Giuseppe Peano’s Latino sine flexione is a short Latin-language treatise—part grammar, part polemic—proposing a radically simplified Latin as a language for international communication. Written in numbered sections and published in the early twentieth century, it strips nouns of case, gender, and number, reduces verbs to a single invariable form, and defends the result against rival projects such as Volapük and Esperanto. Along the way Peano detours into mathematics, attacking the “principle of permanence” that contemporary algebraists used to justify negative and imaginary numbers. The book is thus two arguments in one: a practical case for a minimal Latin, and a logical case against loose reasoning about number.
“Lingua latina fuit internationalis in omni scientia, ab imperio Romano, usque ad finem saeculi XVIII.”
Stripping Latin Down to Its Bones
Peano begins from history. Latin served as the common language of science from the Roman Empire to the end of the eighteenth century, and only in recent times has it come to seem too hard—first in science, then in commerce. His answer is that no one needs all of Latin; a small part of it suffices to express any idea. The grammar that follows is an exercise in proving this claim.
He takes his warrant from Leibniz, quoted at each step. Cases, Leibniz held, can always be eliminated by substituting particles, and Peano shows how: an indeclinable noun is taken in its simplest form, with de marking the genitive, ad the dative, ab or ex the ablative, and the accusative left to word order, as in the modern Romance languages that grew out of popular Latin. A short set of rules converts the familiar dictionary forms—nominative and genitive—into this single invariable shape. Gender goes next, again on Leibniz’s authority: an isolated noun has no gender, and where sex must be indicated one writes mas or femina explicitly, though a word like mater already carries the idea of female within it. Number follows the same logic. A noun alone has no number; uno or plure can be added, and then logical simplification absorbs the addition, so that duo already contains the notion of plurality and uno uno collapses to uno. Peano’s examples have a homely wit: we have one mouth and two ears becomes habemus uno ore et duo aure.
The verb receives the most drastic treatment. Latin, Peano observes, can report speech indirectly—amicitiam inter malos esse non posse rather than the direct amicitia inter malos esse non potest—and if one always writes indirectly, person, mood, and often tense endings simply vanish. What remains is an indeclinable verb form, the imperative being the simplest, with -re added to form infinitives and to turn actives into passives. Person is carried by me, te, nos; mood by si, ut, quod; tense by adverbs like heri, nunc, cras, or by vol and debe. A second reduction goes further, dissolving participles and gerunds into relative clauses by logical equality—lauda-nte becomes qui lauda, lauda-ndo becomes dum lauda—so that every ending can in principle disappear, though Peano concedes a few, like -nte and -to, may prove convenient enough to keep.
The Case Against Volapük, Esperanto, and Living Languages
The middle of the book widens into a survey of the international-language question. Peano notes that English itself, formed from Saxon in contact with the Angles, has shed case, gender, and much of person and mood, and tends toward monosyllabism; history also offers the Lingua franca of Mediterranean ports, Pidgin in China, Urdu in India. The demand for a common tongue is real, he argues, because Russians, Poles, Rumanians, and Japanese now publish original work in their own languages, not merely schoolbooks. But adopting a living national language is politically impossible, and classical Latin, though proposed by Professor Valdarnini of Bologna and endorsed by a Roman congress that wished Latin held common among all nations, is a lost cause: the congressists themselves spoke Neo-Latin rather than classical Latin, and the periodicals promoting the idea—Phenix in London, Praeco latinus in Philadelphia—died in 1892 and 1902.
Artificial languages fare no better under his scrutiny. Couturat’s researches into Leibniz’s unpublished manuscripts, and the Couturat–Leau history cataloguing fifty-six projects, set the stage. Schleyer’s Volapük, published in 1881, was a transformation of English that regularized declension and conjugation but introduced no rational simplification and bristled with conventions; it briefly flourished—283 clubs and 25 periodicals worldwide by 1888—before discord over those conventions killed it after the Paris congress of 1889. Zamenhof’s Esperanto, published in 1887, simplifies gender and person but not case, number, or mood, and reduces grammar to sixteen rules, none of them necessary; Peano judges that it too follows the path of Volapük. He has warmer words for Henderson’s Lingua of 1888, a Latin vocabulary with English-type grammar, and for Dr. Daniel Rosa’s Le nov-latin, which requires no congress for adoption because anyone can write it at once with the given rules—a project close to Leibniz’s lingua rationale and to Peano’s own latino sine flexione.
The Detour Through Mathematics
The final movement turns from language to number, and the target is the “principle of permanence.” Some authors, Peano reports, introduce negative, fractional, and imaginary numbers by assigning a sense to every sign-combination, treating it by the old rules, calling it a number in the broad sense, and proving the old theorems still hold. Schubert states the principle this way in the Encyclopädie der Mathematischen Wissenschaften; Hankel speaks of the permanence of formal laws; Christal’s Algebra assumes a − b always exists and then demonstrates that commutation and association follow.
Peano’s objection is logical and decisive. If every property of narrow-sense numbers holds of broad-sense numbers, the two must be identical, since by Leibniz’s definition things are equal when one can be substituted for the other without loss of truth. Whenever the domain genuinely widens, some property is always dropped—a + b > a holds for absolute but not signed numbers, and commutativity of the product fails when passing from simple imaginaries to quaternions. To assume an absurdity, he adds, licenses any conclusion whatever. He cites Gauss, who said that applying triangle properties to an impossible triangle would be playing with words, or rather abusing them. What Peano will accept is the principle as advice rather than law: new notation should resemble the old as closely as possible—as similar as possible, not identical. The same economy that recommends uniform signs for algebraic sums and vector resultants, reducing Euclid’s Book X to a single lesson, is the economy Mach describes in linguistics, didactics, and politics alike. The book closes with the signature G. PEANO and a transcriber’s list of corrections to the original text.
One Logic Behind Language and Number
The two halves of the treatise are not as separate as they first appear. In both, Peano is asking what is genuinely necessary and what is inherited clutter. Cases, genders, and conjugations are conventions that can be dissolved into particles, word order, and adverbs; the principle of permanence is a convention dressed up as a law. His simplified Latin is built by the same method he demands of mathematicians—define the primitive terms, derive the rest, and refuse to smuggle in assumptions. The recurring appeal to Leibniz, who dreamed of both a rational grammar and a rational calculus, binds the project together.
The book also records a moment in the history of the auxiliary-language movement, when Esperanto was ascendant and its rivals were already predicting its decline. Peano’s own latino sine flexione would later be absorbed into the Interlingua tradition, and his critique of formalism in the foundations of mathematics places him among the precursors of the rigor that Hilbert and others would demand. What remains striking is the confidence of the enterprise: that a few pages of rules could make the learned world intelligible to itself again, and that the same economy of means could tidy both the grammar of speech and the grammar of number.
