Mills` methods are five methods of induction described by the philosopher John Stuart Mill in 1843 in his book A System of Logic.  They must shed light on issues of causation. In this case, you are the only one who is not sick. The only difference between you and the others is that you didn`t make a salad. It`s probably the cause of other people`s illnesses. It is an application of the method of difference. This rule says that if you have a situation that leads to an effect, and another that does not, and the only difference is the presence of only one factor in the first situation, we can infer that factor as the cause of the effect. The corresponding variant (3.2) of the differential method requires only the observation of 1.2; but it merely finds the less complete conclusion that (A…) is a necessary and sufficient condition of P in F. Indeed, while B, C, D and E singly are still eliminated (in the index for 1.2 above) as they were in 1.2, and that all conjunctions such as those that might be present in I1 are eliminated because they are also present in N1 and are therefore not sufficient, a conjunction like AB, which contains A, is present in I1. , and missing in N1, and can therefore be both necessary and sufficient.
Thus, this hypothesis and observation only show that, as Mill said, A is “the cause or an indispensable part of it.” The full cause is represented by the formula (A…), provided that only the possible causes present in I1 can replace the points. However, to justify this, we need an additional general premise, a hypothesis, such a finding to a general causal conclusion. We must assume that there is a condition that is necessary and sufficient with regard to the field (or that is necessary or sufficient) for the phenomenon, and also that this condition can be found in a number of conditions that are limited in one way or another. Indeed, these methods fall within the general class of eliminating reasoning, i.e. arguments for which a possibility is confirmed or justified by the elimination of some or all of its competitors. The assumption is said that there is a reason to find and limit the range of candidates for the role of the cause; The role of compliance will be to exclude enough candidates who were originally admitted to allow for a positive conclusion. To close the list, that is to say to show that certain factors are irrelevant, we must use an analog of the method of agreement. If we assume, as is the case so far, that the complete cause of P to F is a few factors (X, X, X”, etc.), but also that P reacts to all these factors in the sense that for each variation, in, say, X, X, etc. remain constant, p varies, and that X, X, X, X etc. are identical to some of the possible causes A , B, C, D, E, if we discover that P remains constant, while. B, for example, A, C, D and E remain constant, but B varies, we can conclude that B is irrelevant, that none of the X is identical to B. This reasoning illustrates Mill`s method of residues: many elements of a complex effect are demonstrated by reliable causal beliefs from several elements of a complex cause; All that remains of the effect must have been produced by the remnants of the cause.