[The material for this chapter can be found in Modes of the Finite, Part 1, Section 2, Chapters 5-9.]

2.1. Second step: hypothesis

The scientist, then, is not just looking for an explanation of the effect; he is looking for the true one: the one that actually exists and actually does make the effect not a contradiction.

But of course in order to do this, he has to think up an explanation, and probably a lot of them, so that he can pick out the one which is most likely to be the right one.

Again we're in a place that has few rules, really. It takes ingenuity to be able to dream up explanations for a given effect, and common sense to be able to reject the explanations that are not worth pursuing. Nobody would have any trouble rejecting the explanation that gnomes filed down the stones in your back yard, but it might not be so easy to eliminate others without further investigation.

In any case, what the scientist does is pick out one of the explanations he has come up with and use that as his working hypothesis. He is now going to test it to see if it is the true one.

DEFINITION: A HYPOTHESIS is an explanation of the effect in question, which will be tested to see if it is the one which is actually the fact which makes sense out of the effect.

It is called a "hypothesis" because a hypothesis is the "if" clause of an "if-then" statement. Hence, the hypothesis is put into the explanatory statement: "If the stones were dumped in your back yard, then the fact that they are smooth makes sense." You will recall that our hypothesis about science is "If science is looking for the true explanation of effects, then the peculiarities about scientific method make sense."

2.1.1. Occam's razor: simplicity

We are not totally without rules, however, even at this stage of the enterprise. We can rely on what is called "Occam's Razor," after William of Occam, who told us we should "cut away" from our consideration any explanation that involved us in assuming the existence of a lot of unobservable things (like the gnomes).

Of all the explanations, the simplest is most likely to be the true one.

DEFINITION: An explanation is SIMPLE if it assumes THE FEWEST POSSIBLE facts that are not directly in evidence.

We will return to simplicity later, when we discuss the criteria of a good scientific theory; and we will then see why, on our theory, a scientific theory is a good one if it is simple. At this point, it just sort of "stands to reason" that if you can explain something by assuming only one fact you can't directly observe (remember, the effect wouldn't be an effect if you observed what made sense out of it), then this is a better explanation than one that means you have to accept as true a dozen facts you have no direct knowledge of.

(Note that the problem is that the simple explanation may be better, but does that make it truer--and after all, the scientist is interested in the one that's actually the case, not in what is "neat"? We'll see this later.)

Our own explanation of science is a simple one: all we assume is that scientists, confronted with facts that don't make sense, are trying to find the fact that makes sense out of this effect.

NOTE that simplicity does not mean that the explanation is easy to understand or that the logic by which it explains the effect is easy to follow; it only means that you don't make up a lot of unobserved "facts"

The reason I say this will become evident in the next few pages. We are now going to have to take a look at this "true explanation" that the scientist is trying to discover. And it will turn out that there are quite a few ramifications to it.

2.2. Cause and causer

If you refer back to section 1.2. earlier, where I stated the basic hypothesis about science originally, I called the fact that made sense out of the effect the "cause." It is now time to make a technical definition of this.

DEFINITION: The CAUSE is the TRUE EXPLANATION: it is the FACT which in fact makes sense out of the effect. The CAUSE contains ONLY WHAT IS NECESSARY to make the effect not a real contradiction.

DEFINITION: The CAUSER of a given effect is THE CONCRETE OBJECT or set of objects which are doing the causing: that is, which CONTAIN the cause AS PART OF themselves.

The distinction between cause and causer parallels the distinction between "effect" and "affected object" which we made earlier (on page 13).

In the example we gave there, with Neil Armstrong dropping the hammer and the feather in the airless space of the moon, where they hit the moon at the same time, we noted that the shape, color, size, and so on of the two objects were irrelevant to the effect itself and were part of the "affected object," because any two objects of different weight would do.

Of course, it was the moon that attracted these two objects to it; and if they had been dropped in a vacuum chamber on earth it would have been the earth that attracted them. But you can see that it's irrelevant what the nature of the moon as opposed to the earth is, since in both cases, the objects will fall at the same speed. The only thing that is needed is that what makes the objects fall is extremely massive in comparison with the objects themselves.

Hence, bodies of unequal weights will fall with no detectable difference in acceleration (to be technical about it) if the body they are falling toward is many many times as massive as they are. If it isn't, then complications (which we need not go into) arise. The point here is that anything else about the attracting body is irrelevant to it as explaining the accelerations of the falling bodies.

