Here is a second suggestion about the ravens, which is consistent with Good's idea but goes further. Whether or not a black raven or a white shoe confirms "All ravens are black" might depend on the order in which you learn of the two properties of the object.
Suppose you hypothesize that all ravens are black, and someone comes up to you and says, "I have a raven behind my back; want to see what color it is?" You should say yes, because if the person pulls out a white raven, your theory is refuted. You need to find out what is behind his back. But suppose the person comes up and says, "I have a black object behind my back; want to see whether it's a raven?" Then it does not matter to you what is behind his back. You think that all ravens are black, but you don't have to think that all black things are ravens. In both cases, suppose the object behind his back is a black raven and he does show it to you. In the first situation, your observation of the raven seems relevant to your investigation of raven color, but in the other case it's irrelevant.
So perhaps the "All ravens are black" hypothesis is only confirmed by a black raven when this observation had the potential to refute the hypothesis, only when the observation was part of a genuine test.
Now we can see what to do with the white shoe. You believe that all ravens are black, and someone comes up and says, "I have a white object behind my back; want to see what it is?" You should say yes, because if he has a raven behind his back your hypothesis is refuted. He pulls out a shoe, however, so your hypothesis is OK. Then someone comes up and says, "I have a shoe behind my back; want to see what color it is?" In this case you need not care. It seems that in the first of these two cases, you have gained some support for the hypothesis that all ravens are black. In the second case you have not.
So perhaps some white-shoe observations do confirm "All ravens are black," and some black-raven observations don't. Perhaps there is only confirmation when the observations arise during a genuine test, a test that has the potential to disconfirm as well as confirm.
Hempel saw the possibility of a view like this. His responses to Good's argument and to the order-of-observation point were similar, in fact. He said he wanted to analyze a relation of confirmation that exists just between a hypothesis and an observation itself, regardless of extra information we might have, and regardless of the order in which observations were made. But perhaps Hempel was wrong here; there is no such relation. We cannot answer the question of whether an observation of a black raven confirms the generalization unless we know something about the way the observation was made and unless we make assumptions about other matters as well.
Hempel thought that some observations are just "automatically" relevant to hypotheses, regardless of what else is going on. That is true in the case of the deductive refutation of generalizations; no matter how we come to see a nonblack raven, that is bad news for the "All ravens are black" hypothesis. But what is true for deductive disconfirmation is not true for confirmation.
Clearly this discussion of order-of-observation does not entirely solve the ravens problem. Why does order matter, for example, and what if both properties are observed at once? I will return to this issue in chapter 14, using a more complex framework. Putting it briefly, we can only understand confirmation and evidence by taking into account the procedures involved in generating data. Or so I will argue.
I will make one more comment on the ravens problem. This one is a digression, but it does help illustrate what is going on. In psychology there is a famous experiment called the "selection task" (Wason and JohnsonLaird 197z). The experiment has been used to show that many people (including highly educated people) make bad logical errors in certain circumstances. The experimental subject is shown four cards with half of each card masked. The subject is asked to answer this question: "Which masks do you have to remove to know whether it is true that if there is a circle on the left of a card, there is a circle on the right as well?" See fig. 3.1 and try to answer the question yourself before reading the next paragraph.
Large majorities of people in many (though not all) versions of this experiment give the wrong answer. Many people tend to answer "only card A" or "card A and card C." The right answer is A and D. Compare this to the ravens problem; the problems have the same structure. I am sure Hempel would have given the right answer if he had been a subject in the four-card experiment, but the selection task might show something interesting about why confirmation has been hard to analyze. For some reason it is difficult for people to see the importance of "card D" tests in cases like this, and it is easy for people to wrongly think that "card C" tests are important. If you are investigating the hypothesis that all ravens are black, card D is analogous to the situation when someone says he has a white object behind his back. Card C is analogous to the situation where he says he has a black object behind his back. Card D is a real test of the hypothesis, but card C is not. Unmasking Card C is evidentially useless, even though it may fit with what the hypothesis says. Not all observations of cases that fit a hypothesis are useful as tests.
Fig. 3.1
The Wason selection task
3.4 Goodman's "New Riddle of Induction"
In this section I will describe an even more famous problem, revealed by Nelson Goodman (1955). This argument looks strange, and it is easy to misinterpret. But the issues it raises are very deep.
First we need to be clear about what Goodman was trying to do with his argument. His primary goal was to show that there cannot be a purely "formal" theory of confirmation. He does not think that confirmation is impossible, or that induction is a myth. He just thinks they work differently from the way many philosophers-especially logical empiricistshave thought.
