[The contents of this chapter are discussed at length in Modes of the Finite, Part 4, Section 4 and Part 1, Section 2.]

2.1. Where are we?

Let's step back once again and consider where we've come from and where we've arrived. First of all, we found out that the relativist position (that what is true is true only for the person who thinks it is) has to be false, because as a generally applicable truth, it contradicts itself. And so it is absolutely certain that there are some truths that are true for everyone, no matter what your point of view.

This implies that reality is in fact the same for everyone, and if people disagree on what it is, the disagreement is due to the way they understand it, and the real world is not "adapting itself" somehow to their knowledge of it.

We discovered that "evidence" means the reason why you think something is true, and so it is some known truth that couldn't be true unless something else is a true, and this "something else" is what the evidence is evidence for.

We learned the self-evident First Principles of all thought, that what is true is not false in the respect in which it is true, that what is true is true, and that there is no middle ground between something's being true and false. These correspond to the First Principles of reality: that what is is not what it isn't, that what is is what it is, and that there is no middle ground between being and not being something.

By the way, you might try the following on your friends. Ask them to punctuate the following sentence in such a way that it makes sense: "That that is is that that is not is not that that is is not that that is not that that is not is not that that is." Hint: This simply states the Principles of Identity and Contradiction, positively and negatively. Try it yourself, and check with the answer in the footnote(1)

2.2. Scientific curiosity

But aside from the ability to confuse people, where has this got us?

Nowhere, in itself. But actually, the self-evident truth of the Principle of Contradiction is the foundation of science, and the basis of our trying to find out the causes of what we observe.

It turns out that when we notice that in the complex world we live in, it sometimes seems as if the facts contradict each other. But we know a priori (that is, without finding it out from experience) that they don't really contradict each other, since it's self-evident that what's true can't be false in the way in which it's true.

And here's the link between the trivial self-evident Principle that what's true isn't false and finding out things about the world we live in. It's obvious that if the facts as they present themselves to me seem to contradict each other, then I'm not aware of all the facts; because the facts as they actually exist don't contradict each other.

So there's some other fact or facts that I'm not aware of. I don't know what it is; but I know that it is, because otherwise reality really contradicts itself, and that's nonsense.

DEFINITION: Scientific curiosity is the kind of curiosity that occurs when a person is confronted with evidence on both sides of a contradiction.

This is the kind of curiosity that happens when we say, "That's funny," and when somebody asks us what's amusing about it, we answer, "I don't mean 'funny-ha-ha,' I mean 'funny-peculiar.' Something is happening that reason says can't or shouldn't be happening; what's happening doesn't make sense.

Of course, this kind of curiosity isn't confined to science, by any means; it happens all the time in ordinary situations. Mommy, for instance, bakes two dozen cookies at 10 o'clock one morning, and puts them in the cookie jar. At one o'clock in the afternoon, she comes back, and the jar looks nowhere near as full as she remembers it. "That's funny," she says.

On the other hand, this kind of thing is the starting-point of scientific investigation. Sir Isaac Newton, for instance, thought it was funny that things, which fall down apparently because they're heavy, don't fall faster the heavier they are (as Galileo Galilei discovered; they all fall at the same rate of acceleration).

2.2.1. Scientific observation

Now what's the first thing Mommy does when she notices the suspicious emptiness of the jar? She dumps out the cookies and counts them. There are only twelve.

Mommy has made an observation. What has she observed? An apparently contradictory situation: That is, she has information (a) that she put 24 cookies into the jar; (b) that cookies are not alive, and so can't unscrew the top of the jar and climb out; and (c) that 12 cookies that were there are not there any more.

The point here is that it can't be the case that there are still 24 cookies in the jar and that there are only 12 there. But based on the information she has (a) there would still be 24 cookies in the jar, because (1) the cookies couldn't remove themselves, and (2) she saw no one remove them; and yet (b) she has immediate evidence (remember that) of her own eyes that there are only twelve there.

So it's clear that, Now what has Mommy observed an apparently contradictory situation. But there really aren't any contradictions (the 12 cookies are not really "in-the-jar-and-not-in-the-jar"). So she knows that she doesn't have all the information about the cookies and the jar. Some fact makes sense out of the contradiction.

Well of course.

What Newton did was roll balls along a polished table and notice that the slipperier the surface (the less friction), the more the balls tended to move in a straight line at the same speed: they didn't speed up, slow down, or change direction (their velocity tended to be constant the less they were interfered with). But that added a peculiarity to falling bodies, because Galileo noted that not only were all falling bodies the same, but they all increased their speed at the same rate of increase. Yet, on the other hand, nothing observable was pulling them down.