Hence, the massiveness of the moon or the earth is part of the cause; the chemical constitution of the earth and the moon, the relative sizes of the two bodies, the place in the solar system, the color, and all the other qualities that belong to the objects as they concretely exist are part of the causer but NOT of the cause.

This distinction between cause and causer is very important, because including parts of the causer into the cause is going to give you an explanation that is apt to be false. In fact, one of the biggest mistakes in modern philosophy involved precisely a failure to make this distinction.

Rene Descartes noticed that if he were thinking at all, he could not doubt his existence; and so he made the famous statement, "I think, therefore I am." From this, however, he concluded that the "I" was only a thinker (a mind), and that I have a body, which is a different thing from myself. The "I" as a mind is the cause of thinking; but the "I" as causer is actually a body which has a mind as one of its faculties or "powers." Descartes failure to make this distinction split the human being in two, and philosophers since then have been trying to put "them" together again.

2.2.1. Effect and cause as abstract

One of the first things to note, then, about the effect and the cause as we have defined them is that they are abstract aspects of a concrete situation. They are not concrete things themselves; the effect will always be only part of the whole situation which is observed, and there will always be properties of the observed affected object which have nothing to do with it as effect. Similarly, the cause will always be part of a larger situation which contains properties which have nothing to do with it as explaining the effect in question.

This does not mean that the effect and the cause are not real. They are real aspects of a concrete situation, but only aspects of it. Just as the color of a red ball is red, and the color is real, even though it is not a "thing" itself (it is a way the ball exists), similarly, the fact that the effect is an aspect of an affected object doesn't mean it isn't a real aspect of it; and the same goes for the cause. The cause has to be real, or the effect would be a real contradiction, and that is impossible. But the cause isn't a thing; it's an aspect of something.

NOTE that aspects of the CAUSER that are not part of the cause CANNOT BE KNOWN by arguing from the effect.

Why is this? Because these aspects of the causer could be anything at all, and the effect would still be explained by the causer (because all that is needed to explain it is the cause--and by the supposition, the irrelevant aspects have nothing to do with it, and so can vary without affecting it).

Thus, we could go to Jupiter and perform the experiment with the feather and the hammer (if we could find a vacuum there), or Mercury, or the Sun, or any very massive body--and the effect would be always that, dropped from the same height, they'd reach the surface at the same time.

Hence from this effect as defined you cannot tell anything about what planet you're on except that it's very massive with respect to what you're dropping.

It follows from this that science will never tell us all about reality.

Science, looking for causes, will only tell us aspects of the real concrete reality. They will be aspects that will have to be real ones; but they will always leave out some of the real aspects of the situation--the aspects that belong to the causer and not the cause.

To put this another way:

What is NECESSARY does not exhaust WHAT IS REAL.

Why is that? Because of the following:

A FACT is not of itself an EFFECT.

That is, in order for a fact to need explaining, it has to be a contradiction taken by itself; but not every fact is a contradiction when taken by itself; in itself, it's just a fact. You have to have two facts that "fight" in order to have an effect.

So there may very well be all kinds of facts that don't need explaining as such; and there has to be at least one. If every fact needed an explanation, then no explanation would be possible; the whole set of all effects with their causes would itself be an effect--for which there could not be a cause, because it by definition would have to be outside the set, which would put it inside the set.

And so there are some facts that are just facts and don't need causes; and there are aspects of the causers that are just facts and have nothing to do with what is necessary to explain what effects there are.

"There is more in heaven and earth, Horatio, than is dreamed of in your philosophy." It is the rationalist fallacy to assume that because something is a certain way, it has to be that way. This might be so; but there is no reason why it has to be so; and, using Occam's razor, if there is no reason for assuming it to be so, we shouldn't do so--because we certainly don't observe that things always have to be the way they are.

Now then, with that out of the way, we can note that

Since effect and cause are abstract, exactly what the effect is depends on which facts you notice; and the cause will differ depending on what you see as the effect.

This sounds as if the whole thing is subjective; but I can illustrate what I am saying by taking the hammer and the feather on the moon and the earth. If the effect you are interested in is the fact that a heavy and a light object fall at no detectable difference in acceleration, then the effect of the hammer and the feather as falling on the earth and the moon is identical in both cases; and the fact that the earth is more massive than the moon makes no difference.

