Before deciding whether an induction is complete, define the scope of the universal class and ask whether any relevant members remain unknown.
Example 1: A room contains exactly three chairs; all three are checked — complete induction.
Example 2: Three hundred chairs are checked in a market, and a claim is made about every chair in the city — incomplete induction.
The first investigation is small but exhaustive. The second is large but incomplete. “Complete” and “numerous” are not synonyms.
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Induction: Complete and Incomplete Enumeration, Certainty and Probability
Before deciding whether an induction is complete, define the scope of the universal class and ask whether any relevant members remain unknown.
Example 1: A room contains exactly three chairs; all three are checked — complete induction.
Example 2: Three hundred chairs are checked in a market, and a claim is made about every chair in the city — incomplete induction.
The first investigation is small but exhaustive. The second is large but incomplete. “Complete” and “numerous” are not synonyms.