ON THE APPLICATION OF LOGIC TO THE PROBLEM OF AN INTERNATIONAL LANGUAGE

The problem of an international language has a theoretical as well as a practical importance. I have no intention of discussing the latter here and of explaining once more the necessity of an auxiliary language for international relations of every sort, and the practical possibility of making oneself understood by means of an artificial language, a possibility which has been proved by experience. But an international language is also, according to the words of the celebrated philologist H. Schuchardt, a desideratum of science, in which connection it raises at once problems of philology and logic. That these problems are worthy of the study of scientific men is proved by the discussions of Professors Diels and Gomperz, the reports made to the Academy of Sciences of Leipzig by Professors Brugmann and Leskien, and, finally, the labours and decisions of the Committee of the DÉlÉgation pour l'Adoption d'une Langue Internationale. The latter, composed of highly competent scientists and linguists, has determined the principles necessary for an auxiliary language, and has practically realised them.

My desire in what follows is to show briefly the connection of the international language with logic, and its claims on the attention and interest of philosophers. In the words of Leibnitz, "Languages form the best mirror for the human spirit, and an exact analysis of the meaning and relationship of words would be the best means of disclosing the operations of the mind" (N. Essais, III., VII., end). But the majority of philosophers (with some distinguished exceptions, e.g., Professor Wundt) and the majority of linguists (also with some distinguished exceptions, e.g., M. BrÉal) have given little attention to the study of language from the point of view of psychology and logic. Now this study is particularly easy and interesting in the case of an artificial language, since the latter presents a structure analogous to that of our existing languages, but much simpler and more regular.

The words of the international language consist of invariable elements (morphemes) of three sorts: stems, derivative affixes (prefixes and suffixes), and grammatical inflections which, as in the case of European languages, are always final letters or final syllables. The stems themselves can be divided into two categories: verb stems, which express a state, action, or relation, e.g., dorm, parol, frap; and non-verbal or nominal stems, which denote an object (living being or thing), or express an aspect of it, e.g., hom, dom, bel, blind. The latter can produce directly only names (substantives or adjectives): man, house, beautiful, blind (in Ido, homo, domo, bela, blinda); the former, on the contrary, produce directly verbs: to sleep, to speak, to strike (in Ido, dormar, parolar, frapar), but they can also give rise to nouns: sleep, word, blow (in Ido, dormo, parolo, frapo). The proper rÔle of the grammatical terminations is to determine the grammatical function of a stem word and to indicate the category to which the word belongs, whether verb, substantive, or adverb. Thus parol-ar = to speak; parol-o = (spoken) word; parol-a = oral; parol-e = orally. The same idea, namely, that expressed by the stem word, always runs through the various categories. This follows from a principle which dominates the whole structure of the international language: "Every word element" (morpheme) "represents an elementary idea, which is always the same, so that a combination of elements has a meaning determined by the combination of the corresponding ideas." This principle is only a corollary to the general principle of uniqueness so clearly enunciated by Ostwald: "There exists a unique and reciprocal correspondence between the ideas and the morphemes which express them." This principle represents evidently the ideal of all language, for a language, being essentially a system of symbols, is only theoretically perfect (and useful and convenient in practice) when there exists a unique correspondence between the symbol and the idea symbolised.