If, however, you measure how fast the hammer and the feather fall to the moon, and how fast they fall to the earth in a vacuum, you will note that both the hammer and the feather fall toward the moon at the same speed, but this speed is DIFFERENT from the speed at which they both fall to the earth.

Your effect now has become more complicated. You are now asking "Why is it that heavy and light objects fall at the same rate of acceleration as each other; but that this rate of acceleration is different depending on the body they are falling toward?"

The degree of massiveness of the earth and the moon are now part of the effect; and so the cause has to explain this added complication. And the cause will be the fact that differences in massiveness of the attracting body will produce different speeds of attraction. That is, the cause now takes into account the fact that (a) massiveness explains falling, and (b) differences in massiveness explain differences in speeds of falling.

This doesn't make your first effect-cause linkup false; it is still true that the massiveness of the attracting body, if it is very great, will make bodies of different (small) masses fall at (for practical purposes) the same acceleration. The added factor is part of the causer of the effect stated in this simpler way; when you add the difference in the actual rates of acceleration as part of the effect, then this part of the causer slips into being part of the cause of this new effect.

That is, the two effects (bodies of different weights hit the surface at the same time; bodies of different weights fall at one rate of acceleration on earth but a different rate of acceleration on the moon, etc.) are two different effects--slightly different, but different. Hence, the causes (as opposed to the causers) will be different.

2.3. Theorems about cause

This is an interesting development; let us look at it more closely. It turns out that we can, from our definitions of effect and cause, derive some theorems about effects and causes.

DEFINITION: A THEOREM is a statement that is necessarily true just because of the way the terms involved in it are defined.

THEOREM 1: Identical effects have identical causes.

The way this theorem can be proved is the following. Assume that you have two effects that are identical (whether the affected objects are identical or not). Now the cause of Effect 1 has ALL the properties NECESSARY to make sense out of effect one, and ONLY the properties which are NECESSARY. All other properties belong to the causer of effect 1. The same is true of the cause of Effect 2.

Call the cause of Effect 1 Cause 1, and the cause of Effect 2, Cause 2. What is to be proved is that Cause 1 must have exactly the same properties as Cause 2.

Suppose Cause 1 has a property that Cause 2 lacks. Then this property will be NECESSARY to explain Effect 1, but not necessary to explain Effect 2. But Effect 2 is identical with Effect 1; and since the effects are abstract properties of the affected object, then if they are identical, you can substitute one for the other without changing anything. Then substitute Effect 2 for Effect 1. But now Cause 1 has a property which is NOT NECESSARY to explain the "new" Effect 1, which is identical with the "old" one. But that means that it was not necessary to explain the old one either. Hence, Cause 1 cannot have a property that Cause 2 lacks.

If Cause 1 lacks a property that Cause 2 has, then when we substitute Effect 2 for Effect 1, Cause 1 will now NOT BE ABLE to explain the "new" Effect 1, because it lacks what is NECESSARY to explain Effect 2, which is the "new" Effect 1. But since the "new" Effect 1 is identical with the "old" one, Cause 1 was not able to explain the old Effect 1 either.

Hence, Cause 1 can neither contain nor lack any property that is in Cause 2. They must have the same properties. Q. E. D. (Quod Erat Demonstrandum, what was to be demonstrated)

If we use as our example the hammer and the feather falling on the earth and the moon and note as our effect only the fact that both bodies hit the surface together if dropped from the same height, then the difference in massiveness of the earth and the moon are irrelevant to the explanation of this effect. Both the earth and the moon are very massive with respect to the attracted objects, and this is all that is necessary to explain the effect. Hence, as causes they are identical.

THEOREM 2: Different effects have different causes.

To prove this theorem, we note that an effect is defined as such by the fact that there is a fact missing from its intelligibility. It appears as a contradiction only because the fact which explains it was not observed; hence the fact that this fact (the cause) is missing is what makes the effect an effect.

It follows from this that what makes one effect different from another AS an effect is specifically which fact is missing from its intelligibility. That is, if a fact of some sort is missing, you have an effect in general; if this particular fact is missing, you have this particular effect.

But the missing fact is precisely the cause; and therefore, one effect is different from another if and only if its cause is different from the other. Q. E. D.

Again, if you take as the effect in question the fact that the rate of acceleration of falling bodies on earth is 32 ft/sec2, and on the moon it is different, then whatever it is that is attractive about the earth cannot be the same as that on the moon, or they would make the bodies fall at the same rate.

