Observation and hypothesis
Science, of course, assumes (or should assume) that the epistemological problem I talked about in the first five sections of the first part has been solved somehow, and that we can know about the real world, and that our knowledge is objective, however dependent it might be on observations. So science starts from facts about the real world. There have been scientists who have subscribed to phenomenalism, because of difficulties they encountered in their investigations (particularly in quantum mechanics); but as I tried to show in the first part, the solution was to reexamine some of the assumptions about our naive notion of "position," for instance, not to accept it and declare that "nothing is real" or that what you are observing is the observing.
So I am going to take it that what scientists do starts from observing facts about the real world, no matter what scientists say they are doing based on some philosophy of science.
But not every observation, not even every careful observation, not even every careful observation involving meticulous measurement, is a scientific observation. It isn't scientific if it doesn't lead to a hypothesis, experiment, theory, and some kind of verification. So if I were to go into my back yard and meticulously weigh and measure each stone in it, and then carefully put it back where I found it and note its location to the tenth of a centimeter on a detailed map of the yard, and then give the pages and pages of data to a geologist, the best I could hope for is that he would look at me and say, "What did you go to all that trouble for?"
The reason for this, as I indicated in the Chapter 1 of Section 2 of the first part 1.2.1, is that what is prior to the first step in scientific method is curiosity, which means thinking that there is an effect (a case of facts contradicting each other) in the world "out there"; and the observation itself is an attempt by the scientist to assure himself that there really is a pair of facts that contradict each other, and that he hasn't been misreading the evidence, and to be precise on what it is.
So the careful observation which simply establishes the fact that there are a number of stones of different sizes and weights in different places in my back yard excites no curiosity in the scientist or anyone else, because that is what one expects to find there; there is no effect to find the cause of. You have nowhere to go once you have listed all these facts.
So immediately, all the palaver that has been around ever since Comte about philosophy's trying to get at (the impossible) "why" of things and science's simply getting at the "how" and giving laws and not "explanations," is just that: palaver--based, interestingly, on Comte's attempted explanation of why religion and philosophy were supposed to have failed as methods of thought, and why "positivism" necessarily would succeed. It's interesting how much influence those, like Comte and Hume, whose theories disprove themselves, have had in subsequent ages.
The point of starting with an effect is, of course, as I noted in Chapter 2 of Section 2 of the first part 1.2.2, that you know a priori that there can't really be a contradiction in the real world, and so the effect you have discovered means that you don't have all the facts. There will be another fact--the cause--which, when added to the effect you have discovered shows that the effect was not really a contradiction after all. We have seen enough examples of this in the course of this book for me not to have to give any here.
One of the reasons some people like Thomas Kuhn have noticed that new theories come about from prior "paradigms" is that an effect is generally something that happens contrary to expectations. This doesn't preclude that you might come across two facts that contradict each other without your expecting anything in particular; but it would obviously be much more common to find something happening contrary to what your previous experience and reason tells you would be happening in this situation. You then have to search for a new paradigm, as Kuhn says, to fit the past experience and this one together. In other words, you have to find a cause that will make the past and this new event make sense.
Notice that, when we are dealing with small discrepancies, we just simply it that the world is more messy than our neat little theories, and we look for a cause in something wrong with the object. If you see leaves turning yellow and dropping off the trees in July, you don't worry about your theory of the seasons and their effect on deciduous plants, you say that some insect or disease is attacking the trees. Things like this only become significant when you realize that the event, however insignificant in itself, makes the theory you have developed about it impossible. We saw the logic of this in the preceding section. The event is a false consequent of an implication, which refutes the antecedent (your expectations). Then you have to rethink the whole thing.