Now it follows from this principle that it is quite incorrect to say, as is often done, "Being given a stem, it suffices to add to it -ar to form a verb, -o to form a substantive, -a to form an adjective"; we require to define the sense possessed by this verb, substantive, and adjective. In other words, to every derivative of form there must correspond a derivative of sense which is in no wise arbitrary, but determined by general rules. If dorm-ar = to sleep, dorm-o cannot mean indifferently the sleeper, the dormitory, or the desire to sleep; if blind-a = blind, blind-o cannot signify at pleasure either blindness or the act of blinding. The rule which must guide us here is the principle enunciated above, namely, that a stem always preserves the same sense and expresses the same idea; if one wishes to express another idea related to the former in a definite way, it is necessary to add to the stem a morpheme expressing this relationship. The morphemes which denote the relations of our ideas are the affixes of derivation, which permit us to express a whole family of ideas by the aid and as the function of one fundamental idea, and to form correspondingly a family of words all derived from the same stem, as occurs, as a matter of fact, in natural languages. Certain of these affixes are wrongly classed amongst the grammatical inflections, such as, for example, the participial suffixes which serve to derive an adjective or a substantive from a verb, denoting him who performs the action, or is affected by (subject to) the state or relationship expressed by the stem: dorm-ant-a = sleeping, arol-ant-a = speaking, whence, by simple change of the final letter, dorm-ant-o = sleeper, parol-ant-o = speaker. One will perceive thereby the difference between direct derivation, which is effected by means of the grammatical inflections, and indirect derivation, which is effected by means of the addition of affixes. There is nothing arbitrary about this distinction, for it rests on the logical principles enunciated above, which determine the theoretical and practical value of the international language.

From these principles follow at once the rules of direct derivation. If one starts from a verbal stem, what must be the sense of the substantive directly derived from it? This sense can be none other than the state or action expressed by the verb: dormar = to sleep, dormo = sleep; parolar = to speak, parolo = a word; frapar = to strike, frapo = a blow. In these derived words we perceive the sense of the verb stem, and the proof of that is that in our natural languages we often employ the infinitive for this purpose: le manger, le boire, le dormir, le rire; das rennen (in English the verbal in -ing is employed with the sense of the infinitive). Indeed, one might completely identify the verbal substantive with the infinitive.

If one starts from a substantival stem, what must be the relation between the adjective and substantive derived from it? They must necessarily have the same sense, whichever of the two one considers the primary word; if avara = avaricious, avaro = an avaricious person; if blinda = blind, blindo = a blind person. This rule is all the more necessary in practice as there are a crowd of substantival stems concerning which one could not say whether they produce at first a substantive or an adjective: vidva = widowed, vidvo = widower; nobela = noble, nobelo = nobleman; santa = holy, santo = a saint. This is particularly true of the names of followers of this or that doctrine: katoliko, katolika; skeptiko, skeptika, etc. No one would think of using any suffix to derive one of these words from the other. There is only a very slight difference of meaning between a katolika skeptiko and a skeptika katoliko, the substantive indicating in each case the primary and fundamental idea to which the other is superadded.

This brings us to the enunciation of the principle of reversibility, which may be formulated as follows: "Every derivation must be reversible; that is to say, if one passes from one word to another of the same family in virtue of a certain rule, one must be able to pass inversely from the second to the first in virtue of a rule which is exactly the inverse of the preceding." That is an evident corollary of the principle of uniqueness, for otherwise one would be led to give two meanings to the same word. Let us suppose, for example, that from the noun krono, = a crown, one imagines it possible to derive directly (as is the case in certain languages) the verb kronar = to crown. From this verb one could deduce inversely in virtue of the general rule the substantive krono = coronation, so that the same word krono would then mean both crown and coronation. That would be, however, a logical error inadmissible in the international language, however numerous may be the examples of it which occur in living languages. On the contrary, thanks to the principle of reversibility, one can proceed from any word whatsoever of a family and arrive at any other word of the same family, or return to the initial word, in an absolutely unique manner, whereas if one did not observe this principle one would inevitably obtain two meanings for the same word.

The principle of reversibility fixes the rules of direct derivation for the cases which are the converse of those we have studied. Just as the substantive directly derived from a verb denotes the state or action expressed by this verb (or, more strictly, by its root), so a verb can be derived directly from a substantive only if the latter expresses an action or a state. For example, paco = peace; can one form the verb pacar, and if so what will be its meaning? This verb can only signify one thing, to be in the state of peace, and not to pacify or make peace, for in that case paco would mean pacification or conclusion of peace, and not the state of peace. Similarly, if one can and must convert an adjective into a noun by the simple substitution of -o for -a, the adjective immediately derived from a substantive can only mean "what is —." If homo = a man (a human being), homa can only mean human in the sense of which is a man (human being); homa ento = a human being. But if one wishes to obtain an adjective signifying "which belongs to —," "which relates to —," "which depends on —," it is necessary to employ a suffix (-al): homala manuo = a human hand. One might equally well say manuo di homo = the hand of a man (human being). But just as the preposition di is indispensable for indicating the relationship between two ideas which are not simply juxtaposed, but depend on each other, so, if we wish to express one of the ideas in adjectival form, we require a suffix which also expresses this relation or dependence. Besides, a suffix of this nature exists under different forms in all our languages: G. -isch; E. -ic, -al, -ical; F. -ique, -al, -el; I. -ico; S. -ico. The choice of -al rather than -ik was determined by reasons of euphony and also internationality, the derivative adjectives employed in science (the most international of all) ending often in -al: mental, vocal, spatial; rationnel, universel, fonctionnel, etc.