Once having proved both of these theorems, there are two corollaries which follow:

COROLLARY 1: Identical causes have identical effects

Suppose Cause 1 is identical with Cause 2, but their effects are different. Then you have a case of different effects with identical causes, which is disproved by Theorem 2.

COROLLARY 2: Different causes have different effects.

Suppose Cause 1 is different from Cause 2, but their effects are identical. Then you have a case of identical effects with different causes, which is disproved by Theorem 1.

2.3.1. Analogy

There is one more thing we can do with effects and causes, which will give us something useful.

COROLLARY 3: Similar effects have analogous causes.

DEFINITION: Objects are SIMILAR if they are partly identical and partly different--and it can be OBSERVED in what respects they are identical and different.

DEFINITION: Objects are ANALOGOUS if they are partly identical and partly different, but the RESPECTS in which they are identical and different ARE NOT KNOWN FROM OBSERVATION.

That is, when you say two things are similar, you can point to what they have in common, and what makes them different. If you say they are analogous, you know (for some reason) that they are (somehow) similar, but you don't know in what respect they are identical or in exactly what way they differ.

So similarity is called "analogy" when only the fact of being similar is known--not the precise way in which the things are similar.

Now then, to prove the theorem, if two effects are similar, then as effects they are partly identical and partly different. By Theorem 1, the respects in which the two are identical demands that the causes be identical; and by Theorem 2, the respects in which the two are different demands that the causes be different. Hence, the causes of similar effects will themselves be partly identical and partly different.

But since the causes are not observed merely by arguing to them from the effects, all you know from this reasoning is that they are somehow identical and somehow different from each other; but you do not in general know in what respects this is so. But this means that the causes will be analogous. Q. E. D.

COROLLARY 4: Similar causes have analogous effects.

The reasoning is the same. As identical, the causes will have identical effects, and as different they will have different ones; hence the effects will be partly identical and partly different; but again the precise respects in which this is true cannot be known just from knowing the causes. But this means the effects must be called analogous. Q. E. D.

Let me illustrate before I make an important point suggested by this.

If we combine the two effects about bodies falling on the earth and the moon into the similar effects that both the heavy and the light body hit the surface together, but the rate of fall on the earth is different from that of the moon, we can conclude that whatever it is that causes the fall on the moon is partly identical to what causes the fall on the earth (because in each case, light and heavy bodies are treated equally), but there must be some difference in the cause as it exists on the moon and the earth, or the rates of fall would be the same also.

But what is it about the earth and the moon that makes bodies fall towards it? Ah, there is the difficulty. We know that it's connected with the massiveness of the earth, the moon, the hammer, and the feather. But what is it exactly? Newton thought it was a force attached to the mass of an object, which varied directly as the product of the two masses involved, and inversely as the distance between their centers. I.e. F = K(some constant)Mm/r2.

By this theory, if M (the earth's mass, say) is very large with respect to m (that of the hammer), then m adds nothing to it, for practical purposes (i.e. 1,000,000 + 2 is just about the same as 1,000,000 + 4); and so all bodies we can lift will add nothing significant to the product Mm. And if r is the distance from the falling body's center to the center of the earth, then lifting the body up another couple of feet is not going to make this number measurably different. So under these conditions, the whole fraction turns out to be the same all the time--and so four-pound objects fall just as fast as four-ounce objects. (Actually, as you can see, they don't; but the difference is so small as not to be measurable.)

But, by this theory, if M on earth is different from M on the moon by any large amount (and it is), then the reasoning above will apply to the moon as well as the earth, but the actual number the fraction comes out to will be different.

Einstein, however, showed (for reasons we don't have to go into here), that there could not be such a force; and he explained falling bodies by a warping of the geometry of space (actually space-time)--and the geometry of space was the path that a falling body had to fall along. Since greater mass warped space more, then the fall would be different--and would come out to the observed rates of fall.

If you're lost here, the point is that we don't really know what it is that explains why bodies fall, because we can't observe it. But we do know this: whatever it is, it is connected with whatever is responsible for the weight and resistance to acceleration of a body (its "mass"); and all bodies have this tendency to be attracted, but the tendency varies depending on the variation of this "mass," whatever it is.

In other words, because the effects are similar, whatever is responsible for the effects is somehow similar; but we don't know in just what way. One theory is that it is a greater or lesser force of the same type; the other says that the identity is in a warping of space-time, and the difference is in degree of warp.