What is a "formal" theory of confirmation? The easiest way to explain this is to look at deductive arguments. Recall the most famous deductively valid argument:
Argument i
The premises, if they are true, guarantee the truth of the conclusion. But the fact that the argument is a good one does not have anything in particular to do with Socrates or manhood. Any argument that has the same form is just as good. That form is as follows:
Any argument with this form is deductively valid, no matter what we substitute for "F," "G," and "a." As long as the terms we substitute pick out definite properties or classes of objects, and as long as the terms retain the same meaning all the way through the argument, the argument will be valid.
So the deductive validity of arguments depends only on the form or pattern of the argument, not the content. This is one of the features of deductive logic that the logical empiricists wanted to build into their theory of induction and confirmation. Goodman aimed to show that this is impossible; there can never be a formal theory of induction and confirmation.
How did Goodman do it? Consider argument z.
Argument 2
All the many emeralds observed, in diverse circumstances, prior to zoio A.D. have been green.
All emeralds are green.
This looks like a good inductive argument. (Like some of the logical empiricists, I use a double line between premises and conclusion to indicate that the argument is not supposed to be deductively valid.) The argument does not give us a guarantee; inductions never do. And if you would prefer to express the conclusion as "probably, all emeralds are green" that will not make any difference to the rest of the discussion.
(If you know something about minerals, you might object that emeralds are regarded as green by definition: emeralds are beryl crystals made green by trace amounts of chromium. Please just regard this as another unfortunate choice of example by the literature.)
Now consider argument 3:
Argument 3
All the many emeralds observed, in diverse circumstances, prior to zoio A.D. have been grue.
All emeralds are grue.
Argument 3 uses a new word, "grue." We define "grue" as follows:
GRUE: An object is grue if and only if it was first observed before zoro A.D. and is green, or if it was not first observed bef
ore 201 0 A.D. and is blue.
The world contains lots of grue things; there is nothing strange about grue objects, even though there is something strange about the word. The grass outside my door as I write this is grue. The sky outside on July r, zozo, will be grue, if it is a clear day. An individual object does not have to change color in order to be grue-this is a common misinterpretation. Anything green that has been observed before zoio passes the test for being grue. So, all the emeralds we have seen so far have been grue.
Argument 3 does not look like a good inductive argument. Argument 3 leads us to believe that emeralds observed in the future will be blue, on the basis of previously observed emeralds being green. The argument also conflicts with argument z, which looks like a good argument. But arguments z and 3 have exactly the same form. That form is as follows:
All the many E's observed, in diverse circumstances, prior to 2.0 10 A.D., have been G.
All E's are G.
We could represent the form even more schematically than this, but that does not matter to the point. Goodman's point is that two inductive arguments can have the exact same form, but one argument can be good while the other is bad. So what makes an inductive argument a good or bad one cannot be just its form. Consequently, there can be no purely formal theory of induction and confirmation. Note that the word "grue" works perfectly well in deductive arguments. You can use it in the form of argument i, and it will cause no problems. But induction is different.
Suppose Goodman is right, and we abandon the idea of a formal theory of induction. This does not end the issue. We still need to work out what exactly is wrong with argument 3. This is the new riddle of induction.
The obvious thing to say is that there is something wrong with the word "grue" that makes it inappropriate for use in inductions. So a good theory of induction should include a restriction on the terms that occur in inductive arguments. "Green" is OK and "grue" is not.
This has been the most common response to the problem. But as Goodman says, it is very hard to spell out the details of such a restriction. Suppose we say that the problem with "grue" is that its definition includes a reference to a specific time. Goodman's reply is that whether or not a term is defined in this way depends on which language we take as our starting point. To see this, let us define a new term, "bleen."
BLEEN: An object is bleen if and only if it was first observed before zolo A.D. and is blue, or if it was not first observed before zozo A.D. and is green.
We can use the English words "green" and "blue" to define "grue" and "bleen," and if we do so we must build a reference to time into the definitions. But suppose we spoke a language that was like English except that "grue" and "bleen" were basic, familiar terms and "green" and "blue" were not. Then if we wanted to define "green" and "blue," we would need a reference to time.
GREEN: An object is green if and only if it was first observed before zozo A.D. and is grue, or if it was not first observed before 201 0 A.D. and is bleen.
You can see how it will work for "blue.") So Goodman claimed that whether or not a term "contains a reference to time" or "is defined in terms of time" is a language-relative matter. Terms that look OK from the standpoint of one language will look odd from another. So if we want to rule out "grue" from inductions because of its reference to time, then whether an induction is good or bad will depend on what language we treat as our starting point. Goodman thought this conclusion was fine. A good induction, for Goodman, must use terms that have a history of normal use in our community. That was his own solution to his problem. Most other philosophers did not like this at all. It seemed to say that the value of inductive arguments depended on irrelevant facts about which language we happen to use.
