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The following inductive fallacies are described in this section:
Inductive reasoning is inference from the specific to the general, from a sample of a population to a reasonable generalization about that population.
For example, suppose we have a barrel containing 1,000 beans. Some of the beans are black and some of the beans are white. Suppose now we take a random sample of 100 beans from the barrel and find that 50 of them are white, 50 of them black. Then we could infer inductively that the beans in the barrel are probably half — that is, 500 of them — black with the other half white.
The reliability of the inductive inference, of course, depends on the similarity of the sample to the population. The greater the similarity, the more reliable the inductive inference. This is something that statisticians endeavor to ensure by making certain that the sample is selected at random, something that is not always as easy to do as it may sound.
Inductive inference is not perfect. That means that any inductive inference can sometimes fail. Even though the premises are true, the conclusion might be false. Nonetheless, a good inductive inference gives us a reason to believe that the conclusion is probably true, with the possibility that some particular rare instance may have been overlooked (e.g., one purple bean sits at the very bottom of our barrel of beans above).
- 1. Hasty Generalization:
- The size of the sample is too small to support the conclusion.
Examples:
- Fred, the Australian, stole my wallet. Thus, all Australians are thieves. (Of course, we shouldn't judge all Australians by one example.)
- I asked six of my friends what they thought of the new spending restraints and they agreed that the restraints are a good idea. The new restraints are therefore generally popular.
Convincing Others: Identify the size of the sample and the size of the population. Then show that the sample size is too small. Note that a formal proof may require some statistical expertise. This is the subject of probability theory.
References: Barker: 189; Cedarblom and Paulsen: 372; Davis: 103
- 2. Unrepresentative Sample:
- The sample being used in an inductive inference is relevantly different from the population as a whole.
Examples:
- To see how Canadians will likely vote in the next election we polled several hundred people in Calgary. This poll shows conclusively that the Reform Party will sweep the country. (People in Calgary tend to be more conservative than people in the rest of Canada.)
- The apples on the top of the box look good. The entire box of apples must be good. (Of course, the rotten apples are hidden beneath the surface.)
Convincing Others: Show how the sample is relevantly different from the population. Then show that because the sample is different, the conclusion is probably different.
References: Barker: 188; Cedarblom and Paulsen: 226; Davis: 106
- 3. False Analogy:
- In an analogy, two objects (or events), A and B are shown to be similar. This reasoning fails when it is argued that since A and B are similar, if A has property P, so also B must have property P. The analogy fails when the two objects, A and B, are different in a way which affects whether they both have property P.
Examples:
- Employees are like nails. Just as nails must be hit on the head to make them work, so must employees.
- Government is like a business. So, just as a business must be sensitive to the bottom line, so also must government. (But the objectives of government are usually completely different from any business. So, probably they have to meet different criteria.)
Convincing Others: Identify the two objects or events being compared and the property which they both are said to possess. Show that the two objects are different in a way which will affect whether they both have that property.
References: Barker: 192; Cedarblom and Paulsen: 257; Davis: 84
- 4. Slothful Induction:
- The proper conclusion of an inductive argument is denied, despite the evidence to the contrary.
Examples:
- Hugo has had twelve bona fide accidents in the last six months. Yet he still insists that it is just a coincidence and not his fault. (Inductively, the evidence is overwhelming that it is his fault. This example borrowed from Barker, p. 189.)
- Poll after poll shows that the NDP will win fewer than ten seats in Parliament. Yet the party leader insists that the party is doing much better than the polls suggest. (The NDP in fact got nine seats.)
Convincing Others: About all you can do in such a case is to point to the strength of the inference.
Reference: Barker: 189
- 5. Fallacy of Exclusion:
- Important evidence which would undermine an inductive argument is excluded from consideration. The requirement that all relevant information be included is called the "principle of total evidence."
Examples:
- Jones is Albertan, and most Albertans vote Tory. So Jones will probably vote Tory. (The information left out is that Jones lives in Edmonton and that most people in Edmonton vote Liberal or N.D.P.)
- The Leafs will probably win this game because they've won nine out of their last ten. (Eight of the Leafs' wins came over last place teams, and today they are playing the first place team.)
Convincing Others: Show that the missing evidence changes the outcome of the inductive argument. Note that you cannot simply show that some of the evidence is missing; you must demonstrate that the missing evidence will change the conclusion.
Reference: Davis: 115
Reprinted with permission from Professor Stephen Downes.
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