Abduction explained --> via Peirce Studies Helsinki

"Let us now consider non-necessary reasoning. This divides itself, according to the different ways in which it may be valid, into three classes: probable deduction; experimental reasoning, which I now call Induction; and processes of thought capable of producing no conclusion more definite than a conjecture, which I now call Abduction.

[---]
Abduction is no more nor less than guessing, a faculty attributed to Yankees. [---] Such validity as this has consists in the generalization that no new truth is ever otherwise reached while some new truths are thus reached. This is a result of Induction; and therefore in a remote way Abduction rests upon diagrammatic reasoning." ('PAP (Prolegomena for an Apology to Pragmatism)' (MS 293), NEM 4:319-320, c. 1906)

"... there are but three elementary kinds of reasoning. The first, which I call abduction (on the theory, the doubtful theory, I confess, that the meaning of the XXVth chapter of the second book of the Prior Analytics has been completely diverted from Aristotle's meaning by a single wrong word having been inserted by Apellicon where the original word was illegible) consists in examining a mass of facts and in allowing these facts to suggest a theory. In this way we gain new ideas; but there is no force in the reasoning.

[---] ... induction is, as Aristotle says, the inference of the truth of the major premiss of a syllogism of which the minor premiss is made to be true and the conclusion is found to be true, while abduction 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. Abduction furnishes all our ideas concerning real things, beyond what are given in perception, but is mere conjecture, without probative force." (A Letter to Calderoni, CP 8.209, c. 1905)...

more on this subject (and many more) here -> HelsinkiPeirceStudies - very nice site