Hempel’s paradox (20TH CENTURY).
Also known as the confirmation paradox, it was discovered by Carl Gustav Hempel (1905-1997).
The statement ‘All prime ministers live at 10 Downing Street’ tends to be confirmed by finding a kennel containing a dog, because this is an example of a dwelling that is not 10 Downing Street which is the home of a non-prime-minister; which is a logically equivalent statement.
However, the same process could be used to prove that all the roses in a large garden have green leaves by observing that all the plants with other-coloured leaves are not roses, a much easier process. The resolution of the paradox is to restrict the universe in which the search is made.
However, the paradox is not a total surprise because non-mathematical induction is not a logical proof. For example, the assertion that water is a compound of hydrogen and oxygen is based on a study of a tiny proportion of the extant water, and it is conceivable that most of the rest is a compound of carbon and manganese.
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