[The material in this chapter is also covered in Modes of the Finite, Part 4, Section 4, Chapters 1 and 2 and Part 1, Section 2.]

1.1. Why not just ask a scientist?

It would seem to be a simple thing to find out what science is all about: ask a scientist. Scientists presumably know what they are doing; and they are probably willing to talk about it.

Unfortunately, though it's certainly true that scientists are generally willing to talk about what they are doing, and while it's also true that they know what they are doing in a sense, it isn't necessarily the case that they know what they are doing in the relevant sense. A physicist, for instance, is very adept at handling the equations in his science, and even developing mathematical ways of describing things he sees in the laboratory; but why it is that this particular procedure produces results, while others doesn't, is not part of his knowledge as a physicist. Physics itself does not register on an ammeter.

That is, to ask a physicist what the method of physics is and why use this method rather than some other is like asking a skilled driver how his car works, or a person who is very good at using WordStar how the program gets the words on the screen and formats paragraphs. Using a tool (and the method of science is a tool for the scientist) is one thing; knowing how it works is quite another.

Furthermore, different sciences use different variations on scientific method (though the traditional "five steps" of observation, hypothesis, experiment, theory, and verification, are pretty universal); but, of course, a physicist is an expert only at using the method of physics; and he is not skilled in biology or economics or psychology. Hence, his view of what science is "really doing" will be a view of what physics is doing, and may be quite different from what a psychologist would say science is "really about."

So the scientist is actually no better than anyone else in knowing how and why scientific method works, and what science is about--except for the fact that he works intimately with one particular science. But his special skills as a scientist do not adapt him to be able to investigate science itself scientifically.

And that is our purpose here.

The object of this part of the book is to make a scientific investigation of science itself.

1.1.1. A logical difficulty

It might seem that we have got ourselves into a logical bind here, however. We would have to know what science is in order to do a scientific investigation of science--whose purpose is to find out what science is. That is, it would seem that we have to finish our investigation before we can begin it.

But this is more of a logical difficulty than a real one. We know that science observes its material carefully, that it forms hypotheses about it, and that when it is done with its theory, the theory accounts for the observed facts, or somehow makes sense out of them. I doubt if many scientists would have a problem with this description of what scientists are doing; the difficulty comes with what is meant by the terms.

1.2. The basic hypothesis about science

I am now going to state my basic hypothesis about what scientists are doing. The rest of this part of the book will be twofold: (1) developing the implications of the basic idea, and (2) going through what scientists seem actually to be doing (following the "five steps" of their method), and trying to show how this basic idea makes sense out of everything they do.

HYPOTHESIS: Scientists are confronted with a set of facts that do not make sense (an effect); they are trying to find some fact that will make sense out of this effect (the cause).

That's it. Basically, it's that simple. Nor is there anything particularly new about it; the notion of "cause" as something that makes sense out of what doesn't otherwise make sense is as old as Aristotle, who defined "cause," as the answer to the question "why?"; and as the Greek etymology of the term: aitia means literally, "what is asked for" or demanded; the "reason" for something.

The concept of "cause" has undergone all sorts of changes in the course of history, and to trace its evolution to its present-day meaning of "the act that precedes an event" or "the act that makes something happen" is, from a certain point of view, fascinating. Unfortunately, it is that present-day notion which has all sorts of difficulties connected with it, and has been legitimately rejected by philosophers of science. So in a sense, what I am proposing here is that if you go back to the old Aristotelian notion of cause and effect, you will suddenly find that what modern scientists are doing--which seems on the face of it so mysterious--makes sense.

Why, for instance, do scientists make such detailed observations and measurements, and yet why is it a geologist wouldn't be interested if you gave him a list of every last stone in your back yard, with its location carefully marked, its weight carefully measured, its color and shape carefully noted?

Why do scientists contend that they deal with nothing but the observed facts, and then talk about electrons, genes, the unconscious mind, and so on, which cannot be observed?

Why is it that they accept some theories, like the theory that burning combines things with oxygen, and reject others that can't really be disproved, like the theory that burning gives off phlogiston, which has negative mass?

Why is it that they demand that theories predict things, and yet consider the "big bang" theory of the origin of the universe a good scientific theory, even if it can't predict anything (how could you "predict" how the universe got started)?

There are all kinds of problems connected with what scientists do, especially if you add what they are actually doing to what they say they are doing. And there are all kinds of theories which attempt to reconcile these apparently contradictory facts into a coherent view of what science is all about.

