 Around 1890, Giuseppe Peano gave a formalization of logical inference, with the aim of representing formally proofs in arithmetic. His seminal paper Arithmetices principia, nova methodo exposita, written originally in Latin, is included in English translation in the collection  From Frege to Gödel (1967) that Jean van Heijenoort edited. Unfortunately, the editor failed to recognize what Peano did with formal inference, and the view spread that Peano formalized only the language of logic and arithmetic, not its principles of proof. If Peano's proofs are read with even a little care, it transpires that they are purely formal derivations that use two principles: