After Hume, every inductivist attempted to show that Hume was wrong in his contention that the principle of induction could not be justified. The most significant attempt in this connection was made by John Stuart Mill who realized that the main plant of the attack on induction was its inability to lend the claims based on it the degree of certainty comparable to deductive inferences. For example, in a deductive inference such as ‘All men are mortal, X is a man' with certainty. That is to say, given the truth of the premises, the truth of the conclusion necessarily follows. But, in an inductive inference where the premises are about particular observations and the conclusion is a generalization, the generalization does not necessarily follow. That is to say, given the truth of the statements about certain particular observations, the truth of the generalization is not guaranteed. The generalization is at best a probable one. That is why logicians like Aristotle could develop a system of rules for deductive inferences. By knowing those rules, we could find which of our conclusions necessarily follow and which do not. Mill took the cudgels in favour of the method of induction which he attempted to demonstrate to be on equal footing with the rules of deduction whose capacity to lend certainty to the claims based on them was unproblematic. In other words, he set out to construct an inductive logic which was supposed to be almost on par with deductive logic. ‘The business of inductive logic', Mill writes, ‘is to provide rules and models (such as the syllogism and its rules are for ratiocination) to which if inductive arguments conform, those arguments are conclusive' . Five such rules were conceived and articulated: method of agreement, method of difference, joint method of agreement and difference, method of residues and method of concomitant variation. Mill claims for these “methods”, the dual role of aiding discoveries and proving/disproving our claims with certainty. That is, their role is both instrumental and demonstrative. For Mill, the latter is more promising, for he says, ‘even if they are not methods of discovery, it would not be less true that they are the sole methods of proof' . Mill's methods fail to perform either of the two functions for the simple reason that in either case the successful performance involves factors that go beyond the methods or rules that Mill has proposed . Let us elaborate this point.