In my note "Aristotle on Induction," commenter Brian Tinker raised a good question:
Given what you and [Edwin] Locke [in this paper] have said about induction, why does it have such a bad reputation?I think some of its bad reputation is earned: a very small part, that is. Let me explain.
Most people understand induction to be "by enumeration." Something like: "All the enumerated cases of swans I've observed are white, therefore all of them are white," or "the sun has always risen, therefore it will rise tomorrow (and the next day, etc.)."
Philosopher Bertrand Russell gives another example, through parable, of "induction by enumeration" in his book The History of Western Philosophy, page 543. The parable begins: A census officer is questioning homeowners in a village, all of whom seemed to have the same name, William Williams. Finally, the officer decides that every homeowner in the village is named William Williams (an enumerative induction), records the names, and takes a holiday. But he was mistaken: there was one man named John Jones who owned a home there, but the officer had missed him.
This means that the induction is faulty, and illustrates the problem--that inductions by enumeration are never certain; one counter-example can ruin even the strongest of inductive generalizations.
Francis Bacon, the first modern philosopher of science, points out the basic problems with enumerative induction (criticism which I agree wholeheartedly with):
The induction which proceeds by simple enumeration is puerile, leads to uncertain conclusions, and is exposed to danger from one contradictory instance, deciding generally from too small a number of facts, and those only the most obvious. [Bacon, Novum Organum (New Instrument), Book 1, Aphorism 105.]Bacon summarizes why most philosophers (in my opinion) denigrate induction, and why it has a bad reputation. Since what he points out about enumerative induction is true, it is my reason for thinking some of induction's bad reputation is earned.
Also, I agree with Dr. Leonard Peikoff's comments on enumerative induction:
Induction in my judgment is not in any sense a matter of quantity. There's a type of induction called induction by simple enumeration, which means induction simply by enumerating or counting instances. [...]Now, I regard quantity as such as insignificant. It entirely depends on what happens to that quantity, which can be a good suggestive beginning if you see something happening. What happens when you integrate it with everything else you know that's relevant? (Art of Thinking, Lecture 2)While enumerating cases can be instructive in forming ideas, noting similarities and differences, and in figuring out how rare or widespread a certain phenomena may be (say, meteoroid impacts), I think it's a poor candidate for valid inductive thinking.