The Principles of Logic

by Louis Couturat



It will not fail to have struck the reader of the preceding paragraphs that logical theories suggest at each step remarks of a grammatical nature. And this is natural, for, to put it briefly, language is but the vulgar and imperfect though the most usual expression of the thought of which Logic seeks to determine the laws. Nevertheless, the relations between Logic and language have been generally neglected by philosophers. If we are to be guided by their scholastic programmes, they are occupied at most with one sole question, i.e. the origin of language. This preoccupation corresponds to an absolutely false and superannuated conception of Philosophy, according to which the object of the latter is “the beginning and the end of things.” Such questions (in so far as they are at all soluble) evidently belong to the scientific and historical methods and have nothing really philosophical about them (unless by a confusion of ideas springing from the ambiguity of the word principium, “principle” is identified with beginning). It is equally childish to conceive the relations between Logic and language as do certain nominalists who maintain that Logic is based entirely on the forms of language and who do not even shrink from the extreme and absurd conclusion that there are as many logics as languages.

The true relation between Logic and language has been perfectly indicated by Leibniz: “Languages are the best mirror of the human mind, and an exact analysis of the signification of words would reveal to us, better than any thing else, the operations of the understanding.” [1] And he left among his manuscripts numerous attempts at a logical analysis of the forms of language. [2]

1 Nouveaux Essais, iii, vii. end.

2 See Opuscules et fragments inédits de Leibniz, edn. Couturat.


But this branch of research, at once positive and strictly philosophical, has been almost entirely neglected since his time. On the other hand, philologists are generally too preoccupied with the material and physiological part of language (phonetics), and even when they study its intellectual side (in Semantics or the Science of meaning), they are inclined to dwell on the more or less bizarre and illogical particularities (which certainly abound and jump to the eye) rather than to disengage the general features which manifest, in spite of all appearances to the contrary, that there is a latent logic in the formation and evolution of our languages. Philology is too exclusively historical and descriptive, too much in subjection to particular facts; it regards all attempts at appreciation as heresy, and is even averse to all theory. [1] Philologists lack the logical spirit which, essentially critical and normative, does not fear to criticize language by confronting it with its aim, i.e. the exact and complete expression of thought.

Words are signs for our ideas; they are signs like other signs, but more convenient than others, because they are at once oral and graphic, visible and audible; but still they have to satisfy the conditions which govern all signs. The first of these conditions evidently is that there should be a univocal correspondence between the sign and the idea signified; for every idea a single sign and for every sign a single idea. This is the principle of univocity, brought to light principally by Ostwald.

This principle is so evident that it seems little more than a hackneyed truism. But its bearing becomes apparent directly we apply it to the critical analysis of our languages. Every notion ought to be expressed in language once and once only (mere economy would counsel this, even if Logic did not). Now the notion of “plural” is repeated five times in the following phrase : “Les bons enfants sont obéissants”; four times by the plural of the article, the adjectives, and the noun, and once again in the plural form of the verb. Similarly the notion of “feminine” is expressed four times in the following phrase: “Une bonne mère est diligente”; once in the idea of mother itself (which ought to be sufficient), and three times more in the article and the adjectives. Again the notion of “person” is

1 This idolatrous respect for facts goes so far, with certain philologists, that they actually and definitely declare the dialect of any particular place to be good and normal. It is the apotheosis of usage erected into a sovereign and single norm.


always expressed twice in our languages, once by the pronoun (or noun) which is the subject, and a second time by the form of the verb. And here we light on the origin of these pleonasms: it resides in the evolution of our languages which proceeds (speaking roughly) from the synthetic to the analytic. Ancient languages, such as Latin, did not employ the subject-pronoun with the verb: the person was indicated by the verbal form itself (which had already absorbed a pronoun, witness to the primitive Greek endings: mi, si, ti . . .). As these verbal forms weakened and gradually became confused, it was felt necessary to indicate the person more precisely, and a separate pronoun was added, while, at the same time, the personal forms of the verb were preserved. [1] Similarly, case-endings tended at one period (to a certain degree) to replace prepositions themselves, and came from older agglutinated prepositions. But their meaning gradually became confused and faded, and this is why in the classical epoch the Latin of ordinary speech employed prepositions, even with the cases which did not require them. The idea was expressed twice. Nowadays case-endings have nearly disappeared from the Romance languages, the daughters of Latin, and are replaced (advantageously) by prepositions. [2] This is the final result of a logical evolution.