In this connection we shall make a general remark. The international language borrows its stems from the European languages according to the principle of maximum internationality, i.e., adopts for each idea the most international stem, namely, that which is familiar to the greatest number of men. But it cannot, and must not, borrow their derivatives from living languages without losing all its theoretical and practical advantages, because the natural derivatives are too irregular. Sometimes the same affix has several different meanings; sometimes the same relationship is expressed by different affixes. In virtue of the principle of uniqueness, it is necessary to unify and regularise the meaning and employment of the affixes, assigning to each one a perfectly definite significance and function. Undoubtedly one must endeavour to adopt for the affixes forms which are international (as much as possible), or at least known in some language (like the suffix -in of the feminine, borrowed from the German, e.g., kÖnigin, and the prefix mal-, denoting "a contrary," borrowed from the French, e.g., malheureux), so as to reproduce as much as possible international derivatives. But it is chimerical to endeavour to reproduce them all, since they are irregular and consequently incompatible with that logical regularity of the language on which is based not only its fertility, but also its simplicity in practical use and its facility for all nationalities (even for non-European peoples who are not familiar with the anomalies and caprices of European languages). The international language must be autonomous in its formation of words; when the elements which it borrows from our languages have been once chosen (in the best possible manner), it must combine them freely according to its own rules, preserving their form and sense rigorously invariable. It is by virtue of this condition that it becomes a true language, richer in certain respects than our own, since it can form all the useful derivatives which are often wanting in one or the other, and not merely a simple imitation or copy of our languages, which would be as difficult as they, and which would require a previous knowledge of them.

We shall not explain here all the forms of indirect derivation, or enumerate the forty-seven affixes used for this purpose. We shall quote only a few of them for the sake of example, in order to show the application of the principles enunciated above. If there is one suffix which is particularly useful to philosophers, it is that which enables one to derive from an adjective the name of the corresponding abstract quality; that is the Greek suffix -otet and the Latin suffix -itat (-itud), whence have come the French -itÉ, the English -ity, the Italian -ita, the Spanish -itad; and the German suffix -heit or -keit, etc. We perceive here a logical relation well known and made use of in all our languages. It must find a place in the international language, but by what suffix ought it to be represented? Now, if one analyses the idea involved in this suffix, one will find that beauty, health, blindness, are simply the states or facts of being beautiful, healthy, blind. The idea involved in this suffix is then the idea of being, not the idea of existence, but the idea of being such and such, the idea of attribution which is expressed by the copula est. It is natural, therefore, to represent it by the Indo-European stem of the verb to be, namely, es; bel-es-o = beauty; san-es-o = health; blind-es-o = blindness. The fact that this suffix recalls a French suffix (richesse), an Italian suffix (bellezza), and an English suffix -ness (happiness) employed in the same sense can only serve as an accessory confirmation of the above choice, which was dictated by logical motives. Moreover, this agrees perfectly with our general rules; to be well will be translated by esar sana or san-esar, and the fact of being well will be saneso = health. Conversely, if we start from saneso = health, we can form the verb sanesar = to be in (good) health. Whatever may be the point of departure, there is no fear of making a mistake or "going off the rails" in forming these derivatives, if we observe the principle of reversibility. It would, therefore, be not only arbitrary, but absurd, to express health by sano, which latter can only mean a healthy being. For one must not imagine, as is often stated, that an adjective expresses a quality; it expresses precisely he who, or that which, possesses the quality in question. That is why all our languages employ a suffix for the purpose of deriving from an adjective the name of the corresponding quality.