Taking the criteria scientists themselves use about theories, our theory will be a good one if it simply and logically accounts for all of the peculiar facts. That is, the simple assumption above (that scientists are trying to make sense out of what seems nonsense) should illuminate all these conundrums and show how they all make sense.

1.3. Scientific curiosity

As an illustration, before we get into a more detailed development of what we mean by "ef-fect" and "cause," let us look at what starts the scientist going.

Scientists contend that the first step in scientific method is careful observation. But I mentioned above that not every careful observation is a scientific observation, even if it uses measurement, and is very detailed and meticulous. The data to be observed have to have scientific interest before the scientist undertakes measuring them.

What initiates a scientific investigation is scientific curiosity.

DEFINITION: SCIENTIFIC CURIOSITY is puzzlement when confronted with a set of facts that seem to contradict each other.

This is "why-type" curiosity, as opposed to "what-type" curiosity, when you simply don't know something. Even the taxonomist, who seems merely to be looking at plants or animals and examining their various points of similarity, is really not doing this in order to find out what things look like; he is doing it because he has noted in things that are apparently very different striking similarities "below the surface," as it were. How come the bones of vertebrates are so similar, so that you can call wings or fins "arms" and "hands"? How come the panda has a thumb? How come we have an appendix?

The reason the geologist isn't interested in the list of stones in your back yard is that he expects the stones there to be random sizes and shapes--and a superficial glance at your list shows that he was not mistaken. There is nothing there that he would not expect to find; and so he isn't interested in the fact that there were 53,476 stones, and the average weight was 1834 grams. He didn't know that fact; and once you tell him about it, he is going to make no effort at all to remember it.

So what starts scientists off is not what they don't know; they are ignorant of all sorts of things, from poetry to politics, and content to remain ignorant; and they are even ignorant of vast amounts of information in their own fields, and content to remain ignorant even of these facts.

No, what interests scientists is not the fact that they don't know things, but something about what they do already know: and what it is about what they already know is that what they know doesn't make sense.

For instance, if you took your list to the geologist and said, "It's funny. I was counting the stones in my back yard, and I found that on the left side of a line running right up the middle, they were mostly smooth; and on the right, they were rough and just any old shape." He might now perk up and ask if you were near a river--and if you said that there wasn't a river for miles, he might tell you that he'd like to look into this.

Why? Because stones aren't naturally smooth; they are smooth because they have been smoothed--usually by water. It doesn't make sense to have smooth stones in a place where there hasn't been any water, unless they have been dumped there. So the scientist's curiosity has been aroused.

1.3.1. The scientific assumption

Why does this apparently contradictory set of facts make the scientist curious--so curious that to satisfy it, he would be willing to spend years and even decades in a laboratory?

The scientist goes on the assumption that there is no such thing as a real contradiction.

DEFINITION: A CONTRADICTION is something that is both true and false.

Put it another way: A contradiction is something that isn't what it is.

Well, of course it's nonsense to say that something isn't what it is; if it is what it is, then it isn't what it ain't.

Now it's possible for something to be one way at one time and another way at another time, or to be one way in one part of it and another way in another part--as, for instance, it was once true of you that you were a child, and now false that you are a child; or part of you is hard (your bones) and part of you is not hard (your skin). These are not contradictions.

It is only a contradiction when it is asserted that something is now the way it now isn't, when referring to the same aspect of the thing at the same time. Thus, it is a contradiction to say that there are words on this page and the page has no words on it.

This is not just a scientific assumption, of course.

No one can accept contradictions as really occurring.

Why this is so belongs in the branch of philosophy called "epistemology." Basically, it is because if you say something isn't what it is, then you have no way of saying what it is in the first place--you have destroyed the possibility of knowing anything at all.

NOTE that the scientist does not necessarily think that things have to be "neat" or "orderly"; only that they can NOT be positively CONTRADICTORY.

There is an important distinction here. Scientists would like the world to be "reasonable" in the sense of "the way reason would expect to see it"; but this is not a demand of reason, the way non-contradictoriness is.

For instance, the Periodic Table of the chemical elements lists elements by their basic chemical properties; and you find them falling into rows and columns, with chemicals of similar properties underneath each other, as with fluorine, chlorine, bromine, and iodine, for instance, all of which have a chemical valence of -1. But as you classify the elements, you then find that there are certain "boxes," which you would expect to contain just one element, that contain many different elements.