All this perfectly explains the pleonasms which encumber our languages, but does not justify them from the logical point of view. Moreover, we see that the popular and unconscious logic which presides over the evolution of our languages tends to eliminate progressively double uses and superfluities. Conscious logic, therefore, would only be anticipating natural evolution if it suppressed them from now onwards. By an inverse phenomenon, but in virtue of the same interior logic, our languages tend to create special words to express certain ideas which lack proper expression. For example, interrogation has, in our languages, no proper expression (such as have negation, doubt, etc.), except the inversion of the subject, which is an inconvenient and insecure proceeding. This is why many languages have forged special words or locutions to give special expression to this idea; for

1 It is a reduplicative phenomenon analogous to that which has engendered in French aujourd’hui (hui = hodie) and in vulgar French: au jour aujourd’hui!

2 Except in certain cases, e.g. “Je lui donne” and “Je donne à lui.” The form is a dative which becomes useless with the preposition à.


example, the English do (they no longer say, “dream I?” but, “do I dream ?”), the Danish mon, the French est-ceque. And in vulgar French a very convenient interrogative particle has made its appearance: ti, e.g. je sais-ti? jai-ti couru? (taken, by analogy, from the third person, est-il venu?) [1]

Thus the immanent logic of our languages ceaselessly tends to apply the principle of univocity, or at least of approximating to it. But it is constantly impeded by custom and tradition, i.e. by the secular products of evolution which every language bears within it. Our modern languages, even those most highly evolved, carry profound traces of prehistoric (and prelogical) mentality, and they will only disengage themselves from these very slowly and very incompletely. It is only in an artificial language that we can wipe out the past; only there could we apply in all its rigour the principle of univocity, and hope to realise the desiderata of Logic. Few people have an idea to what a degree of simplicity such a language could be reduced, while at the same time it would provide as adequately, and even more than do our traditional languages, all the elements necessary for the exact and precise expression of thought. [2]

It goes without saying that the principle of univocity should be applied not only to grammatical inflexions, but also to the meaning of separate words, especially to particles (prepositions and conjunctions). Few realise the clearness and precision which would characterise a language in which each particle had a perfectly definite meaning, and one only, whereas in all our languages every particle has a crowed of meanings and different uses, determined solely by caprice and ‘‘use.”

But it is above all in derivation, when it ought to be applied with the most rigour, that the principle of univocity is most constantly violated. [3] In principle nothing is more logical or more convenient than the system of derivation of the Indo-European languages; to roots expressing certain notions prefixes and suffixes are added which express certain constant and well-defined relations, the Atrides are the

1 See Jespersen, Progress in Language, p. 93 ff.

2 For example, it is perfectly logical and very convenient to have the three tenses not only in the indicative, but also in the infinitive and the participle; this gives resources comparable and superior to those of ancient Greek.

3 See Couturat, Étude sur la derivation dans la langue internationale (Paris: Delagrave, 1910).


descendants of Atreus, the Pelopides the descendants of Pelops, etc. Confronted with a few examples of this kind even the humblest and least logical mind would understand that id is the suffix which indicates descendant of. To draw this inference there is only required a feeling for analogy, which is the instructive and |popular form of logic. But before we can apply it to our prefixes and suffixes it is necessary, first, that they should be invariable in form, and secondly, invariable in sense. Now this is not the case in our languages; sometimes the same affix is employed in different senses, sometimes the same logical relation is expressed by different affixes. Mange-able, pot-able signify what can be eaten or drunk, but aim-able, admir-able, estim-able, respect-able signify what ought to be loved, admired, etc. . . . The names of professionals or artists are derived from a crowd of different suffixes: art-iste, dent-iste, pian-iste, serrur-ier, charpent-ier, bott-ier, pharmac-ien, char-ron, forger-on, etc. And the same suffixes, moreover, seem to indicate quite different relations: that which contains, encr-ier, plum-ier; the inhabitant of, Brésil-ien, Paris-ien. There are, it is true, partial series in which the analogy is carried out, but they cross one another and are confused together in such a way that the original regularity is no more apparent. It is evident that if the principle of univocity is to be respected, we must employ the same and only suffix (-ist) for the professional, another (-ny) for the recipient, another for the inhabitant (-an), and so on. A language so constructed would be infinitely clearer, more logical, and more regular than our “natural” languages. It is true it would be “artificial,” but neither more nor less so than the nomenclature of chemistry or many other technical terminologies.