So the causes of falling bodies are analogous with each other.

It turns out that many concepts in science are analogous. Energy, for instance is an analogous concept. We know that electricity and heat are somehow the same, because both can move things; but they aren't identical because things are moved in different ways under the influence of heat and electricity. So we give the analogous name "energy" to whatever can account for such similar effects.

We will see later how the concept of analogy helps in explaining the use of models in scientific theories; but let me give a brief account of why I use this term here.

Historically, "analogy" was defined more or less as I defined "similarity"; but the real problem of analogy arose in philosophy in reference to terms used to apply both to finite things and the Supreme Being. For instance, we are good and intelligent, and the Supreme Being is known to be good and intelligent.

But since the Supreme Being is infinite and has no unified "set" of "properties," but is one simple Act, then goodness, intelligence, mercy, justice, etc., in Him are all different names for the same thing, while in us they are different aspects of ourselves. For instance, we can be just without being intelligent; but the Supreme Being can't be, because these are just different ways of naming His Act.

Yet it was also known that it would be false to say that the Supreme being is not good or not intelligent, and so on; and so the dilemma arose of how you could know these terms applied to the Supreme Being when you couldn't see Him and they obviously meant something different when applied to Him than when applied to us.

Various attempts were made to solve the puzzle; but I think you can see that the problem is that of how we can say that something which is a cause (philosophically, the Supreme Being is known as the cause of the finite universe) can be similar to something else (ourselves as good or intelligent), but not know in what respect it is "partly the same and partly different." And this is just what the notion above of analogy explains, arising naturally out of an analysis of effect and cause. So it looks as if our theory is on the right track; we have been able to solve a conundrum thousands of years old while we were accounting for why scientists are looking for what makes sense out of their data.

2.3.2. An important point

Now then, let me make the important point I promised a few pages ago:


In general, a cause will be very different from its effect, because it is a fact not in the effect as such. So these theorems about identical effects and identical causes and similar effects and analogous causes mean that when the effects are identical or similar among themselves, the causes will be identical or similar among themselves, NOT that they will be "like" their effects IN ANY WAY.

This idea that the cause is like the effect came about because very often causers are like affected objects, and philosophy and science has often foundered on the rock of confusion of cause and causer and effect and affected object.

That is, dogs are called the "causes" of puppies, which grow up into dogs; and cats are the "causes" of cats, and guppies of guppies.

But these aren't causes; they're causers. Why a dog begins to exist rather than a cat, for instance, is explained by the configuration of the genetic molecules that get into its initial cell; and this is the cause of the conception of a dog. Now it is true that this particular set of genetic molecules came from a dog, not anything else; but the cause of the molecules' being this way is the mechanism by which the living body builds molecules of this type and this in turn is caused by a complex of several genes in the parent dog's genetic molecules. But this isn't at all like a doggie; so the cause of a doggie is actually a certain complex ACTIVITY of--to be sure--(two, not one) dogs; but the point is that the cause isn't the dogs themselves.

In order to do science, and in order to understand what science is doing, you have to learn to think ABSTRACTLY.

If you let yourself think in terms of concrete objects when investigating effects and their causes, you'll come to all kinds of silly and unwarranted conclusions. Causes are abstract aspects of things, and so are effects.

2.4. The leap into the unobserved

We are now in a position to explain why science, which seems so tied down to observable data, talks about unobserved things like dinosaurs (which no one has ever seen), the early state of the earth (which obviously has not been observed), electrons (which are too small to observe), the unconscious mind (which, if it is unconscious can't be observed by anyone; not the person who has it, nor anyone else--since we can't even observe anyone else's consciousness).

So scientists talk with great confidence, not only about what hasn't been observed, but about what can't (now) be observed, and even what can't be observed in principle. But how can they do this?

The answer should be pretty obvious, if our theory about science is true:

If it can be shown that the cause of some effect has to be something unobserved or even unobservable, the scientist knows, even without observing it, that it is a fact.

Why? Because otherwise there is a real contradiction and things aren't the way they really are.

For instance, suppose there weren't any animals like the dinosaurs. Then how could you explain those fossil bones we see in ancient lakebeds and riverbeds? They belong to no observed animal; but the theory that little men from Mars came down and buried bones they made in their bone-factory just to play a joke on us when we dug them up would take the edge right off Occam's razor, it would need so much trimming. No, there have to have been animals whose skeletons these bones are; and whether we actually dig one up with flesh on it or not, we know that they once roamed the earth.