Of course, this peculiarity is something that makes the scientist curious; but it is not necessarily something that he says can't happen. The point here, however, is that the scientist can be content with a reality that doesn't fit a neatly preconceived pattern; but he absolutely cannot accept a universe in which there are contradictions, and what is is not what it is while it is what it is.

1.4. Effects and affected objects

Simply assuming that contradictions don't happen doesn't get you anywhere, of course, unless it seems to you that a contradiction did happen. Then there's something to be curious about.

DEFINITION: An EFFECT is a set of facts which, taken by themselves, contradict each other.

That is, our definition of an "effect" describes the situation which makes the scientist curious. He seems to have evidence that a contradiction has really taken place; he knows some fact that indicates that X is so, and some other fact that indicates that X is not so.

Thus, our geologist friend knows that rocks are smoothed by water, thus indicating that the rocks in your back yard were either in a river or on an ocean beach. But he also knows that there is no river within miles and no ocean within thousands of miles.

Obviously, there are several possible explanations which make this set of facts not a real contradiction. They might have been hauled in from a beach; there might have once been a river bed where your back yard is; there might once have been an ocean shore where your yard now is. If any one of these is a fact, then there is no contradiction in the rocks in your yard being smooth.

Now the reason an effect is a set of facts which,taken by themselves, contradict each other is that the scientist knows by his assumption that he hasn't got the whole story. That is, if the rocks above were never near moving water--and if moving water is the only way they could turn out to be smooth--then they would not be smooth, when in fact they are. That would be a contradiction. But the geologist has no direct evidence that they ever were near moving water; hence, as far as the information he now has is concerned, he has a contradiction.

But the point is that he knows that the information he now has is not all the information there is, and that is why this situation is an effect and not simply a contradiction.

Now before we go any farther on this, let us make a distinction which will turn out to be important:

DEFINITION: The EFFECT is JUST THE FACTS that make up the contradiction (it contains nothing that is not part of the puzzle itself).

DEFINITION: The AFFECTED OBJECT is THE CONCRETE THING that contains the effect as PART of itself. It may, in fact, be more than one thing; but the point is that it has characteristics that don't belong to the effect as such.

Let me illustrate. Let us say that you are Neil Armstrong on the moon, and you drop a feather and a hammer. They hit the moon at the same time. The effect, of course, here is that heavy things fall no faster than light things--though things fall because they have weight. So the hammer-as-heavy-and-as-falling-at-a-certain-speed and the feather-as-lighter-but-as-falling-at-the-same-speed are the characteristics of the feather and the hammer that belong to the effect.

The fact that one is a hammer and the other is a feather are part of the affected object, but not the effect, because they could be any two objects you want to name, as long as they are of different weights, and the effect itself would occur. The fact that the hammer is steel and the feather is organic, the fact that the hammer is silver and the feather while, etc., etc., are all irrelevant to the effect, and so are of no scientific interest.

In fact, these irrelevant aspects of the affected object tend to get in the scientist's way; because he sometimes (mistakenly) takes them as part of the effect. We will see this later.

So the effect is just those aspects of the affected object which do not make sense by themselves.

NOTE that very often one side of the contradiction that makes up the effect is some well-established SCIENTIFIC THEORY that the scientist takes as a fact.

This is why some philosophers of science have noted that scientific observation is often "theory laden." For instance, the apparent contradiction in having heavy and light things fall (in airless places) is partly due to the fact that we see them fall, generally, when air resistance makes the light one fall slower; but it was also due to Aristotle's (apparently well-established) theory that falling bodies "seek" their "natural place" more or less forcefully depending on the "mixture of their elements of earth, air, fire, and water."

The point here is not that theories determine what observations the scientist is making, but that well-established theories lead you to expect certain things as facts; and when you observe something that contradicts these expectations, you have an effect.

Already, then, our hypothesis explains something philosophers of science have found puzzling: why scientists don't just begin observing; and why, though they seem to be studying facts, their observations usually begin from a background of some previous theory.

1.4.1. Other attitudes toward effects

Seeing an apparently contradictory situation makes the scientist curious. It obviously doesn't have that effect on everyone. It might be useful to distinguish the various ways we react on being confronted with something that seems to be a contradiction.

DEFINITION: A situation is called FUNNY when the facts contradict the way we expect them to be, and we SIMPLY RECOGNIZE THE SITUATION.

