The Paradox of Induction
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The problem or paradox of induction
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We attribute to David Hume the first clear exposition of the paradox of induction. He presents it in his Enquiries Concerning Human Understanding. However, a close reading of Hume's text will reveal that he does not intend to pose quite the same problem that it has come to be handed down to us. So we shall make our first exploration of the paradox in a passage from Bertrand Russell's The Problems of Philosophy. "Now in dealing with this question we must, to begin with, make an important distinction, without which we should soon become involved in hopeless confusions. Experience has shown us that, hitherto, the frequent repetition of some uniform succession or coexistence has been a cause of our expecting the same succession or coexistence on the next occasion. Food that has a certain appearance generally has a certain taste, and it is a severe shock to our expectations when the familiar appearance is found to be associated with an unusual taste. Things which we see become associated, by habit, with certain tactile sensations which we expect if we touch them; one of the horrors of a ghost (in many ghost-stories) is that it fails to give us any sensation of touch. Uneducated people who go abroad for the first time are so surprised as to be incredulous when they find their native language not understood. And this kind of association is not confined to men; in animals also it is very strong. A horse which has been often driven along a certain road resists the attempt to drive him in a different direction. Domestic animals expect food when they see the person who usually feeds them. We know that all these rather crude expectations of uniformity are liable to be misleading. The man who has fed the chicken every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to the chicken." The paradox of induction is the problem that in all scientific reasoning we form conclusions, called laws, that are of a general nature; however, the evidence we have for those laws is based upon particular experiences. For example, we form the conclusion that all rays of light will be bend as the pass from air into glass, but we have only ever observed a finite number of instances of this law. On further reflection we see that there is no necessary connection between something happening on one occasion and the same thing happening in like circumstances on another occasion. We are not directly acquainted with the "power" behind events that ensures the uniformity of nature throughout space and time. Another illustration of this might concern the uniformity of space. Imagine that a space mission is about to be sent to the nearest star, Alpha Centuri. People might be queuing up to volunteer to be the first people to witness life on a distant planet. On the other hand, there might be anxious reluctant passengers, desperate not to be dragged on the fool-hardy mission. Why? Because there is no guarantee that the laws of nature operate in the same way in outer space as they do in our solar system. It is entirely conceivable that once the space ship passes beyond the perimeter of our solar system, that entirely different laws of physics will apply, and the space ship could be destroyed by chaotic forces that cannot be anticipated. We have no way at present of being sure that universe is uniform. We have only sampled physical nature in our own limited portion of the universe. We might regard the fear of the passengers as outlandish, but it is not an irrational fear. Just because things have happened at one point of space and at a given time in a certain way is no guarantee that they always will happen that way. This, then, is the paradox. Every day we reason from particular instances to generalities, and such inference is essential to our way of life; but there is no guarantee that such an inference is valid, and, indeed, very often such inferences prove to be fallacious – as in the case of the chicken that reasoned that its master would always feed it just because its master always has! A schematic representation of the inductive inference is as follows. ... The general law encompasses a potentially infinite number of instances that no amount of observation could possibly affirm. The problem is usually expressed as a problem of inference from past to future, but strictly this is only an instance of the problem; unobserved past events are also subject to the paradox of induction – we can never be sure that any general law has applied uniformly even in the past. No general law can ever be certain. Yet inductive reasoning is (in the very broadest sense) the basis of science, which constructs laws governing all events. One of the purposes of science is to make predictions – in other words to predict that past generalities will also apply in the future. That this species of reasoning from the particular to the general is unsound is illustrated by the existence of many counter-examples. Russell in his passage gives a number of examples of the way in which inductive reasoning can lead to erroneous conclusions. He points out that if the chicken reasoned that it would always be fed by its owner because it always has been fed by its owner, then it is making an error. et in the formal sense, there is no difference between the reasoning in the chicken's case and the reasoning in science generally. The chicken reasoned, this has always happened in the past, therefore, it always will happen in the future, and that is also how we reason. So the sceptical problem is, what exactly is it that makes scientific generalisations justified?
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Contents of
The Paradox of Induction
1 Prescriptive philosophy of science
2 The problem or paradox of induction
3 Hume and the formulation of the paradox of induction
4 Attempts to solve the paradox of induction
5 The paradox of induction and the claim that probability is all we ought to seek
6 Swinburn and confirmation theory
7 Falsificationism and the paradox of induction
8 Extrapolation and interpolation
9 Occam razor and the paradox of induction
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