Justifying theories I: The problem of induction
The problems I have been discussing about the structure of theories and the logic of explanation are central to the philosophy of science. But, as you will quickly see, they do not settle the issue of what makes a theory scientific.
They do not settle the demarcation problem. The reason is simple. That a theory satisfies all the conditions of the received view and is used to make explanations according to the DN model doesn't by itself make it scientific. Suppose Jim turned up with a theory of the gene exactly like Mendel's. If he had no evidence to support it and felt, in fact, that it didn't need experimental support, we would be impressed, no doubt. But we would hardly regard him as a scientist.What would have made this theory scientific would have been the way he set about justifying and developing the theory. Mendel's theory is not scientific just because it is true. After all, it isn’t true! Nor is it scientific just because it can be stated in terms of the received view (modified to take account of theory-ladenness) as we have just seen, someone could offer Mendel's theory in a way that wasn't scientific. It looks as though the answer to the demarcation problem is going to depend not on the structure of the theories but on the way we develop or support them. These are issues in the contexts of discovery and justification.
So how do we develop and justify our scientific theories? The obvious answer is that scientists support their theories by gathering evidence in exactly the sort of way Mendel did. We then use the theory to make predictions and then we see, through experiment and observation, whether those predictions come out right.
The process of gathering evidence and using it to justify general propositions is called “induction.” And in the early days of modern science, the eighteenth-century Scottish philosopher David Hume argued that there was a serious difficulty in justifying induction.
He posed what we now call the “problem of induction.”To see the force of the problem, it helps to begin with a simple picture of how you might go about supporting a scientific generalization. How, for example, would you go about supporting the generalization that purple genes dominate white ones in peas? The answer seems obvious. You would see whether purple genes dominated white ones in a whole series of crosses. The general idea, then, is that to find out if the generalization “All A's are B's” is true, you must look at a lot of A's and see if they are B's. If you find that they are, that supports the generalization. This process of arguing from many cases of A's that are B's to the conclusion that all A's are B's is called enumerative induction. It is the most basic kind of inductive argument. An A that is a B is an instance of the law “All A's are B's.” And if the existence of something gives us grounds for believing a sentence, we can say that it supports the sentence. So we can say that the view that we develop and justify laws by enu- merative induction is the view that laws are supported by their instances. The position that science does and should develop in this way is called inductivism. (Because Sir Francis Bacon, the English Renaissance courtier and philosopher, suggested in the early seventeenth century that science proceeded by generalizing from experience, the view that science proceeds in this way is sometimes called “Baconian.”)
Here is a passage from Hume's Enquiry Concerning Human Understanding where he argues that enumerative induction is unjustified. He considers the problem of how we should confirm the generalization that bread provides nourishment.
From a body of like color and consistence with bread, we expect like nourishment and support. But this surely is a step or progress of the mind, which wants to be explained.
When a man says, I have found, in all past instances, such sensible qualities conjoined with such secret powers: And when he says, similar sensible qualities will always be joined with similar secret powers; he is not guilty of a tautology, nor are these propositions in any respect the same. You say that the one proposition is an inference from the other. But you must confess that the inference is not intuitive; neither is it demonstrative: Of what nature is it then? To say it is experimental, is begging the question. For all inferences from experience suppose, as their foundation, that the future will resemble the past, and that similar 'powers will be conjoined with similar sensible qualities. If there be any suspicion, that the course of nature may change, and that the past may be no rule for the future, all experience becomes useless.Hume's question is what justifies the inference, the “step or progress of the mind”:
I have found, in all past instances, such sensible qualities conjoined with such secret powers.
So: Similar sensible qualities will always be joined with similar secret powers.
He says that it isn't a tautology—by which he means that it isn't an analytic truth—that these two sentences are equivalent, so that the inference is not logically valid or “demonstrative.” That is certainly true. For there are possible worlds where bread is nourishing until today and then not nourishing tomorrow, because, for example, all of us lose the enzymes for digesting the carbohydrates in bread after the Earth is irradiated by intense cosmic rays. And he says that it isn't intuitive: we don't know that it is true by intuition.
But, as he points out, it looks as though it would be a valid inference if we added a further premise:
UNIFORMITY: The future will resemble the past.
That is, it looks as though, if we add this principle of the uniformity of nature, we can reason like this:
INDUCTION: In the past bread was nourishing.
The future will resemble the past.
So: In the future bread will be nourishing.
Hume thought that the problem of induction was that the principle of the uniformity of nature was neither a logical truth nor intuitive and that there was therefore no obvious reason why we should believe it.
After all, it is itself a generalization. If the only way to justify a generalization were to use an argument of this form, we would have to argue for the principle of the uniformity of nature like this:In the past the future resembled the past.
The future will resemble the past.
So: The future will resemble the past.
But this is obviously a question-begging argument! It has its conclusion as one of its premises. Nobody who wasn't already convinced that nature was uniform could be persuaded by this argument.
The major problem with the sort of inference that is involved in INDUCTION is that, unlike deductive inferences, which are logically valid, the conclusion says more than the premises. We call such inferences “ampliative”; they amplify or go beyond the premises. One way of seeing that the inductive inference, is ampliative is to notice that the conclusion is not true in all of the possible worlds where the premises are. As we saw in the last chapter, in a logically valid inference the conclusion is true in every possible world where the premises are true. So in a deductive inference we can reliably draw the conclusion because it is true in all of the worlds where the premises are true. But in an inductive inference, we start with premises that show we are in a certain class of worlds and draw a conclusion that is true in only some of those worlds. Since the information in the conclusion is more than the information in the premises, we seem to have manufactured some information out of thin air!
In a sense, the problem of induction is the first problem in epistemology that was raised by the development of science. For making empirical generalizations—some of them, like Newton's theory of gravitation, generalizations about the whole universe—is absolutely central to the natural sciences.
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