The study of derivation (as it exists in Indo-European languages) leads us to establish an essential and fundamental distinction between two classes of words, or rather roots; nominal roots which signify beings or objects, and verbal roots which signify actions, states or relations. This distinction corresponds roughly to that of classes (concepts) and relations. [1] The second give rise directly to verbs: the first engender directly nouns, i.e. substantives or adjectives. This explains the close affinity between substantives and adjectives: a word

1 There are, it is true, nominal roots which express relation : père, chef, égal, semblable, etc. But they express it under the form of a quality inherent in an object, and hence again applicable to an object.


passes very easily from one class to another: avare, aveugle, veuve, (une) belle, (une) blonde, etc. On the other hand, the verbal roots form a class essentially distinct: dormir, parler, courir, aimer. It is true these words can be transformed into substantives: sommeil, parole, course, amour, but such substantives simply express the fact of sleeping, speaking, etc., they present the action under the form of an object (of a concept), stripped of the element of assertion which the verb implies. They are, in fact, equivalent to the infinitive which some languages substantify directly (das Rennen, das Sprechen, le manger, le boire, le dormir).

We are thus led to distinguish between immediate and mediate derivation: the latter is effected by means of affixes (prefixes or suffixes). In immediate derivation, when no affix appears, the root preserves its meaning (in virtue of the principle of univocity); and this is why an adjective becomes a substantive of the same meaning; and the verb also engenders immediately a substantive of the same meaning, i.e. expressing the verbal idea itself (to love, love; to esteem, esteem; to walk, walk). But the name of an object cannot be derived directly from a verb, nor a verb from the name of an object; this is evident, for they are heterogeneous notions. This logical consequence is confirmed by the comparative study of our languages; they all possess participles which are derived from the verbal root by means of some suffix. Now what is a participle? It is a noun derived from a verb, and this noun signifies in the active the subject doing the action, and in the passive, the object which suffers it. ‘‘Le mendiant est l’homme qui mendie; l’envoyé est l’homme qu’on envoie.” The same relation between noun and verb is indicated by other suffixes (chant-eur, expédit-eur, recev-eur). But a suffix is always necessary to derive these names from verbs, and they must not be confused with verbal substantives, which signify action (chant, envoi, etc.).

Inversely, we cannot immediately derive a verb from the name of an object, for the same logical reason: and it is here that our languages sin most frequently and most seriously against logic. Patronner = être patron, aveugler = rendre aveugle, couronner = orner d’^une couronne; saler = ajouter du sel; plumer = enlever les plumes; fleurir = (1) produire des fleurs, (2) garnir de fleurs, etc. In a word, these “immediate” derivations


express a crowd of diverse and even contrary relations. [1] This is contrary to the principle of univocity; in order to satisfy this principle each derivation having a special meaning must be effected by a special affix, or, more generally, to each element of the idea there must be a corresponding word-element. To be a patronn = patron-es-ar, to render blind is blind-igar, to provide with a crown or with salt is kron-izar, sal-izar, to produce flowers or fruit is flor-ifar, frukt-ifar (to fructify), to deprive of feathers means “to render featherless” and = sen-plum-igar, etc. Thus we obtain a perfect logical derivation, universally clear and hence international (in spite of the example to the contrary of our languages which swarm with idioms of derivation). Such a derivation ought to verify, and does as a matter of fact verify, the principle of reversibility, which is a corollary of the principle of univocity. This principle may be stated as follows: To every derivation of meaning there ought to be a corresponding derivation of form, i.e. the addition or suppression of an element of the word, for if we can pass from one word to another in virtue of a certain rule we ought to be able to pass from the second to the first in virtue of the inverse rule. For example (to quote the most important application of this principle) if the substantive immediately derived from a verb signifies action or state, inversely the verb derived immediately from a substantive can mean nothing but “to do that particular action” or “to be in that state.” Thus from paco = peace, we can derive the verb pacar = to be at peace; from muziko = music we can get muzikar = to make music; for what is the fact of being at peace, but peace; and the fact of making music, if not music? But from krono = crown, we cannot derive kronar = to crown, for from this verb we derive, inversely, krono = coronation, and we should then have two meanings for the same word. Similarly, from domo = home we cannot derive the verb domar = to stay at home, for then domo would mean the fact of staying at home. From bela (beautiful) we cannot derive belar = to be beautiful, for then belo would be beauty and not a beautiful being; and so on. We see that the principle of reversibility is a sure criterion (and practically a very convenient one) in verifying the logical value of a derivation.