The first step in any investigation, scientific or otherwise, is to observe as much about the apparently contradictory situation as you can. The more you know about the "impossibility-which-happens" the more likely it will be that you'll be able to find the missing fact that makes sense out of the problem.

2.2.2. Problems

So let's not call this sort of thing a "contradiction," because there's really no such thing as a contradiction. Let's not even call it an "apparent contradiction," even though that's what it is--because there are two better words in common use for it: problem and effect.

Now I'm going to be giving the word "effect" a very technical sense in the not-too-distant future (as a refinement of what we have now), and so let me here simply define problem and talk about the two kinds of problems there are, and the difference between them.

DEFINITION: A problem is a situation which seems to involve a contradiction.

DEFINITION: A theoretical problem is a situation in which the facts known contradict each other.

DEFINITION: A practical problem is a situation in which a person intends to do something which the evidence at hand indicates is impossible for him to do.

So theoretical problems are the ones we have been seeing so far. A practical problem might be that you intend to get an A in some course of yours, and you've taken it twice before and failed it both times. In both cases, there seems to be a contradiction; but the difference is that in the case of the theoretical problem, the actual facts contradict each other (at least the known facts do in some way), while in the practical problem the facts just tell you you can't reach the goal you want to reach; but the goal doesn't exist (at least not yet) as a fact, and so it's not a real contradiction. In fact you may in fact not be able to reach your goal (in which case, of course, you won't reach it). No contradiction, only disappointment.

But note this:

Theoretical problems always have solutions; practical problems may or may not be solvable.

Since facts can't really be a contradiction, there is, out there somewhere, a fact that makes sense out of the situation, which solves the problem. You may not be able to find it (that's a practical problem); but there's no question that it's there.

--With one exception, of course. Sometimes the "solution" of a theoretical problem is that there was no problem in the first place. The person who thought there was was misreading the facts. If Mommy had baked only twelve cookies, and when she looked at the jar and found "only" twelve, the solution to her problem (there were 24 cookies; I saw nothing take any away; there are only 12 now) is that her memory is faulty.

Similarly, in science, there are many problems that turn out to be non-problems because of a misreading of the evidence. In fact, Albert Einstein in this century showed that the "problem" Newton found with falling bodies was a non-problem. If Einstein is correct, all bodies when left to themselves move with a constant acceleration, which might in some cases (like the balls rolled along the slippery table) be zero (i.e. a constant speed, with zero increase or decrease or change of direction). So, according to Einstein, Newton was finding a difficulty because he took a special case and thought it was the general case.

This is actually a powerful way to solve problems: to show that there was no evidence on both sides of the contradiction in the first place.

But beware of cavalierly "solving" problems by the mere assertion that there's no problem just because you don't find yourself puzzled by it. For instance, even if Einstein is right, you've got the difficulty that falling bodies (which fall because they're heavy or massive) all fall at the same rate of acceleration, whatever their mass.

The point I'm making here is that what could be more natural than that bodies fall. When the physicist says, "Yes, but it's strange that they all fall down, for instance, and they all fall down at the same rate of acceleration," the tendency of the non-physicist is to answer, "Oh, please! You want them to fall sideways? Of course they fall down. And if they all fall down at the same rate of speed, so what? They fall."

That is, the non-physicist is saying that it's a fact that they fall, and so as a fact it does make sense somehow or other. He's just not interested in how it makes sense, because he has other things on his mind, like the latest episode of Ellen. But the scientist can't rest with saying that it makes sense somehow, any more than Mommy (who hadn't in fact had a lapse of memory) can rest with the fact that somehow twelve cookies managed to disappear.

This caution is going to be very necessary in metaphysics, because on the one hand, it's simple to create pseudo-problems out of the way we use language; but on the other, one of the most serious (practical) problems is going to be (as you will discover) to see just exactly what the (theoretical) problem is. Since metaphysics is absolutely the most general of all the sciences (the science of everything, since everything is real), then it finds problems in things we deal with and handle every day; and the inclination is to say, "What on earth is the big deal? So it's real, and it's only this reality. So what is the problem? You're just playing with words."

Sure, and the people who say that the real truth is that there's no real truth are the ones that aren't playing with words.

Aristotle was the first one to see this explicitly. He said that "causes" were the various ways in which "why"-type questions were answered; and his "why"-type questions are basically theoretical problems. He says that there are some "why" questions that are really "what"-type questions in disguise, because the "reason" given in answering them is a definition. For instance, "Why is blue blue?" is answered, "Because it's electromagnetic radiation of a certain wave length." But all that is is a definition of what blue is. On the other hand, "Why is the sky blue and not black, as it is on the moon?" is a legitimate "why" question, because if air is colorless (and it is), then the sky should have no color (or be black). The answer is that the molecules of air are of such a size that they vibrate at a frequency which is the same as the frequency of blue light; and so when blue light hits them, it makes them vibrate, and this bounces the blue light around, and the light that comes bouncing down to us from different parts of the sky because of this is, of course, blue light.

