The main difficulty attending the use of the method of difference is the complexity of phenomenon. The very nature of the method insists as an essential requirement that only one material antecedent shall be varied at a time. In life the variations are more or less confused, and it is often not only impossible to observe cases of a single variation, but frequently error comes through overlooking antecedents which are material to the case under investigation. For these reasons the Method of Difference is more a method of experiment than it is a method of observation. By controlling the circumstances it becomes possible to vary but one antecedent at a time, and also to bring into prominence all of the material antecedents.
Bacon claims that all “crucial instances” are merely applications of the Method of Difference. By crucial instance he means any fact which will enable us to determine at once which supposition is the correct one. Forexample, the physician may not know whether it is malaria or typhoid fever till he takes a blood test; such a test typifies “crucial instances.” The various tests in chemistry are likewise cases of crucial instances, and, in consequence, this science makes use of “Difference” more than any other method.
(5) Characteristic features of Method of Difference.
There are three distinguishing marks of the Method of Difference: these are, (1) The phenomenon does not always happen; (2) One antecedent is variable; (3) The other antecedents are more or less invariable.
The following symbolizations will make these three characteristics evident:
| Antecedents | Consequents | |
| (1) | A B C | P |
| A – C | – | |
| (2) | – B C | – |
| X B C | P | |
| (3) | L M T K | P |
| L M – K | – |
AGREEMENT AND DIFFERENCE COMPARED.
(a) The methods of Agreement and Difference are complementary as may be discerned by comparing their characteristic features: In Agreement the phenomenon always occurs; in Difference the phenomenon does not always occur: In Agreement there is one invariable antecedent; whereas in Difference there is one variable antecedent: In Agreement the other antecedents are more or less variable; but in Difference the other antecedents are more or less invariable.
(b) According to Mill the Method of Agreement insists that what can be eliminated is not connected; whereas the Method of Difference implies that what cannot be eliminated is connected.
(c) The Method of Agreement is more a method of observation, since it is chiefly concerned with the discovery of causes. The Method of Difference is distinctly a method of experiment, because its usual aim is to discover effects.