b. Induction allows inferring a from multiple instantiations of b when a entails b (inferring probable antecedents as a result of observing multiple consequents [epagögé, “bringing in”]) = inferring a law
c. Abduction allows inferring a as an explanation of b (inferring the precondition a from the consequence b [apagögé—note that Peirce translates this term as retroduction]), a.k.a. “inference to the best explanation” = assuming a law (i.e. a hypothesis)
Peirce’s definition of abduction differs: it is “the inference of the truth of the minor premiss of a syllogism of which the major premiss is selected as known already to be true while the conclusion is found to be true,” i.e. it supplies the middle premise of an enthymeme. What is called abduction above, Peirce calls . . .
d. Retroduction, which is “reasoning from consequent to [hypothetical] antecedent” (C. S. Peirce, “A Neglected Argument for the Reality of God” , CP 6.469-70). Peirce sometimes calls it “Hypothetic Inference.” It “depends on our hope, sooner or later, to guess at the conditions under which a given kind of phenomenon will present itself” (Letter to F. A. Woods , CP 8.385-88). Cf. the fallacy of post hoc ergo propter hoc.
Thus, we can infer the conditions of possibility of a state of affairs, e.g. a problem in argumentation, existing.