It is obvious that these methods cannot solve the purpose of discovery, i.e. cannot be sufficient as instruments for theory formation. For, if that were so, by now all the problems of science could have been solved by proposing answers mastering the use of these rules which are only mechanical. The formation of a theory involves factors which go beyond these methods. But what is more important is that even after a theory is proposed, verified and established, it cannot be demonstrated or proved in a manner comparable to deductive proof. The use of any Mill's methods presupposes an antecedent, assumption about which circumstances are relevant for the explanation of the phenomena under investigation. Once these circumstances are chosen as possible causes, the method(s) help to correlate some of them with the phenomena under consideration. But this choice of possible causes might be erroneous. If it is so, the conclusion inferred by Mill's methods first cannot remain unaffected by the original mistake. Secondly, even if a correlation is established, there is no proof that correlation is not fortuitous but necessary (or lawful). Though it is true that greater the number of observed instances of correlation, higher the chances of the correlation being lawful and not fortuitous; we can never assert with certainty, no matter how many the observed instances, that the correlation is not fortuitous. Thus, the logical cleavage between induction and deduction which Mill tried to get rid of remained intact. The cruel fact that induction is induction, and deduction is deduction and the twin shall never meet remained unaltered to the discomfort of the inductivists.

The intention of all these historical details is to set the stage for the discussion on twentieth century deliberations on the method(s) of science. For, the various views that have been developed in twentieth century are to be understood not only as reactions to each other but also as reactions to a whole historical tradition. We shall now come to a detailed discussion on the various theories that have been put forward in the twentieth century regarding the method(s) of science.