Now then, scientific observation has two functions, as I indicated in the Chapter 3 of Section 2 of the first part 1.2.3: (a) to gather all of the information you can on both sides of the contradiction, so that the effect whose cause you want to find is as complete as you can make it, and (b) to separate as far as you can the effect from what is affected, which has properties that have nothing to do with the effect. It is this second thing that mathematics does by default, as I mentioned, when it makes the mental constructs it calls "objects" and gives them only the properties it needs for the relationship it wants to examine. But in the real world, of course, that's not possible, so you might have to develop some complicated apparatus that can produce artificial environments for your objects to act in, so that they won't be affected in ways that aren't the ones you want to observe. For instance, if you want to test the speed of falling bodies, you put them in a bell jar and suck out all the air, so the speed won't be affected by air resistance.
Of course, if your effect might by any chance have to do with the amount of whatever property is involved, then you're going to have to measure your affected objects carefully, at the risk of losing something that could be crucial to the effect as such. For instance, if you didn't measure the rate of fall of falling bodies, you could come up with some theory like "bodies are attracted to each other," but not the kind of thing that Newton and Einstein developed based on Galileo's observations that bodies that fell seemed (a) all to fall with regularly increasing speed, and (b) the rate of acceleration was the same for all bodies, whatever their weight. This led to Newton's sophisticated Theory of Universal Gravitation.
Measurement is very often very useful in science, even necessary in some sciences like physics. But it should not become a fetish, with people thinking that something can't be scientific unless it involves measurement. These people tend to fall into the opposite fallacy also, that if something is measured carefully, it is scientific. A former dean of the college where I teach, who was a physicist, took the students' evaluations of the teachers (which were on a ten-point scale at the time), averaged up each student's answers to get a general number for that student, then averaged that for the whole class, and then compared that average with the "average average" of all the faculty. If you got a 7.5 (which meant that "average student" thought you in the top quarter of the faculty), but the "average" professor got a 7.8, then you were "below average," because the students in your class didn't think you were as far "above average" as the "average" professor was "above average." When I remonstrated with him that it didn't make sense to say that a person was below average because he was above average, he answered, "Well, that's what the numbers say." I never could convince him that the numbers as he was using them were completely meaningless.
And this points up another handy aspect of using mathematics in science, which is also a serious danger. Since mathematical operations have inverses, then if you are describing your data mathematically, you ought to be able to go either from effect to cause or cause to effect simply by choosing the right operation. For instance, if you start with a derivative, you can set it up as a differential equation and integrate it; and so you don't have to worry trying to figure out ingenious explanations for the effect, it would seem; the mathematics just does it for you.
And of course, since mathematics is a system with strict and defined rules, then when you are applying mathematics, you don't have to think at all; once you get the equation into the proper form, you simply do the operation and out comes the answer. Machines can do this sort of thing just as well as human minds, because it is just a question of mechanically applying the rules--which is why we can hit Mars and Jupiter with our space probes; because the computers with no trouble spit out equations that are fifty pages long, which it would take human beings millennia to do.
No wonder, then, that scientists like mathematics. But it isn't because it gives you that much more insight into the "true nature of things," as Galileo thought; it is just that it's easy to use (it is, really, once you get the hang of it), it looks exact (even when it isn't(1) ), you can perform complicated operations and get an answer even when you don't have the foggiest idea of what the argument you have constructed is, you can épater les bourgeois with all the letters, numbers, and symbols, and know that they couldn't follow you no matter how hard they tried, you can work the mathematics both ways, which looks as if you can even work backwards from the answer to the question, and so on.
It is a great help, no question about it, even though the remarks I made may be taken as disparaging. I am only disparaging those who, like ignorant religious people, mistake the ritual for the worship. We need every help we can get in investigating the extremely complex world of effects; and if mathematics can be applied, by all means apply it to the limit of what it can do. But don't depend on it as being what is "scientific" about science, or as a key to the truth. What is scientific about science is showing how the world is not really self-contradictory, by uncovering the facts that resolve its apparent contradictions.
And this has particular relevance when moving from the stage of observation to that of hypothesis. The hypothesis is, of course, a stab at the explanation of the effect; the picking out of a "p" to go into the implication "p implies q," where "q" is the effect you observed which can't be true unless "p" is true.
