like the beaver, because the beaver "gave something of itself" to the dam; and so once again we have the beaver with a little picture of the dam in its head, because the "damness" of the dam (its "perfection") had to be in the beaver in order to for the dam to "receive it" from the beaver. And of course, since the beaver doesn't really understand what it is doing, this plan for the dam would have to have been put into its head by somebody who could understand; and therefore, beavers' dams imply indirectly God the Engineer.
Now I'm not saying that things like dams can't have effects in them (such as the particular configuration) whose cause is the plan of the engineer, in which case the effect is, in a certain sense, like its cause. But this likeness doesn't have anything to do with the effect's being an effect, but is part of the particular effect which it happens to be. There is absolutely nothing about a cause's being an ignored or unknown fact that says that it has to be at all like the "remainder" that is known and forms a problem because of the missing information; and so at least on this view of effect and cause, even though if the effects are similar among themselves, then the causes of these effects have to be somehow similar among themselves, this does not imply in the least that the cause is similar to its effect.
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