The point is that blue as blue isn't a contradiction. Something colorless appearing as blue is.

Note well

A fact by itself does not evoke the question "why" or need a reason for it. In order to ask "why" of anything and demand a reason for it, you must be able to show at least two facts that contradict each other.

So the solution to some of "the great metaphysical questions" is that they're stupid questions, asking "why" of something that's just a fact. For instance, "Why is there something rather than nothing?" Why shouldn't there be something rather than nothing? Unless you can show evidence that (a) it makes more sense to say, "There is nothing at all," (and how could it, because then you couldn't make that statement, which is something?), or (b) that there's something about what exists which says that it ought not to exist, and show what that something is, then your "great metaphysical question" is simply the fact that you can construct in language the contradiction "a nothing," and suppose that it (which isn't) might just as well exist as something. In other words, asking this question implies that you're talking nonsense.

Similarly, "Why am I here?" Because your parents had sex. "But why me rather than any of the millions of other people I could have been?" What?! If you were "some other person" (black, say, if you happen to be white), then you wouldn't be you, would you? It's a contradiction in terms to say, "I might have been somebody else." But then you would be you-and-not-you.

"But I don't mean it that way," you say. "I mean, 'What's the purpose of my being here? What's the reason in that sense that I exist?'" Your "purpose" is to be you. You've disguised a "what" question as a "why" question. "No, I mean, there has to be a reason for my being here: I must have some task to perform. What is it?"

What you're implying is that as you now exist, you are not (completely) yourself. You're supposing that mere existence doesn't make sense by itself, and there has to be a "reason" for it. Now, it is true that you're not fully developed, in the sense that you haven't realized all that you're theoretically capable of. But (a) does the fact that you're less than you could theoretically be mean that there's some kind of command to overcome this limitation, or is it just a limitation? and (b) in the last analysis, all this means is that your "purpose" is to be you.

"But there has to be a reason for everything." Precisely not. There can't be a reason for everything, or there's a reason for nothing. If "everything," taken all together, is a problem, then, as we saw above, the mere fact that it's a problem means that there's something else that makes sense out of it. But then that something else is something in addition to "everything," which is a contradiction in terms. You're talking nonsense again.

Put it this way: A fact is a fact is a fact. It is only when two or more facts are in conflict that there's a problem.

Remember that. Metaphysics is difficult enough without saddling it with conundrums that are only conundrums because you can't think straight.

2.3. Hypothesis and explanation

But this shouldn't blind us to the fact that there are real problems, and that they do have real solutions.

So Mommy has counted the cookies and established that there were 24 and now there are only twelve. So she says, "Johnny took them!" and goes looking for him.

Mommy has made a guess as to what makes sense out of the problem. If (the "if" part of a sentence like this is the "hypothesis"--the "supposing that" part) Johnny took the cookies when Mommy wasn't looking, then there'd only be twelve now.

Problem solved.

Similarly, Newton said that if is some invisible force acting between two objects pulling them together with a certain strength, then bodies would fall as they are observed to fall. His force, which he called "gravity," would have to be stronger the closer the two objects got to each other (because they move faster as they approach each other) and be greater the greater the mass of the objects. If you want to make it look technical F= G m1m2/r2, where "G" is just a constant number.

How does this solve the problem? Well, the distance between the centers of two different falling bodies and the center of the earth is not going to be measurably different, if they fall ten feet or even a hundred feet, since the distance inside the earth is thousands of miles; so "r" is for practical purposes a constant, unless you're an orbiting satellite or something. Similarly, the mass of the earth (which is also enormous with respect to the falling object) is also a constant--so the "force" which he supposed ("hypothesized") had to exist had to be stronger the greater the mass of the falling object, and weaker the less the mass. And since F=ma (force is the product of mass and acceleration), and the force and the mass vary together, then a = F/m, so that the fraction remains the same, and so the acceleration is always the same.

Problem solved.

DEFINITION: a hypothesis is a statement in which a possible solution to the problem is offered.

DEFINITION: an explanation is a possible fact that could make sense out of (i.e. remove the contradictoriness in) the problem.

In other words, science, in trying to solve problems, is offering explanations for things that don't seem to make sense in the world as we observe it. Anyone who's trying to solve problems does this; it's just that science is systematic about it.