Unfortunately, there are an infinity of possibilities for "p," only one of which in fact makes sense out of the effect in question. And there is no mechanical way, and no mathematical way either, to make an exhaustive list of the possible explanations for any given effect, let alone to pick out which of them actually did the job in the case you are considering.
Here is where insight and genius come in. There are no rules here, because it is a question of seeing a relationship--and a relationship, moreover, with something created by using your imagination. At this stage, the crucial one, the logic of science is supremely illogical, though not unintellectual; it is very much like the "inspiration" of the artist, which we will treat in the next section.
The scientist, then, after becoming very clear about what is apparently contradictory about his problem, tries to imagine a situation such that (a) it makes sense in itself, and (b) it will make sense out of his effect.
It is actually quite important to stress this, obvious as it may seem. What science is all about is making sense out of what otherwise doesn't make sense. It is only secondarily trying to "find out the facts about our world." If it were trying to amass facts, then the kind of observation I mentioned about stones in my back yard would be of interest to scientists; but that's not it at all. Scientists are, if you will, anti-existentialists, who simply will not accept the world as absurd and say, "Well, that's the way things are," as Camus and Sartre would have it, for instance. They say, "Things may not be neat and rational, but they can't make nonsense. And they allege all of the progress that science has made as verification of the fact that their attitude is the correct one. (Of course, if you happen to think that things are absurd, then this argument, like all rational arguments, just washes right over you.) Still, I'm with them; I can't see any reason to hold that the world is unreasonable.
Some people call this finding of an explanation for an effect "induction," and so I suppose that this is the place to discuss the subject. I would rather restrict induction to deriving somehow statements about every instance of a given type of thing based on observation of only a few instances of that thing.
Let me make a bridge between this section on observation and hypothesis and the next on experiment and verification by treating the problem of induction as an example of a scientific effect, and giving some hypotheses that have been advanced to account for it; and then giving what I think is the cause of it--which, interestingly, is the facts about effects and causes.
The effect is this. We know that it's silly to question whether the next instance of hydrogen we find will combine with oxygen to form water, because we know that every instance of hydrogen will do this. But obviously, we haven't observed every instance of hydrogen; and so based on our observation, it would seem we have no grounds for saying this will happen every time. It looks like a case of reasoning from the indefinite to the definite, which is illogical. On the other hand, it obviously works, and in fact is underneath all logic (as Aristotle himself saw), because deductive logic starts from "universal" statements. There is some kind of reasoning going on here, because we are making statements about what we have not seen based on what we have seen; and the only way you can do that is to reason to them. But how can reason be illogical? How can you go beyond your evidence?
Deductively, you can go beyond your evidence, because the conclusion is implied in it. Then inductively the conclusion must be implied in the evidence also. But how can all instances be implied by just some?
That's the effect. Now one hypothesis is that of Hume, who simply says, "We can't actually get at what happens every time." If things have happened invariably in the past, we expect them to happen again, and the more often they have happened, the more we tend to think they always happen this way. And that's how we get our general statements, according to him. There's no logic behind it; any statement like, "Hydrogen combines with oxygen to form water" means nothing more than, "All the hydrogen I have seen so far has combined with oxygen to form water."
To test this, we want to know, remember, whether it makes sense in itself, and whether it makes sense out of what we have observed. First, does it make sense in itself? I don't see how it can. Presumably, Hume came to his generalization about inductions based on some observations. Hence, all his hypothesis amounts to, on his showing, is his saying, "All the inductions I have seen so far have been only summations of the past." Why he then expects others to listen to him when he is obviously predicting that this will be the case for others is beyond me.