1 We may add that these relations may differ between one language and another; e.g. Fr. documenter = provide with documents, while the German dokumentieren = to prove by documents.


But we must not turn aside here to discuss logical derivation in detail. There is one form of derivation, however, to which I should like to call the attention of philosophers: it is that which binds an adjective of quality to the noun of the same quality. It seems to certain minds (led astray as they are by the example of their national language) illogical that since bela means beautiful, beauty should be rendered by belo (i.e.bela substantified). But this is a serious error. Bela, like all qualifying adjectives, is a class-concept which applies to all beautiful individuals, but the abstract quality of “beautiful” is not a beautiful object, it is the fact of being beautiful; and just as to be beautiful must be expressed by bel-esar, and not belar, so the fact of being beautiful must be rendered bel-eso. Moreover, this is more conformable with the logic immanent in our languages, which all have a special suffix in order to derive abstract quality, e.g. G. Schön-heit, E. ill-ness, F. rich-esse, I. bell-ezza, etc. No doubt primitive languages did not have the verb to be, and expressed I am beautiful by Me beautiful. But the invention of the verb to be is one of the conquests of the logical spirit, and the more abstract this notion is the later its acquisition. To suppress or neglect this essential element of civilized language and the suffix which is its equivalent would be to mutilate logical thought. It is, moreover, this element which serves to transform a noun into an attributive verb, into a “predication.” Doubtless we must not take the traditional analysis literally. I sing = I am singing, according to which all verbs of action or state are transformed into attributive verbs. It is no less true that there is an equivalence (if not identity of meaning) between attributive verbs and the others.

The element es (root of the verb être) is the inverse or converse of the suffix of participles (when this is (-ant). For indeed, as we have seen, the latter serves inversely to transform a verb into a noun (qualifying adjective or substantive: parolanta = parlant, parolanto = orateuri.e. he who speaks). According to the analysis quoted above we have the following equivalence, me kant-as = me es-as kant-anta. If we abstract the elements common to the two members, we find: es + anta = o. This can be confirmed in another way: bel-esar = être beau (to be beautiful); bel-es-anta = étant beau (being beautiful) = beau (beautiful) = bela. Thus es + ant = o and these two elements cancel one another.


Moreover, the relative pronoun (qua) plays exactly the same role as the suffix of the participle, as is proved by the synonym: aimant = qui aime (lover = he who loves), chantant = qui chante. Consequently, it too is the reciprocal (réciproque) of the verb to be: qua esas bela = bela simply; qua and esas cancelling one another. As we have said, the effect of the relative pronoun is to transform a proposition into a concept, into an epithet: who speaks is the orator; who sings, the singer. It results from this that all adjectives can be immediately substantified; who is eternal is the Eternal (“who is” = o). Those classical but vague expressions, the beautiful, the good, the true, really mean what is beautiful, good, true, i.e. objects. We may say, after Plato, that these expressions signify the essence of the beautiful, the good, the true, in other words, the abstract qualities, beauty, goodness, truth (it matters little whether Plato did or did not conceive them as existing apart from beautiful, good, etc., objects; that does not affect their nature). Plato himself insisted on the point, paradoxical but evident after what we have said, that the beautiful in itself the essence of the beautiful, cannot be qualified as beautiful; it is not itself beautiful, but is that which causes to be beautiful, and is thus the cause or “form” of the beautiful.

