Inductive reasoning

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Induction is one of the two main forms of logical reasoning. The other is deduction. In induction, we find a general rule by using a large number of particular cases. For example, watching water in many different situations, we can conclude that water always flows downhill.

Induction is the method of science. A scientist makes a large number of observations, and then suggests a general rule that all of these observations follow. He then publishes his ideas, and they are checked in many other cases by other scientists. The general rule becomes a scientific theory only if it passes all of these tests. If it fails even one test, then the theory must be either changed or thrown out. The major scientific theories of today have been tested many thousands of times and have passed every test.

The method of induction must be used carefully, because even one failure disproves the theory. For example, people noticed that when the letters "i" and "e" appear together in a word, the "i" usually comes first, as in "sieve", "bier", and "die". So, should we use induction to make a rule "Always put 'i' before 'e'?" No, because there are exceptions: "ceiling", "deceive", and "receive". Then do we want a rule, "i before e except after c"? But there is another set of exceptions, "neighbor" and "weigh". So someone proposed the rule, "i before e except after c, or when sounded like 'a' as in 'neighbor' and 'weigh'." Even that rule is not always true. Consider the word "weird".

You can see how hard it is to come up with a rule that is always true.

When a person uses induction carelessly, and believes a rule that is not always true, we say that they "jump to a conclusion".