Here is the difference between "funny-ha-ha" and "funny-peculiar." They are both the same thing; the actual facts aren't what we expect them to be. If we simply accept this, then we laugh; if we say, "Now wait a minute, how can that happen?" we have noticed an effect (and we are about to start looking for a cause).

Noticing an effect involves a dissatisfaction, then, with what is observed; laughing at it does not; it simply accepts it.

DEFINITION A situation is called BAD when the facts contradict the way we expect them to be, and WE REFUSE TO ACCEPT THEM. The psychological experience here is neither curiosity nor humor, but SUFFERING.

That is, the scientist is curious when he confronts something that his reason tells him "ought not to be happening." And he then looks for a cause which will explain how the situation really isn't a contradiction. So, for instance, a scientist investigating a person who has suddenly gone blind will wonder how it is that he could see yesterday, and now all of a sudden he can't. And as a scientist, he will look to find out what explains the sudden lack of sight.

The blind person himself, however, is not really interested in the cause of his blindness--except insofar as knowing it might lead to a cure. If he can be cured without ever finding the cause, he doesn't care why he got blind. He regards being blind as bad; and what he wants is to change the facts until they agree with his idea of the way the facts "ought" to be.

The point of all of this, of course, is that not everyone confronted with an effect is motivated to start a scientific investigation; he might suffer it, or laugh it off. It is only the scientist who can't rest until he finds what fact makes sense out of the effect.

1.5. First step: observation

Now then, what does the scientist do when he notices an effect? He doesn't immediately leap to a conclusion. That's what most of us do, and we come out with some pretty strange theories, which, if we had been more careful, we would have seen couldn't be the real explanation for our effect.

And the very first thing we should have done that the scientist is careful to do is make a careful observation of all the aspects of the effect as such.

The first step in scientific method is OBSERVE CAREFULLY THE EFFECT.

One of the most difficult parts of scientific observation is separating out the effect from the affected object.

Of course, what you observe is a concrete situation (an affected object) with all sorts of details, any one of which may be part of the effect, and then again may not.

For instance, to take falling bodies as the effect, we usually see them fall in air. It seems clear that things fall because they are heavy; and this might lead us to ignore the air resistance as irrelevant and part of the affected object. It turns out, however, that air resistance messes up how fast a body will fall; and unless you check to see whether it's relevant or not to the speed of fall, then you'll miss the most peculiar part of the effect.

Or again, people laughed at Gregor Mendel when he was observing how pea plants had characteristics that were transmitted from parent to offspring in definite ratios. The plants were either tall or short (to take just one characteristic), and depending on the parentage, you could predict either tall or short plants (and in a definite ratio), but none in between. This, of course, flies in the face of the fact that a black person marrying a white one will not have a certain number of children black and another number white; there are all the intermediate colors.

We know now that this is because there are many genes determining things like skin color; but Mendel's observations got at the effect itself, and observations of things like skin color involve part of the affected object.

But how do you separate out the effect from the irrelevant aspects of the affected object?

...Ah, that is the difficulty. There are no real rules for this; it is the genius that sees things in a certain peculiar light who seems to be able to do it. But even he only knows he has done it when he gets through the whole process and finds that his insight into just what the "problem" to be solved (the effect) is was correct.

So for those of you who want science to be a mechanical process where you can make great discoveries by just following rules, I am sorry to disappoint you. Right here at the beginning, seeing what the effect is, is what separates the great scientific geniuses from the rule-followers; and, as history has so abundantly verified, there are no rules for seeing what the problem is.

But by the same token, this is what makes science exciting; it isn't by plodding along in a mechanical way, following rules, that great breakthroughs occur; it's by seeing things in a new light--and this can happen even with novices in science. In fact, it's the young people who tend to make the great breakthroughs, because they haven't got the traditional thought-patterns established yet. They look at things in a way that the traditional scientist thinks of as stupid, naive, or wierd; and he says, "Why do it that way?" and they answer, "Well, why not?" And sometimes--unfortunately, only sometimes--this wierd point of view is the lens that focuses on the real problem and not side issues.

The point to note here, however, is that what the scientist is observing is not just a fact or set of facts, but an EFFECT. He wants first of all to discover in just what way things don't make sense--before he attempts to find out what makes sense out of them.

1.6. Explanations

If there aren't any real contradictions and things don't make sense by themselves, then obviously they aren't really "by themselves." There has to be some fact that the scientist hasn't yet observed which will make sense out of the effect.

