  But now let us see what happens if we form a new argument by interchanging the conclusion (the Result) with the major premise (the Rule). The resultant argument becomes: All Ss are Ps (Result); all Ss are Ms (Case); therefore, all Ms are Ps (Rule). This is the invalid syllogism AAA-3. But let us now construe it as pertaining to drawing conclusions on the basis of taking samples. The argument then becomes: All balls in this particular random sample are red; all balls in this particular random sample are taken from this urn; therefore, all balls in this urn are red. What we have here is an argument from sample to population. This sort of argument is what Peirce understood to be the core meaning of induction.  That is to say, for Peirce, induction in the most basic sense is argument from random sample to population. It  should be clear that inductive inference is not necessary inference: it  might well turn out that the claims stated in the premises are true  even though the claim made in the conclusion is false.