  Let us now go further and see what happens if, from the deduction AAA-1, we form a new argument by interchanging the conclusion (the Result) with the minor premise (the Case). The resultant argument becomes: All Ms are Ps (Rule); all Ss are Ps (Result); therefore, all Ss are Ms (Case). This is the invalid syllogism AAA-2. But let us now regard it as pertaining to drawing conclusions on the basis of taking samples. The argument then becomes: All balls in this urn are red; all balls in this particular random sample are red; therefore, all balls in this particular random sample are taken from this urn. What we have here is nothing at all like an argument from population to sample or an argument from sample to population: rather, it is a form of probable argument entirely different from both deduction and induction. It has the air of conjecture or “educated  guess” about it. This new type of argument Peirce called hypothesis (also, retroduction, and also,  abduction). It should be clear that abduction is never necessary  inference