First note that the fact that makes sense out of the effect has to be missing from the observation, or no effect would have been observed. For instance, you wouldn't have been curious about the smooth stones in your back yard if you had seen a truck drive up and dump them. (You might, of course, be curious as to why the trucker did this, if, say, you hadn't ordered them dumped; but you wouldn't be curious about how smooth stones got there).

Secondly, note that this missing information that creates an effect has to be a fact and isn't something just "made up" by the scientist to satisfy his mind; because if the whatever-it-is that "makes sense out of" the effect is just in the scientist's mind, then there really is a contradiction--which means that there really is something that really isn't what it really is.

So this is no game the scientist is playing. He knows that there's a fact missing from what he has observed; and since that fact really exists, then it's at least in principle possible to find it.

And this is what drives scientists onward: the knowledge that the goal (the explanation) is not just a dream, or something like the Holy Grail, where the "quest for the ideal" is supposed to be what's important, even if the goal doesn't exist; this goal is really there. All that's needed is the ingenuity to find it.


DEFINITION: A PRACTICAL PROBLEM can be stated as the following type of contradiction: "I intend to do X; the facts I know indicate that it is not possible for me to do X."

The difference between theoretical and practical problems is that theoretical problems ALWAYS have solutions, but practical problems do not always have them.

That is, it might really not be possible for you to do X, however much you might want to do it, because things are really limited, and you might be going beyond the limits of what you're dealing with. Of course, you might simply think you know what the limits are, and your practical problem might actually be solvable. It's a problem because it seems you can't do what you want to do; but the seeming may or may not be accurate.

On the other hand, as I said above, theoretical problems are guaranteed to have solutions; and if you don't find one, it isn't because there isn't one. There are no real contradictions.

DEFINITION: An EXPLANATION is a POSSIBLE SITUATION which, if it were a fact, would make the effect make sense.

That is, an explanation may or may not be a fact, but if it is a fact, then this fact would make sense out of the effect in question.

For instance, one explanation of the smooth stones in your back yard is that they were dumped there by someone. Now you don't know, just from your observation (supposing that you didn't see it happen) that they were dumped there; but if they were, then it makes sense for them to be there.

Another explanation is that this land was once a riverbed. Again, you don't know from observation that it was; but if it was, then your problem is solved.

NOTE that there are AN INFINITY OF EXPLANATIONS for any given effect.

Some of these explanations might be more far-fetched than others. For instance, that there were little gnomes who lived beneath the ground in your yard and came out at night and filed the stones smooth. That's an explanation; if there were such things and they did this, then the stones would be smooth.

So all an explanation has to be is not itself contradictory; it doesn't have to be a fact to be an explanation. Obviously, if it contradicts itself, then it doesn't make sense itself--and so it can't make sense out of anything else. The gnomes above don't involve a contradiction; there just aren't (so far as we know) such things; but they could exist, in the sense that there's nothing about them that contradicts anything else about them. Explanations have to be possible (not self-contradictory) to be explanations; but they don't have to be factual.

Obviously, scientists aren't really interested in the explanations that aren't facts; they want to know what really does make the effect not really a contradiction.

That is, once the scientist finds out that someone dumped the stones in your yard, he's satisfied; and if you pester him with, "Well, but they could have been on a riverbed there anyway," he won't listen to you--unless you can show him that not all the stones can be explained by the dump truck.

1.6.1. The logic of explanation

Modern philosophers of science have noticed that scientific theories are of the form "if (theory), then (data)." Our theory of science interprets this as "if (explanation), then (effect)." That is, the effect forms the "then" clause of an "if-then" type of sentence.

Now the logic of "if-then" is such that, supposing the connection between the if-part and the then-part to be true (i.e., supposing that the whole statement describes a state of affairs such that the "then"-part is connected somehow with the "if"-part, so that whenever the "if" occurs, the "then" also will happen), then (a) knowing (by observation) that the "if" has happened, it must be the case that the "then" also occurs.; or (b) knowing that the "THEN" has NOT occurred it must be the case that the "if" has not occurred either.

This sounds confusing, so let me give an example.

The statement, "If it is raining out, then the cat is inside" asserts a connection between the weather and the cat (i.e. that the cat hates the rain enough so that whenever it's raining, the cat will go in). For purposes of this example, we have to take the statement as universally true, so that there never are instances when the cat is caught outside in the rain.