Secondly, it does not allow us to distinguish between Arthur Pap's "lawlike generalizations" that I spoke of in Section 2 of this part and invariable occurrences where we find no grounds for predicting the future. It may be that a person has lived to be thirty years old and has not yet moved out of his parents home; and every day for the past fifteen years, he has come back at night to this house. Would he then say, "For my whole life long I will come back to this house at night," as if it were some universal law like hydrogen and oxygen? He may expect to go back there tonight; but this expectation is very different from the expectation that the next batch of hydrogen will combine with oxygen to form water. "We've always done it this way," is something those who have formed habits complain to the innovator--who then answers, "Is that any reason to keep doing it?" when he shows them a more efficient way. Yet we precisely think reason says that we can't live forever, because every human being dies.
Besides, if a person mixes a gas from a bottle labeled "hydrogen" with one labeled "oxygen" and passes a spark through the mixture and the result is a pink solid rather than water, he wouldn't say, "Well, now, not every instance of hydrogen combines with oxygen to form water." He would say, "Somebody mislabeled one of these bottles," and would test them, confident that that hypothesis would be the one to be verified--and, let's face it, it would be.
So this hypothesis is just plain silly. You can make a little more sense out of it (but not much) if you say that, on being confronted with an invariable occurrence, you then define the object that is behaving invariably as "That which performs this particular act in these circumstances." Obviously, then, every case of the object so defined will act in the way in question. So, for example, you observe a lot of instances of hydrogen combining with oxygen to form water. You then define "hydrogen" to be "whatever it is that combines with oxygen to form water" (in fact, the name is Greek for "water-former"); and clearly if something combines with oxygen to form water, it is hydrogen, and if it doesn't it isn't. Your "universal" is now established.
But that won't work either, because it will now be like a mathematical object and have one and only one property. That is, if the behavior of hydrogen with oxygen and its results were invariable solely because you chose to define the substance based on this behavior, then you would have no grounds for talking about any other invariant behavior of hydrogen--such as the lines of its spectrum when excited, what it does with sulfur to form that gas that smells like rotten eggs, how it gets involved in acids, etc., etc.
What I am saying is that if you know hydrogen always combines with oxygen to form water because you defined it to be "whatever does this," then how do you know that this same thing also combines with sulfur to form hydrogen sulfide? You can't simply define it to do so, because you don't know whether both definitions will go together all the time.
"Well, they do go together, so why not make the definition, 'whatever combines with oxygen to form water and combines with sulfur to form hydrogen sulfide'"? Because (a) you are leaving open the possibility that you might find something combining with oxygen to form water which was not hydrogen (because it formed a pink solid instead of that gas when it combined with sulfur)--and you know that that won't happen--and (b) think of all the properties of hydrogen that scientists have discovered. The more you get, the more behaviors you would have to add to your arbitrary definition, making it that much more unlikely (if that was the sole basis for the generalization) that you'd find many objects with all the behaviors together, just by coincidence. No, it's only by induction that we know that the same stuff that combines with oxygen to form water also combines in this particular way with sulfur and has this particular spectrum when not excited and this other one when excited, and so on. So that hypothesis does not pass the experiment.
Some philosophers, like Rudolf Carnap, have regarded induction as an application of probability. You observe a number of instances (a sample) and argue from there to the whole population, by the use of statistics.
Clearly, we do make use of statistics; that's what pollsters do when predicting elections, and what insurance people do in deciding how much to charge for insurance, and so on. But every statistician knows that your statistics depend on your having a representative sample of the whole population when you make your observations. If you want to predict an election, you make sure that you don't just see Republicans, or the people who work for the League of Women Voters; the sample has to reflect the whole and the conditions in which the whole is expected to act. To the extent that you aren't sure if your sample is representative, to that extent your statement about the whole population is shakier.
Now the problem with this is that the generalizations we are most certain of are the ones where we have the least representative samples. After all, the only hydrogen we have observed combining with oxygen to form water is hydrogen on the surface of the earth--and under the special conditions of the laboratory at that. But hydrogen is the most abundant element in the universe, and is found mainly in stars and interstellar clouds. So we have observed the behavior, on a conservative estimate, of a billion billionth of the whole population, and under conditions totally unlike for practical purposes a hundred per cent of it. To call our sample "representative" of all the hydrogen there is would be like asking two people in New England what their favorite food was and concluding that everyone in the world including the Chinese was inordinately fond of baked beans and codfish ("scrod," if you want to be really Bostonian).
