Babbage-Chambers Paradox

Charles Babbage (1791–1871), mathematician and almost-inventor of the digital computer, observed in his Ninth Bridgwater Thesis (1838) that his calculating engine could produce the series of natural numbers from 1 to 100,000,000, and then—without any interference— produce 100,000,001; 100,010,002; 100,030,003; 100,060,004; ‘and so on’ for many hundred terms, till yet another rule came into play. This realization, that the same process might suddenly reveal another law (and so that miracles could not be ruled out), was further developed by Robert Chambers (1802–71) to explain the differences between successive geological eras: the ‘same process’ operated by different laws to produce unpredictable changes. As an account of evolution , or of miracles, the story proved unpopular. As an anticipation of Goodman's problem with grue, and Wittgenstein's with the notion of rule-following, it retains its interest: no finite string of observations or operations can identify what rule is being followed, or what its correct application might require in the future.