Now then, if you see that it's raining out, you don't have to waste your time looking outside for the cat; because if it's raining out, the cat is inside. On the other hand, if you look out your window on a cloudy day and see the cat outside, then you know it hasn't started to rain yet; because if it's raining, then the cat is inside.

However, the if-then statement is not an if-and-only-if-then statement. It only asserts that whenever the "if" is true, the "then" is also true, but not that when the "if" is false, the then is also false.

That is, you know that if it's raining out, the cat is inside; but the cat is sometimes inside also when it's sunny. The cat is always inside when it rains; but sometimes inside when it isn't raining (e.g. it may also be the case that the cat is inside when there's a dog in the neighborhood--whether it's raining out or not).

Hence, from the if-then statement you can conclude nothing from either (a) the falseness of the "if" or (b) the truth of the "then."

That is, if you see that the sun is shining, you can't tell from that whether the cat is inside or not; or if you see the cat inside, you can't tell that it's raining out.

Now why is this important for scientific investigations?

Because, as I said, the logic of the scientific explanation is "if (explanation), then (observed effect)." And that means that if you happen to know that the explanation is a fact, it follows that the effect will occur; or if you happen to know that the effect doesn't happen, then you know that the explanation can't be a fact.

But the difficulty is that what you know from direct observation is the truth (the factuality) of the effect, which is the then-part of the statement. But from the truth of the "then," you can reach no conclusion as to the truth or falseness of the "if" (the explanation). That is, you have looked and seen the cat inside, so to speak; but you can't conclude that it's actually raining out.

It is NOT possible to PROVE LOGICALLY that a particular scientific explanation is THE TRUE ONE.

There are, as I said, an infinity of explanations for any given effect; and any one of them fits the "if-then" logic; so that, if it is a fact, then the effect makes sense. Hence, the actual observed occurrence of the effect does not pick out any one of the explanations as the true one. The fact that the cat is inside doesn't mean you can say that it's raining out; because it might be sunny and there's dog in the neighborhood.

That's maddening, isn't it? However, there is one thing you can do, logically. If the then-part is false, then either the if-part is false or (and this is the possibility we ignored earlier), the connection itself is false.

Thus, if you see the cat outside, then it must either be that it's not raining or that you misunderstood the connection between the cat and the rain (i.e. it's not true that whenever it's raining, then the cat is inside).

How does this apply to science?

If you find out some aspect of the effect that the explanation says has to occur, and you observe that it doesn't occur, then you know that this is NOT the true explanation of the effect.

Scientific explanations can be FALSIFIED by showing that they "explain" something that does not actually happen.

We will see how this works later; but for now, just let this example suffice: You explain the line of smooth stones in your back yard by supposing that they were in a riverbed. You then look at the yards adjoining yours on both sides, and you find no smooth stones that would continue the line.

But if there was a river, then it would have had to have risen in a spring from your property line, and sunk into the earth at your other property line. Absurd. That is, the explanation that the stones were there because of a river that ran through your property would also demand that it be a fact that (because the river would not just be on your property) there be stones along the line on the other properties. But there aren't. Hence, this explanation of the stones is false.

1.6.2. A modern complication

The philosophy of science of a few years ago has added a complication to this treatment of the logic of scientific explanation, and a word about it is due here. Scientists like to do mathematics (for reasons we'll discuss later); and philosophers of science are either scientists or are interested in science; and so they like mathematics also.

There was, then, an attempt to "mathematize" logic, which is still regarded as valid. But a difficulty comes in precisely this "if-then" statement, because traditionally--as I mentioned above--no conclusion can be drawn from the falseness of the "if" or the truth of the "then."

But this messes up the mathematical "truth-tables," because you have to put question marks in some of the boxes, instead of being able to fill all possibilities with T's or F's. [If this doesn't make a great deal of sense to you, don't worry about it.] Mathematics likes closed systems, where everything is defined, and there aren't any "maybe's"; and so the inventors of symbolic (mathematical) logic decided to create a convention.

Based on statements like, "If you win this race, I'll eat my hat," where what the person means is "No way I'll eat my hat; you're not going to win this race."--or the person is asserting the falseness of the "if" by connecting it with something impossible--based, as I say, on such statements, the mathematical logicians said, "Let's say that anything follows from a false statement." Hence, the "new-logic" of what they call "material implication" is that if you know that the "if" is false, you can conclude that the then is true. Instead of not concluding anything. [Of course, you can also conclude to a false statement. That is, the connection is valid when the "if" is false, whether the "then" is true or false; so a conclusion can be drawn; but any conclusion can be drawn. If this sounds silly to you, you're not a mathematician.]