But our languages often require to express the inverse relation, namely, that of the individual possessing a quality to that quality. For just as there are names of qualities which are derived from adjectives, as beautÉ, gaietÉ, bellezza, tapferkeit, gleichheit, so there are others which are primary and from which, therefore, the corresponding adjectives are derived: courage, courageux; joie, joyeux; beauty, beautiful; glÜck, glÜcklich; freude, freudig. And, as one sees, our languages employ in these cases a series of analogous suffixes. The international language must evidently imitate them, for it cannot decree that all the names of qualities shall be derivative, nor that they shall all be primary; that would amount to an arbitrary uniformity contrary to the spirit of our languages and probably also to our logical instincts. The international language must, therefore, have a suffix which will serve to derive from the name of a quality the name of the possessor of that quality. That will be -oz, a Latin suffix (formosus, generosus, etc.), occurring very frequently in the Romance and even Germanic languages (mysteriÖs, mysterious, mystÉrieux, misterioso). This suffix is the logical inverse of the preceding one (-es) and is quite as indispensable as it. It is a curious fact that our languages exhibit examples of the superposition of these two suffixes considered in respect of their sense, if not their form: glÜck, glÜcklich, glÜcklichkeit; beauty, beautiful, beautifulness. Latin has derived formosus from forma; Spanish in its turn has derived hermosura from hermoso, etc. Languages also provide us with frequent examples of the reciprocity of these suffixes.

The international language is, therefore, faithful not only to logic, but to the spirit of our languages, in admitting at the same time the two inverse derivations: gaya, gayeso; joyo, joyoza. A language which contained the suffix -es, and not the suffix -oz, would be lame or one-armed.

Besides, this lacuna would manifest itself very quickly in further derivations, for the latter would violate the principle of reversibility and therefore that of uniqueness. If from joyo were derived joya, from this adjective, analogous to gaya, one could derive inversely joyeso = joyo, thus producing two names for the same quality (just as above sano would have been synonymous with saneso). If from kurajo (courage) were derived kuraja (courageous), one could derive from the latter kurajeso, synonymous with kurajo. And, on the other hand, kurajo being the substantive of kuraja, this word would signify both courage and a courageous person. From want of a single suffix the whole series of derivations would become confused and illogical, just as in a chain of reasoning a single error, or in an algebraical calculation a single false equation, would lead to the most absurd conclusions.

To sum up, one must take care not to derive a word directly from another, except when they both express the same idea (apart from the difference of their grammatical rÔle in the sentence). Consequently, whenever the sense changes, a word element must be added or disappear, in order to translate the modification of the idea. It is by virtue of this condition that the language will become the exact and faithful expression of our thoughts, and will conform to that indwelling and instinctive logic which, in spite of all sorts of irregularities and exceptions, animates our languages. In its system of derivation as well as in the rest of its structure, the international language is nothing but a purified and idealised extract, a quintessence of the European languages. The logic which holds sway there is not the Aristotelian logic of genus and species, but rather that logic newly constituted under the name of the logic of relationships, which is, however, as old as the world, since it lies, though obscurely, at the basis of the formative processes in our natural languages. That is the reason why the international language offers to philosophers a particularly instructive field of study. It is worthy of their interest in other respects. Not only does it offer to them, as it does to all men, a medium of communication between all countries, but it furnishes them also with an instrument of precision for the analysis and exact expression of the forms of thought, which is very superior, from the point of view of logic, to our traditional languages, encumbered as these are with confused and ambiguous expressions. It is their duty to contribute to the development and perfecting of a language which, without losing anything of its practical qualities, can and must realise by degrees the ideal of human language; if it is true that there does exist an ideal in our languages, though hidden and irremediably disfigured by all sorts of anomalies. To quote a saying of Schuchardt, Was die Sprache gewollt haben die Sprachen zerstÖrt.[5]

L. Couturat.