Similarly, if we don't have unconscious minds, where we do things because of mental operations (i.e. activities of our brain) we are not consciously aware of, then you have to assume that all neurotics are liars--and liars who are spending upwards of fifty dollars an hour to get cured of what is just deception on their part. And that theory is worse.

...And so on. Scientists, for all their protestations of "sticking to the observed facts" are very glib in talking about things as facts that they couldn't possibly have observed; and the reason they're so confident that they're talking about facts is simply that they will not accept a real contradiction as occurring, and they are convinced that one would have occurred if their unobservable cause doesn't really exist.

2.4.1. Operational definitions

So our hypothesis about effects and causes has enabled us to give a simple explanation of something that contemporary philosophers of science have stood on their heads trying to account for.

Since they don't want to talk about effects and causes, or admit that scientists are actually asserting the existence of unobservable "entities" like electrons or forces of gravity or space-time warps, they have tried to account for these "unobservables" as simply collections of observable facts.

P. W. Bridgman, in fact, coined the phrase "operational definition" as a kind of way you could define a "mental construct" (an electron, for instance) in terms of what you did in dealing with these things.

It goes something like this: "Electron" means "Set up your Van de Graf generator, put a photographic plate in a certain position, put a positive charge beside it, turn on the current, take out the plate and develop it and you will find little curly lines on the plate veering off toward the positive charge."

That is, the set of operations which are supposed to indicate that an electron was actually "lurking there behind the scenes" is actually the definition of the term "electron." There aren't actually any electrons; only that set of operations.

Come now, Mr. Bridgman. If that photographic plate was blank when you put it in the machine, and then when you developed it it had little marks on it, mental constructs don't scratch photographic plates. Nor do "definitions of things that don't really exist." Something other than a mental construct had to put those marks there; and if we can't see it, it has to be something real, and capable of marking photographic plates, and marking them in this way.

So Mr. Bridgman's little device doesn't do the job he wants it to do; the world makes more nonsense by his view than it did with the "unobservable entities" that he wanted to replace by it. And later philosophers have shown that if you want to replace these "theoretical entities" with observed operations, you would need an infinity of operations to define any one of them.

Nevertheless, his way of definining things, stripped of its silliness, can be very useful.

DEFINITION: An OPERATIONAL or CAUSAL DEFINITION of something is a definition of the cause of some particular effect as "the whatever-it-is-that-causes-this-effect."

So you can define an electron, if you want to as the "whatever-it-is that causes marks of a certain type on photographic plates when put into Van de Graf generators in a certain way."

Or you could define a "dinosaur" as "whatever it is that accounts for these bones." Or the unconscious mind as "whatever accounts for behavior that a person does but chooses not to do." And so on.

We may not know what it is--as we saw that we don't know what makes bodies fall--but we do know that, whatever it is, it has to have all the properties necessary to explain the effect; and so, even though we don't know what it is, we can often say a good deal about it.

So when Sir Isaac Newton said he "made no guesses" about what gravity (his "force") was, this didn't mean either that he didn't think there was such a thing, or that he didn't know what he was talking about. Gravity is the "whatever it is that causes bodies to fall" and all he knew about it was the properties it had to have to do this job.

Operational definitions, then, are very useful in science, in spite of the fact that the theory that gave them their name makes no sense. And our theory explains why this is so. So I think it is legitimate to keep the term.

2.5. Causality

We have a couple more implications about causes before we resume our look at what scientists are doing as they try to find the cause among the many explanations that might be true but aren't.

DEFINITION: CAUSALITY is the RELATION between the cause and its effect. It is the WAY IN WHICH the cause makes sense out of the effect.

Generally speaking in the real world, the cause is some activity; and it makes sense out of the effect by doing something to it; this action of the cause on the effect is the cause's causality. (It is what the cause is doing to the effect, as opposed to what it is in itself.)

Thus, the gravitational field of the moon is the cause of the falling of the hammer and the feather; but it is there whether there is a hammer or a feather to be acted on by it or not. The force this energy-field exerts on the hammer and the feather is the causality of the field on the objects in question.

DEFINITION: BEING-AFFECTED is the RELATION between the EFFECT AND THE CAUSE. It is the same as the causality, but looked at in the other direction.