But when you apply this to science, then this means that when the explanation is false, the scientific theory (the connection) is a good theory!

That is, by "material implication" and symbolic logic, the statement, "If phlogiston is given off in burning, then the products of combustion weigh more afterwards than they did before" is a true statement because phlogiston is not given off in burning.

You might say, "Well yes, but if it were, then this would explain why the products weigh more." True; but the following statement would also make a good theory: "If Los Angeles is a suburb of Tokyo, then the products of combustion weigh more afterwards than before burning." Because it's false that Los Angeles is a suburb of Tokyo, then it follows logically that the products of combustion weigh more--because "anything follows from a false statement."

This is logic?

Philosophers of science have tied themselves into knots trying to make this sort of thing not totally ridiculous; but they haven't really succeeded. And it isn't surprising, because this convention to make logic fit into a mathematical scheme contradicts the way we use words.

1.7. Evidence

So let us leave contemporary logicians to polish the ivory in their towers and get back to one more thing before we try to follow the scientist in his search for the true explanation of the effect he has observed.

Scientists are very fond of saying that they are looking for evidence; and when you make a statement of any sort, they want you to give the evidence for it. What are they talking about?

DEFINITION: The EVIDENCE for the truth of a statement is some admitted fact which COULD NOT BE A FACT if the statement in question were FALSE.

That is, a statement is evidence for another if it fits into the following scheme "If (evidence), then (fact in question); and (evidence is true)." We saw by the logic of "if-then" that if the connection is true and the "if" is true, the "then" must be true. Hence, the truth of the "if" proves the truth of the "then"--and that is what we mean by "is evidence for."

So two things are needed for evidence: (a) to show that the statement in question logically follows from the alleged evidence (i.e. that the connection is valid); and (b) that the alleged evidence is a fact.

What this all amounts to is that the fact in question is an EFFECT of the evidence which is its TRUE EXPLANATION.

You have to be able to show, however, that the evidence is not just an explanation of the fact in question, but the true one.

Let me give an example. In a law case, the witness testifies that he saw the defendant shoot the victim. He is then cross-examined by the defense attorney, and in the course of the examination, it becomes clear that (a) the witness is not lying, because he is suffering because of his testimony, and people don't lie when it's to their disadvantage to do so; and (b) he couldn't have been mistaken about what he saw, because he was too close to the scene to have been fooled. So he must have seen the shooting.

But it is impossible for him to have seen the shooting and the shooting not to have occurred. Hence, his testimony, having been established as a fact, is evidence for the prosecution.

To take another example, evidence that the stones in your back yard were not due to a river is the observed fact that there aren't smooth stones where the river would have to have been. This lack of smooth stones would make it impossible for the river to have been there.

Some things are SELF-EVIDENT.

Generally speaking, directly observed facts are self-evident. If you "see it with your own eyes," you need no evidence except the observation itself to prove what it was you saw.

There is, of course, the possibility that you could have been mistaken, especially under extreme conditions. For instance, if you see something in dim light, then you might have reason for not trusting your eyes, and you might need evidence that what you thought you saw was what you actually saw--evidence you might get by asking someone else, for instance.

Your own experience that you are having a certain experience is IMMEDIATELY EVIDENT.

"Immediately" here means "without any medium or anything 'between.'" That is, if you think you see a red apple in front of you, you might conceivably be mistaken and there isn't actually an apple there; but you can't be mistaken that you're having the experience of seeing-an-apple-in-front-of-you; the experience is always also the experience-of-the-experience; they are one and the same thing; and so, this kind of thing is not only self-evident, it's immediately evident. There is no possibility that you could be mistaken here.

Generally speaking, however, if we are careful (and scientists are), we don't have to go all the way back to what is immediately evident; we can take the direct evidence of observation as self-evident (and not needing proof), and use this as our evidence for things that we can't directly observe.

And this is why science relies on direct observation. Science is looking for explanations; but the explanations are not themselves observed (and, as we will see, sometimes can't be); and so must somehow be proved to be the true ones. But the evidence for them must then be something that is directly observed.

So our theory of science explains why scientists rely so heavily on direct observation. But let us now see how scientists take explanations and try to weed out the true one from all the ones that could be true but aren't.