The argument essentially exploits the differences between induction and deduction. A contradiction is involved for the building of a good deductive argument to be true, but its conclusion to be false. A good deductive argument is necessarily truth preserving. As per Hume's argument, an inductive argument cannot be used to justify inferring an inductive argument's conclusion from its premises on pain of circularity. Also, a deductive argument cannot be used to justify this as there is no deductive argument from the premises of an inductive argument to its conclusion.
The Problem of Induction (1953, 1974)
And then there is the normative problem: Are beliefs formed in this way justified? Does someone who "reasons" as we normally do really have reason to believe his conclusions about the parts of nature he has not observed? Let's suppose, for now, that perception and memory are clearly sources of knowledge. If you see an apple on the table, you know that there is an apple on the table; If you saw an apple on the table yesterday and you now remember that you saw it, then you know now that yesterday there was an apple on the table.
We will raise questions about these matters later on. But let us set them aside for now in order to focus instead on our knowledge of things we have not observed. Some of this knowledge is trivial. I have not examined every triangle in the universe.
Hume and the classical problem of induction
But I know in advance that each of them has three sides. I have not examined every bachelor in the universe. But I know in advance that none of them is married. These propositions concern what Hume calls relations of ideas. A proposition expresses of relation of ideas if and only if its denial is strictly impossible, inconceivable, or self-contradictory. Hume seems to regard these notions as equivalent. For Hume there is no mystery as to how I can know such propositions a priori. I simply consider the proposition, attempt to imagine its falsity, and notice that I am immediately involved in a contradiction or some similar incoherence.
This provides one straightforward route to knowledge about things we have not observed. But this is not the knowledge that interests us here. We are rather concerned with knowledge of unobserved matters of fact. A matter of fact proposition has the following feature: both it and its denial are fully conceivable, possible, and non-self-contradictory.
Consider the proposition that my house is blue.
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You can easily conceive of this proposition's being true; but you can just as easily conceive of its falsity. Neither proposition is incoherent or impossible.
Hume and the classical problem of induction
So both count as claims about matters of fact. There is no doubt that we have a multitude of opinions of this sort, and that practical life would be impossible without them. To take only the most obvious class of examples: every substantive claim about the future fall into this category.
But if you had no opinions at all about the future, you would be paralyzed. You might be hungry; but you would have no idea whatsoever where the food was. You might be cold, but you would have no idea what would happen if you turned up the thermostat or put on an extra sweater. There is no doubt that we have opinions about unobserved mattters of fact, and no doubt that we should be grateful for having. The descriptive question is, How do we arrive at them? Hume's first claim is negative: Knowledge of unobserved matters fact cannot be derived a priori.
Rather it must somehow result from experience. Imagine an adult human being who has neither seen snow nor heard stories about it. He is shown a snowball for the very first time and asked to predict -- before he has touched it -- whether it will be hot or cold. We all spontaneously predict that it will be cold, and we're right. But all he can do is consider the possibilities. He can conceive that it will be cold; he can conceive that it will be hot. Neither supposition involves any kind of internal contradiction, and so long as he is not allowed to investigate the matter, he cannot rule either proposition out of consideration.
So a priori -- before he has made any relevant observations -- he has no grounds for an opinion. The difference between us and him is not a difference in intellectual power. He can reason as well as we can. It is rather a difference in experience. And this seems to be completely general. We do not yet know how our experience is relevant to our prediction.
But that it is somehow relevant is obvious. On this basis Hume asserts a general proposition:. But how exactly does the derivation work? In the case of snow, the answer seems straightforward. In our experience the visual appearance of snow has been regularly and invariably associated with a sensation of cold. We have noticed, in other words, that.
This is the general pattern of inductive inference or induction. Hume's answer to the Descriptive Problem may then be framed as follows:. Before we proceed you should ask yourself: Is it really true that all of my beliefs about the future and the other unobserved parts of nature have been derived in this way from experience? Can you think of a counter-instance?
Suppose that Hume is right about how we actually think. So far all we have is a fact about human cognitive psychology. And this fact, however interesting, does not settle the normative question: Is it legitimate for us to proceed in this way? Are the conclusions we reach as a result of inductive inference really justified? It is logically possible for the conclusion to be false when the premise is true.
So a skeptic might say: In so-called inductive reasoning, human beings commit a fallacy. They accept a general proposition on the basis of an invalid argument. And this means that their acceptance of that general proposition is unjustified. Now this is not exactly Hume's way of raising skeptical worries. That we unheasitatingly pass from DATA to THEORY shows that we accept a principle connecting the two, a principle that normally passes unnoticed because we take it so completely for granted, but which figures implicitly in every instance of inductive reasoning.
Hume formulates this missing premise as the claim that the future will resemble the past.
But for our purposes it will be useful to work with a somewhat more precise formulation. This is a traditional post-Humean label for the missing premise, though in fact it is misleading. For UN is not simply the claim that nature exhibits regularities. It is the claim that the regularities that have emerged in my experience are among the regularities that hold throughout nature. It might better be called a principle or representativeness, for its central message is that my experience, though limited in time and space to a tiny fraction of the universe, is nonetheless a representative sample of the universe.
Moreover, there is no question for now about our right to accept the DATA. This brings us to the heart of the matter. What reason do we have to believe that our experience is a representative sample of nature? What reason is there to believe UN? I take it that A and B are straightforward. So if there are questions about this line of thought, they will be questions about C and D.
Related Humes Problems with Induction
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