The rationality of hypotheses has been questioned throughout the whole history of logic. Twentieth-century philosophy held two standard views. On the one hand, hypothesis was simply something that transcended the limits of logic and was better left to “pre-theoretical intuitions”. On the other hand, historicism and hermeneutics defined hypotheses as a relationship with truth that belonged to tradition and to the history of effects of ideas. Both these views, by rejecting the inherent rationality of hypothesis, end up leaving scientific discoveries to the mere force of arbitrary will or to the force of social conventions and politics. Is it possible to find a third definition, respectful of both logical method and happening events? C. S. Peirce (1839-1914) was a scientist and a logician who strove all his life to define the rationale of hypothesis. He called this kind of reasoning “abduction”. This is a subject-matter that has been frequently studied over the last forty years, but those accounts have often blended abduction with induction, thereby missing the originality of the abductive pattern. I intend to present Peirce’s original insight and then to complete it with slight modifications and integrations that should make it fully operable – I will thus complete the sketch that Peirce was unable to finalize due to the precarious ending years of his life.