We see that these essays at grammatical and logical analysis, disdained by certain philosophers, may sometimes, as Leibniz foresaw, penetrate to the intimate foundations of language and lead to the analysis of forms of thought. It is therefore no unworthy task for a philosopher to collaborate in the institution of a language which joins to the theoretical advantage of being logical and clear the immense practical advantage of being infinitely easier than any national language, of being “the easiest for the greatest number of men”; while it would also furnish us with an instrument of international communication more convenient and more perfect, in certain respects, than our languages. As that illustrious philologist, H. Schuchardt, has said, an international language is a scientific as well as a practical desideratum. Is not the language of the sciences to a great extent artificial? and is not every science obliged to elaborate its language in proportion to its development? Such a language, then, answers to the highest needs of the mind as well as to those of ordinary life; it tends to realize the ideal of human language at which our languages are only confused and complicated attempts,


according to the profound saying, “Was die Sprache gewollt, haben die Sprachen zerstört.” [1]

Can we doubt that existing languages realize only very imperfectly the ideal of language ? Language, too long regarded by certain savants with a superstitious and almost mystic respect, is, after all, nothing but one instrument (amongst others) of thought; thought can and ought to fashion and modify it according to its own needs and convenience, and if linguistics teaches us how languages have been, as a matter of fact, formed and evolved, Logic teaches us what language ought to be if it is to serve as an adequate expression of thought. Doubtless observation and an exact analysis of the forms of language can teach us much as to the mechanism of thought. But the human mind has the right to perfect this instrument, like all others, and to make it fit for the end it has to serve. Here Logic, like all the other sciences, can find a practical application, and while contributing to the elaboration of a language truly international and rational, may also further the amelioration of human life and the progress of civilization.

1 See La Langue intemationale et la science, by Couturat, Jespersen, Lorenz, Ostwald and Pfander (Paris: Delagrave, 1909). Weltsprache und Wissenschaft (Jena; G. Fischer, 1909). International Language and Science (London: Constable, 1910). Varldsspråk och Vetenskap (Stockholm: Bagge, 1910).

SOURCE:Couturat, Louis. “The Principles of Logic,” in Logic, by Arnold Ruge, Wilhelm Windelband, Josiah Royce, Louis Couturat, Benedetto Croce, Federigo Enriques and Nicolaj Losskij; translated by B. Ethel Meyer (London, Macmillan, 1913), pp. 136-198. This excerpt: section VI: Logic and Language, pp. 189-198.

Note: This Arnold Ruge (1881-1945) is not the Young Hegelian Arnold Ruge (1802-1880). The examples of the artificial language given here are from Ido, of which Couturat was a principal co-founder (1907). Ido was an offshoot and rival of Esperanto.

Histoire de la Langue Universelle
par Louis Couturat & Léopold Leau (1903)

Leibniz, Couturat kaj la Teorio de Ido” de Tazio Carlevaro

“Lingvoplanado” (Language Planning) de Rudolf Carnap

Antaŭparolo de Eugène de Zilah
al Diskurso pri la Metodo de Kartezio (René Descartes)

Philosophical and Universal Languages, 1600-1800, and Related Themes: Selected Bibliography

Esperanto & Interlinguistics Study Guide / Gvidilo al Esperanto & Interlingvistiko

Leibniz & Ideology: Selected Bibliography


Louis Couturat @ Ĝirafo

Louis Couturat - Wikipedia, the free encyclopedia

Louis Couturat - Vikipedio
(in Esperanto)

Louis Couturat - Wikipedio
(in Ido)

Louis Couturat, modern logic, and the international auxiliary language
by Başak ARAY

Opuscules et fragments inédits de Leibniz
, extraits des manuscrits de la Bibliothèque royale de Hanovre
par Louis Couturat (1903)

Histoire de la Langue Universelle
par Louis Couturat & Léopold Leau (1903)

Selected chapters of 1903 ed. also online here

Louis Couturat : The Logic of Leibniz

Chapter 3 The Universal Language

The Algebra of Logic
by Louis Couturat (1905, trans. 1914)

International Language and Science
by L. Couturat, O. Jespersen, R. Lorenz, W. Ostwald & L. Pfaundler (1910)
Also at Project Gutenberg

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