DEFINITION: Speculation is the attempt to find an explanation for a problem.

So don't let scientists bamboozle you. They are engaged is speculation, however much they might say that they "stick to the facts." The facts they stick to are problems; and whenever you have a problem, you're pointing to a fact you don't otherwise know about.


The evidence for some fact is the problem for which the fact is the solution.

That is, evidence is something that doesn't make sense unless something else is true--which means that by itself it's a contradiction, or in other words, it's a problem whose solution makes sense out of it, and therefore, whose solution must exist.

But science (and most people) don't just stop with speculation. That is, Mommy doesn't just sit there and say, "Well, the problem of the missing cookies could make sense if Johnny took them, or it could make sense if a rat got into the jar and ate them, or it could make sense if I'd used self-destructing dough with half of them and they evaporated, and ..." She's interested in how the cookies actually got out of the jar, not in the infinity of possible ways (however fantastic) that they could have got out of it.

That is, whatever solves the problem is a fact, it has to exist, or the problem would be a real contradiction that only had a theoretical solution but not a real one. So which of these is the fact?

2.4. Experiment and theory

So Mommy tests the hypothesis that Johnny took the cookies. She goes looking for him and says, "Johnny, what happened to the cookies I left in the jar this morning?"

"I don't know."

"Johnny, someone or something took twelve cookies out of the cookie jar this morning. You were here, and I wasn't in the kitchen all the time."

Mommy has performed an experiment testing the hypothesis. If Johnny was there and Mommy had left the kitchen, it is possible for Johnny to have taken the cookies, which explains why twelve are now missing. She then asks:

"What happened to them?"

"A cockroach ate them."

Johnny has proposed an alternative hypothesis. Mommy now performs an experiment on this one:

"Johnny, how could a cockroach unscrew the top of the jar and get the cookies out and then screw it back again? Because there's no cockroach in the jar now. And if there was one and it ate twelve cookies, there'd be one humongous cockroach running around. Besides, there are no cockroaches anywhere in my house!"

What Mommy has shown with this experiment is that the proposed "explanation" can't solve the problem. In removing the one contradiction, it leaves unexplained a number of other contradictions. So it can't be the true explanation.

In the "experiment" phase of an investigation, the hypothesis is tested against the known facts, to see if it removes the contradiction and leaves nothing unexplained.

With Newton's gravity hypothesis, part of the experiment was actually done by Galileo, who was testing his hypothesis that the earth was not at the center of the universe (which Aristotle thought he had proved by the common-sense observation that heavy things--like rocks, made solely of earth--fall down faster than, say, cloth--made of a mixture of earth, water, and air). In showing that the earth didn't have to be in the "lowest" place in the universe, Galileo had to show that heavy things didn't fall faster than light things. So he rolled balls of different weights down a ramp and found that after definite lengths of time, each reached the same point as every other one. While he was at it, however, he discovered that they fell faster at a definite rate of increase of speed.

Newton then took these data and plugged them into his hypothesized force of gravity, and it fit. So if there is a force of gravity like Newton's, then the falling of bodies is explained.

If a hypothesis passes the experiment, it is no longer called a hypothesis, but now is a theory.

2.5. Prediction and verification

So a theory is nothing but a hypothesis that works. But, of course, there may be many hypotheses that work. For instance, it might be the case that Daddy came home briefly and took the cookies--or it might be that someone else came in and took them. So the theory doesn't necessarily tell you what actually did happen, which, of course, is what Mommy or any scientist is really interested it. And notice that Johnny has denied taking the cookies.

Now of course this additional fact still fits the theory, since if he had taken them, he would be likely to lie when confronted with an accusation. So Mommy now tries to figure out a way to establish beyond a reasonable doubt that he took them. She reasons this way: "If Johnny took the cookies, then he ate them, because he's greedy. But that means he'll have spoiled his dinner. So I'll cook hamburgers and see if he eats his usual six or not."

Mommy has made a prediction from her theory. If Johnny at the cookies, he won't be able to eat all six of the hamburgers.

DEFINITION: A prediction from a theory is something that must be true if the theory is true; it logically follows from the theory.

So a prediction is further evidence, but in a peculiar sense. Remember, evidence is some fact which is impossible unless something else is a fact. What we are saying here is that if the prediction turns out to be false, then the theory can't be true. But we are not saying that if the prediction turns out to be true, the theory has to be true.

Think of Johnny and the hamburgers. Suppose he only eats two. But suppose the real situation was that Daddy came home and took the cookies, and Johnny wasn't hungry, not because he hadn't eaten the cookies, but because he'd gone over to Jimmy's house in the afternoon, where he'd polished off three bags of nachos. The point is that there are an infinity of possible explanations of why Johnny didn't eat the hamburgers.

