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The Problem of Induction

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The Problem of Induction The problem of induction Last time we discussed a few arguments which seem to show that we can have no knowledge of the properties of things which are outside of us. Let’s set those problems to the side, for now, and just grant that perception does, at least some times, give us knowledge of the properties of the things we encounter in our experience. Of course, not all the knowledge that we take ourselves to have is the kind of direct perceptual knowledge exemplified by me claiming, on the basis of visual experience of my hands, that I have hands. Sometimes we take ourselves to know things which go beyond our own perceptual experience. Science is a rich source of such knowledge claims. Consider the following claims for which we seem to have good scientific evidence: Massive objects attract one another. The earth rotates on its axis about once every 24 hours. Dinosaurs (not counting birds) became extinct about 60 million years ago. These claims are not, on a natural interpretation, claims which we can know to be true directly on the basis of sense experience: for example, though we can observe some massive objects attracting each other, we certainly have not observed this of all presently existing massive bodies, let alone all massive bodies past and future. However, experience clearly plays some role in our justification for believing that massive bodies attract: we take ourselves to know this because we have observed many massive bodies interacting, and infer from the fact that we have observed this in many cases that it is also true of unobserved cases. Today we will be focusing a simple variety of inductive reasoning, known as enumerative induction, which is exemplified by the following argument. The sun came up on 3/26/09. The sun came up on 3/25/09. The sun came up on 3/24/09. .... .... ____________________________ The sun will come up tomorrow. In this sort of reasoning, we infer from a list of observed instances of some generalization that some unobserved instance is also true. It is not essential that the conclusion be some claim about the future; it could be about any unobserved state of affairs, including the distant past. Enumerative induction seems to play a central role in the justification of scientific claims, even where this is not immediately obvious. Consider, for example, the following claim: Typical adult members of the species tyrannosaurus rex were about 13 feet tall. How would you defend a claim of this sort? Would enumerative induction play a role? In the reading for today, Hume critically examines the sort of inductive reasoning exemplified by the argument above. We can begin this examination with a question: Is this argument valid? Today we will be focusing a simple variety of inductive reasoning, known as enumerative induction, which is exemplified by the following argument. The sun came up on 3/26/09. The sun came up on 3/25/09. The sun came up on 3/24/09. .... .... ____________________________ The sun will come up tomorrow. In the reading for today, Hume critically examines the sort of inductive reasoning exemplified by the argument above. We can begin this examination with a question: Is this argument valid? One way to pose Hume’s challenge to inductive reasoning is to ask: given that this argument (and other examples of enumerative induction) is not valid, how can induction be a reasonable way of forming beliefs? A natural response to this question is that we can, of course, make the argument we just discussed valid by adding a premise. If the sun came up on 3/26/09 and the sun came up on 3/25/09 and ... then the sun will come up tomorrow. A natural response to this question is that we can, of course, make the argument we just discussed valid by adding a premise. The sun came up on 3/26/09. The sun came up on 3/25/09. The sun came up on 3/24/09. .... .... If the sun came up on 3/26/09 and the sun came up on 3/25/09 and ... then the sun will come up tomorrow. ____________________________ The sun will come up tomorrow. Does this make the argument valid? A valid argument only gives provides good reason for believing its conclusion if we can know that the premises of that argument are true. So what we have to ask is: can we know that the if-then statement above is true and, if so, how? Hume raises a dilemma for any attempt to explain how we can know this extra premise. This dilemma is based on a distinction between two kinds of knowledge. The sun came up on 3/26/09. The sun came up on 3/25/09. The sun came up on 3/24/09. .... .... If the sun came up on 3/26/09 and the sun came up on 3/25/09 and ... then the sun will come up tomorrow. ____________________________ The sun will come up tomorrow. Hume raises a dilemma for any attempt to explain how we can know this extra premise. This dilemma is based on a distinction between two kinds of knowledge. “All the objects of human reason or inquiry may naturally be divided into two kinds, to wit, relations of ideas, and matters of fact. Of the first kind are the sciences of geometry, algebra, and arithmetic; and in short, every affirmation which is either intuitively or demonstratively certain. ...Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe. ... Matters of fact, which are the second objects of human reason, are not ascertained in the same manner; ...The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if ever so conformable to reality. That the sun will not rise tomorrow is no less intelligible a proposition, and implies no more contradiction than the affirmation, that it will rise. ...” Here Hume not only distinguishes between knowledge of relations of ideas and knowledge of matters of fact; he also gives an argument that the extra premise in our argument, is not just a matter of the relations of ideas, and therefore cannot be known by “the mere operation of thought.” How would you state Hume’s argument for this point? The sun came up on 3/26/09. The sun came up on 3/25/09. The sun came up on 3/24/09. .... .... If the sun came up on 3/26/09 and the sun came up on 3/25/09 and ... then the sun will come up tomorrow. ____________________________ The sun will come up tomorrow. Hume raises a dilemma for any attempt to explain how we can know this extra premise. This dilemma is based on a distinction between two kinds of knowledge. Here Hume not only distinguishes between knowledge of relations of ideas and knowledge of matters of fact; he also gives an argument that the extra premise in our argument, is not just a matter of the relations of ideas, and therefore cannot be known by “the mere operation of thought.” How would you state Hume’s argument for this point? Knowledge that some claim p is the case p is a matter of the relations of ideas p is a matter of fact p can be known by mere thought p can only be known by experience The opposite of p is a contradiction, or unintelligible The sun came up on 3/26/09. The sun came up on 3/25/09. The sun came up on 3/24/09. .... .... If the sun came up on 3/26/09 and the sun came up on 3/25/09 and ... then the sun will come up tomorrow. ____________________________ The sun will come up tomorrow. Knowledge that some claim p is the case p is a matter of the relations of ideas p is a matter of fact p can be known by mere thought p can only be known by experience The opposite of p is a contradiction, or unintelligible Given that the opposite -- the negation -- of the extra premise is not unintelligible, the extra premise cannot be known by mere thought, and is not simply a matter of the relations of ideas. So if we can know that this extra premise is true, we must know this by experience. But can we know this by experience? The sun came up on 3/26/09. The sun came up on 3/25/09. The sun came up on 3/24/09. .... .... If the sun came up on 3/26/09 and the sun came up on 3/25/09 and ... then the sun will come up tomorrow. ____________________________ The sun will come up tomorrow. Knowledge that some claim p is the case p is a matter of the relations of ideas p is a matter of fact p can be known by mere thought p can only be known by experience The opposite of p is a contradiction, or unintelligible So we can’t know the truth of the extra premise by thought alone, or by experience. But if we cannot know that it is true, it is hard to see how the reasoning exemplified by our argument above could be rational. The sun came up on 3/26/09. The sun came up on 3/25/09. The sun came up on 3/24/09. .... .... If the sun came up on 3/26/09 and the sun came up on 3/25/09 and ..
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