Based on statistics and probability, then, it is unlikely to the highest degree that every instance of hydrogen would form water when combined with oxygen. Yet no one in his right mind would say that it is problematic that hydrogen does this.
And all the inductions we make are basically like this, except the ones that are specifically statistical, like generalizations about automobile accidents on holiday weekends. How, for instance, do you know you have a brain, and aren't, like the Scarecrow in Oz, bereft of one? The only people we've seen with brains inside their skulls have been people who have been very sick or injured, after all; and that has been a very small proportion of the population. Again, based on this, it is highly improbable that you have a brain.
Clearly, this theory is no better than the others. We will discuss statistics later, and show when it is applicable and why it is applicable; but the point here is that it is not the explanation of how we can make inductions.
Well then, how do we do it?
My theory is that we first observe enough instances of constant behavior that we become curious as to whether this is coincidence or something forcing the constancy. That is, the constancy is first seen as an effect.
We then hypothesize that the constancy of the behavior is caused by the structure of what is behaving (its "nature," if you will recall our definition of the term from Chapter 4 of Section 2 of the second part) 2.2.4.
We then examine the object in question to find out if there is something about it that would allow us to predict the behavior in question; and insofar as that aspect of the being's structure is part of its essence, then we say that the object, just because it is this kind of object, behaves in the way in question under the proper circumstances.
Thus, we find water when we combine hydrogen with oxygen. One or two instances are enough to show a scientist that this is unlikely to be coincidence.
He then hypothesizes that the behavior is due to the structure of hydrogen (and of oxygen, of course). Examining hydrogen(2)
we find that the atom has only one electron, in a "shell" that can hold two; while oxygen has two "holes" in its outer shell. Two atoms of hydrogen would fill up these holes; and the results of analyzing water into hydrogen and oxygen confirm that there are two hydrogen atoms in water and one oxygen atom.
Hence, it is because of the nature of hydrogen that water results from what it does with oxygen; and in that case, hydrogen, to the extent that it is hydrogen, will combine with oxygen to form water. Voilà.
Now of course, these "universal" generalizations are compatible with variations. For instance, heavy hydrogen (which has a neutron as well as a proton) will form heavy water, which, among other things, is radioactive, while ordinary water isn't. There is hydrogen peroxide, which has two atoms of oxygen bound to the hydrogen, and doesn't behave like ordinary water--and so on.
We recognize that inductions give us general truths, not necessarily "universal" ones in the sense that they take in absolutely every instance; but they are generalizations based on the nature of the thing in question, and are by no means arbitrary. This is why they support "counterfactual conditionals(3)" and don't lose their force.
So yes, we can say that every human being can see, even if we recognize that some human beings are blind. "Every human being can see" means, "Every human being is a seeing kind of thing," or why do we have eyes? But not every human being actually can see, because there are defective natures.
So it is effect and cause and actual investigation of the structures of things which allows us to make inductions, and it isn't either an illogical leap or something that belongs in logic, because logic is not directly founded on the nature of reality but on the nature (the structure) of the way we speak about reality.Next
1. For instance, those professors who give grades based on 100 points, and delude students into thinking that 83.2 means something. Or take IQ scores, where a 10-point difference is almost universally thought to have some significance.
2. The examination in this case would not be a strict observation, but is actually how hydrogen fits into the whole of the atomic theory of substances, which explains so much that it would be fantastic to think that it was radically wrong.
3. Just to refresh you, the form of this is, "If this case of hydrogen does not combine with oxygen to form water (the 'counterfactual conditional') it is still true nevertheless that hydrogen in general combines with oxygen to form water." A counter-instance of a summation that is not an induction destroys the generalization, which simply becomes "most of the time (so far, at least)."