That is, the causality is what the cause is doing to the affected object; the being-affected is what is being done to the affected object by the cause. Causality looks at the relation as from cause to effect; being-affected looks at the relation as from effect to cause (passively, not actively). But it is the same relation in both cases. As Aristotle noted long ago in this context, "The road from Athens to Thebes is the same road as the road from Thebes to Athens."

Let us make a little scheme showing causer, cause, causality, affected object, effect, and being-affected, taking the hammer as it falls to the moon as our objects.

The HAMMER is the AFFECTED OBJECT; the hammer AS falling at the same speed as the feather is the EFFECT.

The MOON is the CAUSER; the moon's GRAVITATIONAL FIELD (the moon AS attractive to things like hammers) is the CAUSE.

The moon's field AS PULLING the hammer at a certain speed is the CAUSALITY of the moon on the hammer.

The hammer as BEING PULLED in the field (i.e. the motion as being caused by the field) is the BEING-AFFECTED.

If it is hard to know what the cause is from the effect, it is in general considerably harder to know just exactly what the causality is. That is, we may be able to zero in pretty well on the characteristics of the moon and the earth that are necessary to account for bodies' falling toward them; but how the gravitational field attracts objects through their masses, or what it does to them is a mystery to us. We know the moon does something to objects to make them fall; but no one really knows what it really does.

2.5.1. Another important point

This discussion of causality uncovers another peculiar fact about the cause in its relation to the effect; and leads us to make another important point.

The cause is NOT AFFECTED by the fact that it is HAVING an effect on something.

The way we have defined cause, it would be impossible for it to be altered by the fact that it is the cause of some effect. As cause (not causer) it is simply a fact: the one not observed, which (because it is not observed) allows the effect to appear as a contradiction. So it just is what it is.

And this actually can be seen from experience. Suppose you are in your car, and you hear on the radio a news report that a certain house (which you recognize is yours) is on fire. You swerve the car round and rush back home.

Obviously, the cause of the fact that you suddenly changed direction is the words the news broadcaster said. But clearly, if you did not have the radio on, you would not have changed direction; yet the broadcaster would have said those words whether you had the radio on or not. The reality which is the cause (the activity) is the same whether it is actually having an effect or not; it is just that, if it isn't acting on something, you can call it the cause of this effect (because there's no effect).

Similarly, what is needed to pull the hammer down to the moon at the speed it falls is a gravitational field of the moon of a certain definite potential (strength) at the point where the hammer is. But the moon has that potential at that point whether there is a hammer to be pulled down or not. So the cause as such is what it is whether there is an an effect or not.

Well, but what of Newton's Third Law of Motion: "For every action there is an equal and opposite reaction"? This deals with causers and affected objects (if they are bodies), not (even bodily) causes. For instance, the hammer does have a gravitational field of its own, which is acting on the moon, and therefore pulling the moon (to an infinitesimal degree) toward it. And in general, in the physical world, whenever a causer exerts causality on an affected object, it does so through a form of energy which the affected object also has; and so the affected object is also exerting causality on the causer.

But all this means is that in one causer-affected-object pair, you generally have a cause in each object and an effect in each one. Very often, however, one of the objects is so much greater than the other as cause that we tend to call it the "cause" (in that usual sense) and ignore the causality going the other way. Thus, you ignore the fact that when you walk, you are pushing the earth backwards a little bit; what you notice is that it doesn't go far as you exert backward causality on it (and for practical purposes doesn't move at all); and so it resists your backward push, making you move forward.

I don't know if you are aware of this, but according to the General Theory of Relativity it is as legitimate in theory to consider the earth at rest and the sun moving about it as it is to consider that we are moving about the sun. Why don't we do it, then? Because the sun is millions of times more massive than the earth, and it makes more sense to consider it to be the body "about which" the other moves--just as it makes more sense to consider yourself as moving over the face of the earth as you walk than to think of walking as pushing the earth out from under you.

So Newton's laws don't contradict this notion that the cause (not the causer but the cause) is not affected by the fact that it is a cause. And this leads us to say the following:

The relation of CAUSALITY is NOT a REAL relation; but the relation of BEING-AFFECTED is a real relation.

That is, the relation between cause and effect is really a one-way relation; and it is from effect to cause, not the other way round. The effect is really different because there is a cause; but the cause is what it is whether the effect is there or not. The effect could not exist if there weren't a cause; but the cause can exist (as a reality, though you couldn't call it a cause) without the effect.

