Peano’s axioms for arithmetic, published in 1889, are ubiquitously cited in writings on modern axiomatics, and his Formulario is often quoted as the precursor of Russell’s Principia Mathematica. Yet, a comprehensive historical and philosophical evaluation of the contributions of the Peano School to mathematics, logic, and the foundation of mathematics remains to be made. In line with increased interest in the philosophy of mathematics for the investigation of mathematical practices, this them...

This contribution examines the scientific background of Latino sine Flexione (LSF), an international auxiliary language constructed by Peano. LSF is part of a larger linguistic movement resulting from new technologies that accelerated globalisation. Science is a major driving force behind the international auxiliary language movement, both for creating an increased need for international contacts and for lending its data and methods to language construction. With LSF, Peano attempted to realize part of Leibniz’s dream of a universal language, of which a (...) temporary simplified form of Latin would become the first step. LSF was designed following Leibniz’s fragments compiled by Couturat. By eliminating conventional features from standard Latin, Peano attempted to reduce it to its logical expression. Inspired by the same concerns that motivated the symbolism of Formulario, he aimed for a simple language that owed its fit for international use to its being stripped down to the logical core shared by all languages. To achieve this, Peano proceeded by eliminating inflections from all words and establishing an “algebra of grammar” that governed the rules of word-formation. Simplicity, non-redundancy and computability are key values of LSF inspired from Peano’s mathematical practice. (shrink)