On the other hand, the theory says that if he did eat the cookies, then he couldn't eat all six hamburgers. So that if he did eat all six of them, then it would be impossible for him to have eaten the cookies.

A prediction from a theory allows the theory to be falsified if it doesn't occur, but it "verifies" the theory only to the extent that it is unlikely that the theory would predict it, and it would happen for some other reason just by coincidence.

In Newton's case, what he predicted from his theory of gravitation was that bodies like planets were actually falling toward each other (at the rate of acceleration in the formula). But if the planet had an additional speed at right angles to the fall, then that speed would make the two of them miss each other, and so they would be like two balls tied together with a thin elastic band; they would be continually "falling" around each other, but keep missing. And if one was much more massive than the other (like the earth and the moon), then the smaller body would orbit around the bigger one, traveling in an ellipse, with the "elastic band" of gravity alternately stretching and contracting. So the theory predicts not only why bodies fall down, but why sometimes they stay up. And the mathematics of the results fit the observations made of the motions of the planets.

So the theory was verified. It could be false; but it was extremely unlikely that Newton was wrong, and that bodies fell as he predicted and simultaneously bodies orbited each other as he predicted.

Now it turns out that in fact the theory is false; because at the turn of the twentieth century, very accurate observations were made of the planet Mercury, which showed that it was not in the position that Newton's theory of gravitation predicted that it would have to be (the actual data here are complicated, but that's the gist of it). The prediction was very, very close to the actual facts; but when the observations were checked and rechecked, there was this tiny discrepancy.

People didn't know what to do with this for a while until Albert Einstein, in his General Theory of Relativity, showed that his theory that bodies move with constant acceleration (and that the space between them gets warped as they go through time) predicted, not only falling bodies as we observe them, but that orbiting bodies would behave as we observe them (and not as Newton said they should). And he also predicted that objects without mass (technically, without "rest mass") like light, also follow this warping of space-time, and so light rays coming from stars behind the sun (which could be seen during an eclipse) would be bent, and the stars would have to appear out of the positions we know them to be in. And this prediction has been verified.

So, while even Einstein's theory could be false, again it is extremely unlikely that it would have predicted the bending of light in the presence of mass, and light would have been bent for some other reason, which just happened to fit Einstein's prediction. So up to this point, there is no reason to doubt Einstein's theory. Unless evidence like what overthrew Newton's comes up, it is unreasonable to doubt that it is what really explains the peculiar facts about falling and orbiting bodies.

Therefore, while a verified scientific theory can in principle be false, in practice it is to be accepted as true unless further incompatible facts falsify it. This is because one has no reason to think that it is false, and has evidence (reason) to think that it is true.

DEFINITION: Something is physically certain if there is (a) evidence to think that it is true, and (b) no evidence indicating that it is false. Such things can be false, but no reasonable person would think they are.

DEFINITION: Something is absolutely certain if it is self-evident. In this case, it is known that it is impossible for it to be false.

The point here is that it is possible to be certain that something is true without being absolutely certain. You are certain beyond any doubt, in the sense that you have no reason to believe that it is false.

This is the best that science can do, because there are an infinity of possible explanations for any problem, all of which fit all of the details of the problem, but only one of which is what actually happened. Still, it does not mean that science is useless because scientific theories are not absolutely certain. It just means that only irrational people would think that they are false.

Now let's connect this with proof.

DEFINITION: Something is proved when it is not self-evident or immediately evident, and there is external evidence for it, and no external evidence against it.

If it is self-evident, then strictly speaking it isn't proved, because it is its own evidence; its falseness is a contradiction in terms. Nor does what is self-evident need to be proved, because it is known with absolute certainty without needing any other fact to know it. Anything else has to have external evidence: that is, some fact other than itself which is a contradiction unless the thing in question is a fact.

As I said, the best external evidence is immediate evidence: the evidence of your senses. Note that the sensation itself is self-evident. That is, if there's a brown dog coming toward you, and it looks to you like a black cat, then the subjective impression you have of it as a black cat is self-evident, because the impression is the consciousness, and the consciousness is one and the same as your awareness of the consciousness. So the way things seem inside your consciousness is self-evident.

But of course, it is not self-evident that what you are looking at (what looks to you like a black cat) is in fact a black cat (and in this case it isn't; it's a brown dog). Generally speaking, our senses are reliable, and so what they report about what is "out there" making them respond in a given way can be counted on; but not always.

So, while this immediate evidence of the senses is the best external evidence, it's not infallible. We'll see later on why it sometimes fails, when we investigate in detail what truth is.

