The method of subtraction is simply a useful dodge when attempting logical analysis. In order to see whether a certain condition c is, or is not, a necessary condition for the occurrence of a certain sort of situation s, try conceiving of cases of s where it is given that c does not hold. It may turn out to be fairly clear that the notion of s without c is an incoherent conception, and so fairly clear that c is necessary for s. This simple technique, which resembles the method of reductio ad absurdum in mathematics and logic, and the 'method of difference' in empirical research, can be astonishingly fruitful. The neglect to apply it can lead to a lot of unnecessary beating about the bush.
D. M. Armstrong. Belief, Truth and Knowledge, Cambridge University Press, 1973, pp. 81–82.
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