In the past, the term ‘induction’ has been used mainly in two senses. The first is repetitive induction (or induction by enumeration). This consists of often repeated observations and experiments, which are supposed to serve as premises in an argument establishing some generalization or theory. The invalidity of this kind of argument is obvious: no amount of observation of white swans establishes that all swans are white (or that the probability of finding a non-white swan is small). In the same way, no amount of observed spectra of hydrogen atoms on earth establishes that all hydrogen atoms emit spectra of the same kind. Theoretical considerations, however, may suggest the latter generalization, and further theoretical considerations may suggest that we should modify it by introducing Doppler shifts and Einsteinian gravitational redshifts.
Thus repetitive induction is out: it cannot establish anything.
The second main sense in which the term ‘induction’ has been used in the past is eliminative induction – induction by the method of eliminating or refuting false theories. This may look at first sight very much like the method of critical discussion that I am advocating. But in fact it is very different. For Bacon and Mill and other exponents of this method of eliminative induction believed that by eliminating all false theories we can finally establish the true theory. In other words, they were unaware of the fact that the number of competing theories is always infinite – even though there are as a rule at any particular moment only a finite number of theories before us for consideration. [104-5]