The point here is that with self-evidence and immediate evidence, no proof is possible or necessary. You can't find any external evidence to prove what is self-evident, and you can't find any better evidence to prove what is immediately evident. You might corroborate it by asking other people if they see what you see; but in the last analysis, you have to rely on the immediate evidence of what you hear them say in order to use their statements; and so this evidence is no better than the immediate evidence of your own experience.

But there are times when the immediate evidence (as in the case of the missing cookies) involves a contradiction. In that case, some other thing that is not immediately evident must be true. And since the immediate evidence is contradicted unless this other thing is a fact, the immediate evidence proves the other fact.

DEFINITION: Something is conclusively proved if the external evidence shows that it cannot be false.

DEFINITION: Something is scientifically proved if it is a verified scientific theory.

It is possible (but very difficult) to construct a theory that conclusively proves some fact. For instance, you can conclusively prove a theory false by showing that some prediction is not verified. In that case, it is impossible for the theory to be true. But you can also in some cases prove that all other explanations except yours fail to explain the problem in question; in which case, as Sherlock Holmes used to say, "When you have eliminated all other possibilities, my dear Watson, the one remaining, however unlikely, must be the truth." We will in fact come up later on with a conclusive proof for the existence of God.

But here, while Mommy may have proved scientifically that Johnny took the cookies, she didn't prove it conclusively. Scientific proof is always open to further evidence which falsifies the theory, because, though the verification process (making a prediction from the theory of what else must be true if the theory is true and finding that what is predicted actually is true) makes it more unlikely that the theory is false (because then the prediction "just comes true" by coincidence), it does not make it impossible that the theory is false.

2.6. Metaphysical method

Obviously, it would be a good idea to be able to formulate a conclusive proof rather than a merely scientific one. And it turns out that, if you want to sacrifice concrete information and remain on a very abstract level, there's a way to do it. As you will see shortly, this does not mean that we abandon the real world, but just that we don't pay attention to anything but a very abstract aspect of it. There's a reason for this, as we will also see.


From this point on, you are going to have to think on an extremely abstract level. Your temptation will be to say, "Well, yes, but what exactly is he referring to?" and what I will mean will be just exactly what the words say. I will be referring to very abstract aspects of concrete objects, aspects that can't be visualized or pointed to in any way. They are real, but there's no way to imagine them. You will see what I mean if you stick with me, but get ready to think in a new way.

Don't let that warning scare you too much. It happens on the scientific level too. For instance, when people asked Newton what this "force of gravity" he talked about actually was, he said, "I make no guesses." That is, he knew (a) that there had to be an invisible force of some sort pulling bodies together, (b) that its strength had to be what the mathematical formula described it to be, and (c) that it was undetectable in any way except for the otherwise-contradictory-condition of the motions of the bodies themselves. But what it "really was" in the sense of "show me some" he had no idea. He just knew these facts about it, whatever it was. He named it "gravity" not because he had any special insight into what it was in itself, but because it was easier to say "gravity" than "the invisible whatever that pulls bodies together."

In the ordinary case, suppose Mommy wasn't really interested in who took the cookies, but just in what was the minimum necessary for the problem to make sense, or in other words, for whatever properties any explanation would have to have in order for the problem not to be a real contradiction, then she could have reasoned this way:

"Well, the cookies couldn't move themselves and the jar couldn't unscrew itself; but in order to get the cookies out of the jar, whatever did it would have to be able to (1) unscrew the top, (2) move 12 cookies out, and (3) screw the top back on. Now in order to do this it would have to (a) have enough energy to do each action (b) be able to apply the energy in a screwing motion to the top, and (c) be able to attach itself to the cookies and move them from one place to the other."

So Mommy knows three facts about what removed the cookies, whatever it might be; because anything that doesn't have these three properties can't explain the effect. Daddy obviously has all three, and so has Johnny--and so has Mommy, for that matter, or a robot, or maybe some weird kind of tornado.

The point is that if Mommy is content with knowing only this much, and defines anything that has these three properties as "the taker," she now has conclusive proof that (a) there was a taker, and (b) that the taker has at least these properties, whatever others he or it might have. And the reason is that if there was no "taker" in this sense, the situation is a real contradiction (the cookies got taken but were not taken, because there was no taker); and if the taker lacks even one of these properties, the cookies couldn't get taken.


Even here, it is still possible to be mistaken if you have misread the original evidence, or if there is a flaw in the logic by which you have concluded that without such-and-such a property in whatever is the explanation, the problem still remains a contradiction.

So, for instance, as I said, Mommy might actually have only baked 12 cookies and thought that she baked 24; and so there is no "taker" at all. Or it might be that she didn't take into account that half of the cookies could have been made with "self-gassifying dough" so that the cookies spontaneously turned into carbon dioxide after an hour.

So the "conclusive" proof is conclusive only on these suppositions; and so the method we offer here is in fact subject to refutation by showing that the effect we thought we discovered isn't really an effect, or that we messed up the logic somehow.

Nevertheless, this kind of "minimalist" proof is better than a scientific proof, because scientific proofs also have these difficulties in addition to the fact that they can't rule out alternative explanations. This kind of proof does that, by the simple expedient of talking about only the characteristics that any explanation has to have in order to be an explanation at all.

And actually, this kind of thing does have a place in science: when the cause it is looking for is in principle unobservable, as sometimes happens. For instance, light itself (that is, a photon) cannot be directly observed (What could you use to observe it with but another photon? And anyway, it's far too small to see.) But things about photons can be known from the effects they are the explanations of. It turns out, for instance, that a photon has effects like those of a little ball moving through space, but also effects like a wave, which is a disturbance in a medium. In the macroscopic world (the objects we can see), a particle can't simultaneously be a wave; but no one is saying that a photon is a real "wavicle," because the photon doesn't have all the properties that a macroscopic particle does, or all the properties that a wave does; and the ones it does have aren't incompatible with each other (obviously, or photons couldn't exist).

No, the "wave-particle" theory of the photon is just one of these "minimalist" notions where the scientist is saying, "Whatever photons are, they have to have this and this and this properties. How these properties go together or what other properties there are, we just don't know." That's the best we can do if we can't get down there and actually look at them as they are. Like Newton's "gravity."

2.6.1. Effect and affected object

In order to be clearer in what we are doing, I now want to make some refinements on the notion of a problem and its explanation, and use the terms "effect" and "cause," giving them a very precise, technical sense.

DEFINITION: An effect is precisely a theoretical problem: as such it contains all and only the properties by which the situation is a contradiction.

DEFINITION: The affected object is the concrete object (or set of objects) which contains the effect as an abstract part of itself.

Thus, in the missing cookie problem, the affected object is the cookie jar with the 24 and then the 12 cookies. The fact that the jar is in the kitchen, that it is cylindrical, that it is a foot in diameter, that it is ceramic, with brown-colored glaze, and so on, are all irrelevant to the problem.

But as we saw, the fact that it has a top that can't unscrew itself is relevant.

So the effect contains the following facts: (1) the top of the jar can't unscrew itself; (2) it got unscrewed; (3) it got screwed back on; (4) the cookies can't move themselves; (5) the cookies moved out of the jar. Anything else is not part of the effect, but part of the affected object.

2.6.2. Cause and causer

Parallel to the distinction between the effect and the affected object, we will now make a distinction between the abstract and the concrete dealing with the cause.

DEFINITION: The cause is the fact or set of facts which contains all and only the properties necessary to explain the effect.

DEFINITION: The causer is the concrete object (or situation) that contains the cause as an abstract aspect of itself.

That is, the cause is an abstraction, since it is just a fact (or a set of facts). So, in the case of the missing cookies, the cause is the three facts listed on page 42 (the energy needed to unscrew the jar, to move cookies, and replace the lid).

The causer in this situation is Daddy (or actually, Daddy's coming in and unscrewing the top of the cookie jar, taking the cookies out, and rescrewing the jar top back on).

Notice that it is quite possible for part of the causer to be part of the affected object. For example, when you rub your hands together and make them hot, the effect in this case is the increase in temperature of your hands beyond their natural temperature; the affected object is your hands; the cause is the energy needed to raise the temperature (not even the friction your hands made as you rubbed them together, since there are other things that could raise your hands' temperature), and the causer is (like the affected object) your hands as rubbing together.

So the cause (like the effect) is a very abstract aspect of the real situation. It is real, but it is only a part of the concrete whole.

Notice further that, since we are dealing with abstractions from the concrete situation, the cause will be different depending on how you define the effect. For instance, in the case of rubbing your hands together, you might define the effect to be "My hands now are above their normal temperature, and the rest of my body is at its natural temperature."

So the cause now has to contain the properties necessary to explain why only the hands are at the unnatural temperature, and also why this is happening at the present moment. So in this case, the cause is going to be energy applied at this point only at this time, and the causer is going to be the friction together with your choice to rub your hands together. But the friction is still not actually part of the cause here, since holding your hands to a fire would also do the job, and the cause contains only what is necessary to account for the effect.

In order to get the actual friction into the cause, you would have to notice some other aspect of the affected object that doesn't make sense by itself, such that your hands are rubbing together and simultaneously resisting the motion against each other.


