History, mathematics and abduction ¹, or hypothesis, is one of the main modes of inference used by the human mind, alongside deduction and induction. It is a logical process that allows one to draw a conclusion starting from two premises. In practice, abduction is the reasoning that allows us to infer a cause or explanation starting from an observed result and a general rule. Abduction The process develops in this way: a surprising phenomenon (C) is observed and it is hypothesized that, if a certain condition (A) were true, then that phenomenon (C) would be its natural consequence, meaning that the observed phenomenon can be explained as a normal result of that condition. An example provided by the famous mathematician Charles Peirce helps clarify this concept better. Suppose a person enters a room and finds several bags filled with beans of various types. On the table there is a handful of white beans. After careful observation, the person discovers that one of the bags contains only white beans. From this observation, they infer that the handful of white beans probably comes from that bag, since that bag contains only white beans. ¹ Cf. Umberto Eco and Thomas A. Sebeok, (eds.), , Milan, Bompiani, 1983; Massimo Bonfantini, , Milan, Bompiani, 1987; Veronica Canirato, , University of Ferrara, 2006; Francesco Menini, , at Il Segno dei Tre: Holmes, Dupin, Peirce La semiosi e l'abduzione Per una filosofia dell'indizio: Charles Peirce e la serendipity Deduzione - Induzione / Abduzione, modellino per alcuni accostamenti tra ragionamento logico e ascolto musicale www.suonosonda.it/wp-content/uploads/2018/26/Menini-Francesco-deduzione-induzione-abduzione.pdf