A fundamental and widely accepted objection to the assertion that these methods constitute an important part of the scientific method is that science is not or not much related to cause-and-effect contexts in the sense that these methods can detect them. It can be said that the formulation and confirmation of hypotheses and theories, which constitute the bulk of a science such as physics, is a scientific process different from the actual application of these methods. Even the discovery of a functional law of dependency is, as we have seen, a task that goes beyond what is achieved by our method of accompanied variation. It is also understandable that in many sciences it is primarily a question of discovering new objects and tracing processes, not of making causal correlations. Moreover, it was found that these methods could logically not be the whole scientific procedure, as they require assumptions that they cannot support themselves. The common method deals with both the method of agreement and the method of difference as indicated by the diagram above. The application of the common method should therefore tell us that this time it is beef that is the cause. In addition to the positive method of agreement in which candidates are eliminated as unreased because they are absent in positive cases, there are appropriate variants of a negative agreement method in which candidates are deemed insufficient because they are present in negative cases. This requires the following observation: A group of one or more negative instances, so that a possible cause, for example. B A, is absent from each instance, but for any other possible cause, there is a instance in which it is present. For example: a comprehensive study of such functional dependence would involve two tasks: first, identifying all the factors on which the size of P in F depends and, second, discovering how this order of magnitude depends on these factors.
Completion of the first task would give a simple list of terms, those of the second a mathematical formula. Only the first of these tasks can be performed by a method of elimination similar to the one that has already been questioned. We therefore find that, although we had to identify very different variants of these methods according to the different types of hypotheses used, and that the argument that validates the simplest variants fails when it is permissible for different negations and combinations of factors to be the real cause, there are nevertheless valid demonstrative methods that use even the least strict form of acceptance. , that is, which assume only that there is a necessary and sufficient condition for P in F, which consists, to some extent, of a limited set of possible causes. However, in such a scenario, we must either simply draw (until 8.2) a very incomplete conclusion from the classical observation of differences, or (par 8.12, 8.14, the combination of these two or 8.4) to draw more complete conclusions only from a large number of cases where possible causes are systematically or non-existent. Mills methods should not come as a surprise, as these rules articulate some of the principles we use implicitly in causal reasoning in everyday life. But it is important to respect the limits of these rules. The common method as an indirect method of difference no longer works as soon as we allow both conjunctions and disjunctions; but a dual method of agreement comes into force with this eighth type of acceptance. In 8.12, as in 6.12, if there are possible causes except A, the set of 2n positive instances with A that are present in each, but with the other possible causes present and absent in all possible combinations, show that (A or…) is necessary and sufficient, and therefore that A is sufficient.