For instance, the hammer couldn't fall without the moon's gravitational field; but the moon's gravitational field is what it is without any hammer in it. Hence, the falling (the being pulled down or being-affected) is the real relation; the pulling (the causality) is what is called a "mental relation with a foundation in reality."

Aristotle called "teaching" the relation between the teacher and the student (or the teacher's words and what is going on in the student's head); and he said that there is no teaching unless there is learning. That is, if the teacher is lecturing and none of the students is learning, then the teacher isn't teaching, he's just talking. So teaching as a causality exists in the student, and is the change in the student which is due to the teacher's words. But this is really the being-affected (i.e. the effect--the change--as due to these particular words--the cause). But the teacher often does not even know whether he is teaching or not, so much is this relation between teacher and student one-way.

2.6. Condition

One final piece of the theory of cause and we can get back to science. We often talk about the "conditions" under which a given cause operations. What are we referring to? In general, a condition means that if it's present, the cause can have its effect; if it's absent, the cause can't. For instance, a condition for seeing pictures on a screen is film in the projector; otherwise, you just see light.

DEFINITION: A CONDITION is a cause of a cause.

That is, if you take a given effect, it may very well be that its cause will only operate if something else happens; so the cause is impossible as cause unless this other something happens. But that means that this cause is itself the effect of the other event; and so from the point of view of the original effect, that more remote cause (which makes the immediate cause possible) is a condition of the effect.

Let us say that you hear scratching noises in the wall of your house. Walls don't scratch themselves, and so this is an effect; something in the wall is making the noise. You open the wall and find a squirrel. The squirrel is the causer of the noise, its claws as hard and the wood as hard are the cause of the noise.

But of course, the squirrel's claws couldn't make noises on the wood if the squirrel weren't there; but squirrels don't grow inside walls; so how did it get there? It fell through a hole in the roof, say. So the hole is the causer of this effect, and the presence of the squirrel at the hole and the gravitational field of the earth is the cause. From the squirrel's point of view, this situation is the cause; from the point of view of you listening to the noise, it is the condition for your hearing a noise.

NOTE that you don't have to go back through the conditions in order to make sense out of the effect.

The problem of what explains the noise in the wall is solved as soon as you find the squirrel; supposing it to be there, moving its claws on the wood, and the noise makes sense--the wall did not indeed scratch itself.

The fact that this "solution" is itself problematic is not really relevant to the effect as such; the cause is a fact, and once discovered, explains the effect. If it needs explaining, it is nonetheless a fact, and it is as a fact that it does this job.

So you can, if you want to, pursue the conditions for a given effect as far back as you like--from how the squirrel got there to how the hole got in the roof, to how the stone that made the hole got up so high that it could fall through, to how the planet blew up that made the stone which fell from the sky as a meteorite, to how that planet got formed in the first place, to how the star that was the Sun's companion blew up, to how that star got formed, to how the hydrogen cloud the stars formed got there, to how the Big bang took place that the cloud formed from--to, I suppose, God; where you have to stop, for reasons I don't want to go into.

But the point is that how far back you go into the conditions for a given effect is up to your own curiosity; your effect is explained as soon as you find the fact that is the cause; and that fact is a fact somehow; either by itself or by means of some cause, which itself is self-explanatory (and so is not an effect) or is the effect of a more remote condition.

NOTE that ALL the conditions for a given effect MUST NECESSARILY BE FULFILLED.

This is obviously true. If a cause is necessary for the effect to exist, and if a condition is the cause of a cause, then if some condition were not a fact (were not fulfilled), the effect would not occur--because its cause could not exist; and in that case, it couldn't exist itself.

Hence, you know that, however it may happen, the conditions are fulfilled all the way back to the ultimate condition (Yes, there always is an ultimate condition, but I am not going to discuss why, because it would take about sixteen pages to prove it, and the point isn't that important here). So you may act on that assumption and stop when you stop being curious any more.

So if scientists don't pursue some of their investigations back to God, we don't have to fault them for stopping short of going as far as it is possible to go. If they're not that curious, then that's all right. But what satisfies them may not satisfy others--and just because they feel comfortable stopping where they stop, it doesn't mean that people who find their causes problematic are somehow "not scientific" or "want to wander off into mythology."

I seem on the verge of making a prediction from this view of science. But let me hold off on it, and let us get back to scientific procedure.