Consequently, many philosophers have tried to focus not on the words "green" and "grue" but on the properties that these words pick out, or the classes or kinds of objects that are grouped by these words. We might argue that greenness is a natural and objective feature of the world, and grueness is not. Putting it another way, the green objects make up a "natural kind;' a kind unified by real similarity, while the grue objects are an artificial or arbitrary collection. Then we might say: a good induction has to use terms that we have reason to believe pick out natural kinds. Taking this approach plunges us into hard problems in other parts of philosophy. What is a property? What is a "natural kind"? These are problems that have been controversial since the time of Plato.
Although Goodman's problem is abstract, it has interesting links to real problems in science. In fact, Goodman's problem encapsulates within it several distinct hard methodological issues in science; that is partly why the problem is so interesting. First, there is a connection between Goodman's problem and the "curve-fitting problem" in data analysis. Suppose you have a set of data points in the form of x and y values, and you want to discern a general relationship expressed by the points by fitting a function to them. The points in figure 3.2 fall almost exactly on a straight line, and that seems to give us a natural prediction for the y value we expect for x = 4. However, there is an infinite number of different mathematical functions that fit our three data points (as well or better) but which make different predictions for the case of x = 4. How do we know which function to use? Fitting a strange function to the points seems to be like preferring a grue induction over a green induction when inferring from the emeralds we have seen.
Scientists dealing with a curve-fitting problem like this may have extra information telling them what sort of function is likely here, or they may prefer a straight line on the basis of simplicity. That suggests a way in which we might deal with Goodman's original problem. Perhaps the green induction is to be preferred on the basis of its simplicity?
That might work, but there are problems. First, is it really so clear that the green induction is simpler? Goodman will argue that the simplicity of an inductive argument depends on which language we assume as our starting point, for the kinds of reasons given earlier in this section. For Goodman, what counts as a simple pattern depends on which language you speak or which categorization you assume. Also, though a preference for simplicity is very common in science, such a preference is often hard to justify. Simpler theories are easier for us to work with, but that does not seem to give us reason to prefer them if we are seeking to learn what the world is really like. Why should the world be simple rather than complex?
Fig. 3.2
The curve-fitting problem
Earlier I mentioned attempts to solve Goodman's problem using the idea of a "natural kind," a collection unified by real similarity as opposed to stipulation or convention. Though this term is philosophical, a lot of argument within science is concerned just this sort of problem-with getting the right categories for prediction and extrapolation. The problem is especially acute in sciences like economics and psychology that deal with complex networks of similarities and differences across the cases they try to generalize about. Do all economies with very high inflation fall into a natural kind that can be used to make general predictions? Are the mental disorders categorized in psychiatric reference books like the DSM IV really natural kinds, or have we applied standard labels like "schizophrenia" to groups of cases that have no real underlying similarity? The periodic table of elements in chemistry seems to pick out a set of real natural kinds, but is this something we can hope for in all sciences? If so, what does that tell us about inductive arguments in different fields?
That concludes our initial foray into the problems of induction and confirmation. These problems are simple, but they are very resistant to solution. For a good part of the twentieth century, it seemed that even the most innocent-looking principles about induction and confirmation led straight into trouble.
Later (especially in chapter 14) I will return to these problems. But in the next chapter we will look at a philosophy that gets a good part of its motivation from the frustrations discussed in this chapter.
Further Reading
Once again, Hempel's Aspects
of Scientific Explanation (1965) is a key source, containing a long (and exhausting) chapter on confirmation. Skyrms, Choice and Chance (zooo), is a classic introductory book on these issues, and it introduces probability theory as well. Even though it argues for a view that will not be discussed until chapter 14, Howson and Urbach's Scientific Reasoning (1993) is a useful introduction to various approaches to confirmation. It has the most helpful short summary of Carnap's ideas that I have read. Carnap's magnum opus on these issues is his Logical Foundations of Probability (1950). For a discussion of explanatory inference, see Lipton, Inference to the Best Explanation (1991).
For the use of order-of-observation to address the ravens problem, see Horwich, Probability and Evidence (1982.), but you should probably read chapter 14 of this book first.
Goodman's most famous presentation of his "new riddle of induction" is in Fact, Fiction & Forecast (1955). The problem is in chapter 3 (along with other interesting ideas), and his solution is in chapter 4. His subsequent papers on the topic are collected in Problems and Projects (1972). Douglas Stalker has edited a collection on Goodman's riddle, called Grue! (1994). It includes a very detailed bibliography. The Quine and Jackson papers are particularly good.
For discussions of properties and kinds, and their relevance to induction, see Armstrong 1989, Lewis 1983, Dupre 1993, and Kornblith 1993. (These are fairly advanced discussions, except for Armstrong's, which is introductory.) There is a good discussion of simplicity in Sober 1988.
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