Today we begin the final component of our study of logic, a survey of the most common methods of inductive reasoning.
Although inductive inferences never guarantee the truth of their conclusions, as valid deductive inferences do, we can evaluate them by considering how each could be made stronger or weaker by the addition of further information.
The simplest variety of inductive reasoning is
argument by analogy, which takes note of the fact that two or more things are similar in some respects and concludes that they are probably also similar in some further respect.
Not every analogy is an argument; we frequently use such comparisons simply to explain or illustrate what we mean.
But arguments by analogy are common, too.
Suppose, for example, that I am thinking about buying a new car.
I'm very likely to speak with other people who have recently bought new cars, noting their experiences with various makes, models, and dealers.
If I discover that three of my friends have recently bought Geo Prizms from Burg and that all three have been delighted with their purchases, then I will conclude by analogy that if I buy a Geo Prizm from Burg, I will be delighted, too.
Of course, this argument is not deductively valid; it is always possible that my new car may turn out to be an exception.
But there are several considerations that clearly matter in determining the relative strength or weakness of my inductive inference:
- Number of instances.
If five friends instead of three report their satisfaction with the model I intend to buy, that tends to make it even more likely that I will be satisfied, too.
In general, more instances strengthen an analogy; fewer weaken it.
- Instance variety.
If my three friends bought their Prizms from three different dealers but were all delighted, then my conclusion is somewhat more likely to be true, no matter where I decide to buy mine.
In general, the more variety there is among the instances, the stronger the analogical argument becomes.
- Number of similarities.
If my new purchase is not only the same make and model from the same dealer but also has the same engine, then my conclusion is more likely to be true.
In general, the more similarities there are between the instances and my conclusion, the better for the analogical argument.
Of course, the criteria we're considering apply only if the matters with which they are concerned are relevant to the argument.
Ordinarily, for example, we would assume that the day of the week on which a car was purchased is irrelevant to a buyer's satisfaction with it.
But relevance is not something about which we can be terribly precise; it is always possible in principle to tell a story in the context of which anything may turn out to be relevant.
So we just have to use our best judgment in deciding whether or not some respect deserves to be considered.
- Number of dissimilarities.
If my friends all bought Geos with automatic transmissions and I plan to buy a Geo with a standard transmission, then the conclusion that I will be delighted with my purchase is a little less likely to be true.
In general, the fewer dissimilarities between instances and conclusion, the better an analogical argument is.
- Modesty of conclusion.
If all three of my friends were delighted with their auto purchases but I conclude only that I will be satisfied with mine, then this relatively modest conclusion is more likely to be true.
In general, arguments by analogy are improved when their conclusions are modest with respect to their premises.
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Last modified 12 November 2011.
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