"Cause" in the ordinary sense is close to what this book means by "causer." Be sure to keep these two straight.

But why make this distinction, which is apt to be confusing? Because the "cause" in the ordinary sense (the sense in which Daddy is the "cause" of the missing cookies) is a loose way of speaking. In ordinary investigations, even many scientific ones, this might not get you into trouble. But when what solves the problem is unobservable, then you can only say about it what has to be said in order for the problem not to be a contradiction.

And what does this distinction say? That the ordinary notion of "the cause," as I stressed, is the thing that I have defined as the "causer." But what aspect of the causer is actually doing the job is not necessarily obvious from just looking at the situation--but again, in ordinary sorts of situations, this doesn't make much difference. The aspect of Johnny's hands by which he is able actually to grab the jar and twist off the top and then take hold of the cookies is something that even physiologists would have trouble specifying perfectly accurately; and all we care about in most cases is whether Johnny was the causer or whether someone else was.

But, as I say, if the causer is not something you can actually look at, then you don't have this luxury, and you're stuck with the abstraction that is the cause--or you're going to wind up saying things you have no justification for saying, as when believers, having proved that there is an infinite being, start attributing to it the characteristics of the God they believe in. This is all too common in metaphysical investigations, and in fact is what has given "metaphysics" a bad name. You can't conduct an honest investigation this way. For instance, if it is not necessary for the infinite being (supposing we proved that there is one) to be conscious or a person, then we must (in this investigation) call it It rather than "Him" or "Him/Her" or whatever.


The Principle of Contradiction states that what is is not what it is not, or that there are no real contradictions. If one finds facts that, taken by themselves, are a contradiction, this arouses the kind of scientific curiosity that leads to discovering new facts. The first step in scientific method is the observation of as much as possible about the apparently contradictory situation.

This is not really a contradiction (there's no such thing) but a problem. A theoretical problem is a conflict in known facts; a practical problem is evidence that says you can't do what you want to do. Theoretical problems always have a solution; practical problems aren't always solvable. Sometimes problems are "solved" because the original data were misread, leading you to think that there is a contradiction when there isn't one. This can happen, but beware of claiming that there's no problem because you haven't looked hard enough to find it. Problems are "why"-type questions, which always imply that two or more facts contradict each other. A fact by itself does not admit the question "why?"

Once the problem is observed, then the second step in scientific method is the formation of a hypothesis: a statement of an explanation, which is a possible fact that could make sense out of the problem. This attempt to dream up an explanation is called speculation. (The evidence for some fact is the problem it is the explanation of.)

The third step is to test this hypothesis against the facts by making an experiment to see if it leaves nothing still a contradiction. If it does, the hypothesis is discarded. If it passes the test, the fourth step renames the hypothesis as a theory.

Next, the scientist finds what else must be true if the theory is true, and thus makes a prediction from the theory, which, in the fifth step of scientific method, he tests against the facts as a verification of the theory. Actually, if the prediction does not come true, the theory is falsified; but if it does happen, then it is still possible for the theory to be false, but unlikely that it would be false and by coincidence its prediction would turn out true.

Something is proved when it is not self-evident or immediately evident, and there is external evidence for it, and no external evidence against it. It is conclusively proved if the evidence shows that it can't be false; it is scientifically proved if it is a verified scientific theory. Though scientific theories can be false, no reasonable person would think they are false, precisely because there is no evidence (no reason) for thinking them false, and there is evidence (reason) for thinking them true.

If one thinks abstractly, as we do in metaphysics, then it is possible to come up with conclusive proofs, simply by taking only the characteristics that any possible explanation must have, and ignoring all the rest. Obviously, since there are no contradictions, there is an explanation; and since any possible explanation must have at least the characteristics in question, then the solution offered is conclusively proved. It still can be false, if one has misread the evidence, or has committed a fault in logic; but, barring that, the solution in this abstract sense must be the true one.

To make this investigation easier, an effect is defined as all and only the facts that form the contradiction; the affected object is the concrete situation that contains the effect as part of itself. Parallel to this, the cause is the fact which contains all and only the properties necessary to explain the effect. The causer is the concrete situation that contains the cause as an abstract aspect of itself. Since effects and causes are abstractions from the concrete situation, a single concrete situation may contain many different effects (and these would have many different causes) depending on what facts you pick out as contradicting each other (because you've left something else--the cause--out). Note that "cause" in the ordinary sense of the term is what we mean by causer. This distinction turns out to be necessary when you can't observe what explains the effect; because then you only know what has to be true or the effect would be a contradiction.



1. That that is, is; that that is not, is not; that that is, is not that that is not; that that is not, is not that that is.