Leibnic
Posted: Sat Jul 04, 2009 1:31 pm
The Universal Language
1. Leibniz did not initially conceive of his characteristic as an algebra or calculus—doubtless because he was still "a novice in mathematics"1—but rather as a universal language or writing. This, in fact, is the first application he makes of his logical invention in On the Art of Combinations.2 It was no doubt suggested to him by various contemporary projects for a universal or international language, which he enumerates following Caspar Schott. One of these projects was conceived by an anonymous Spaniard (also cited by Kenelm Digby3) who had been in Rome in 1653. He had organized "things" (that is, concepts) into several classes and had numbered the classes and the concepts in each of them. He then designated each concept by the number of its class and by its number in that class. It is interesting to note that he was obliged to add to this two-digit number certain signs that would replace grammatical inflections and serve as a syntax (just as Leibniz was obliged to employ articles and prepositions in his attempt at a geometrical characteristic4); this shows that he had not analyzed the relations of concepts and did not know how to translate them into symbols.
Another attempt at a universal language was made by Johann Joachim Becher, a physician from Mainz.5 He had simply numbered (in alphabetical order) all the words in a Latin dictionary and created dictionaries in different languages in which the words were arranged according to the order of their numbers. In this way he established a correspondence between the vocabularies of different languages, so that a text written in numbers could be read and translated at will into any language by means of the corresponding lexicon.6
Finally, the third attempt Leibniz cites is that of Athanasius Kircher7 who had already had the idea of employing the art of combinations in his plan, though (as we shall see) in a far cruder fashion. He had composed a double dictionary in five languages (Latin, Italian, French, Spanish, and German). The first dictionary was intended for composition: the words of each language were arranged in alphabetical order and opposite each was found its translation into numbers. The second dictionary was intended for translation: the corresponding words of the five languages (those having the same meaning) were arranged on the same line in five parallel columns (according to the alphabetical order of the Latin words); when the lines on each page and the pages themselves were numbered, each word (or concept) was designated by the number of its page (in Roman numerals) and the number of its line (in Arabic numerals).8 If necessary, a sign or letter indicating the inflection of the word (for nouns, the case and number; for verbs, the voice, mood, tense, number, and person) were added to these two numbers. By means of this system—analogous to that of the anonymous Spaniard but more artificial—a text from any one of the five languages could be translated into numbers and, conversely, a text written in numbers could be translated with equal ease into any of the five languages.9
In an unpublished fragment, Leibniz summarizes an earlier project of Kircher, which appears to have been an outline for the preceding one.10 The dictionary (in only one language) consists of nine folio pages; each of these contains six columns, yielding 54 columns in all. Each column bears a distinctive character or sign and contains 30 words numbered in order. (This is followed by a list of the titles of the 54 columns and their signs.11) In order to designate a word, it is enough to indicate its number in a column and the sign of its column. This project shows a greater similarity to that of the anonymous Spaniard, the concepts being distributed into natural classes or logical categories.
It seems Kircher was not fully satisfied with either of these projects, for around 1670 he wrote to Leibniz that he was preparing a new work, to be entitled The Tower of Babel.12
2. On the whole, the various plans for a universal language with which Leibniz was acquainted at this time were fairly crude and scarcely merited the title of a language.13 They were, as we have seen, rather convention-based systems of writing, analogous to telegraphic codes or diplomatic ciphers, in which the correspondence between words and numbers was wholly arbitrary and artificial. Thus Leibniz clearly indicated the inadequacy of these systems, whose primary failing was the lack of any logical or philosophical basis and whose interest was merely practical. The ambiguity of the terms, which had several senses in each language; the lack of exact synonyms, so that the words of different languages never corresponded precisely with each other; the diversity of syntaxes, so that a sentence translated word for word became barbarous or unintelligible; and finally, the nuisance of constantly having to check a dictionary, the memory being unable to retain the numbers referring to all the words of a language—these were the principal shortcomings Leibniz rightly criticized in these ingenious, but in reality unworkable, projects.
The universal writing he envisioned would, on the contrary, be extremely simple to learn and easy to retain because it would rest on a logical foundation, namely, the complete analysis of concepts and their reduction to simple terms.14 Each simple term would be represented by a sign that was as natural and fitting as possible.15 In this way, one would construct a sort of ideographic alphabet, composed of as many symbols as there are elementary concepts or categories. Thereafter, each complex or derivative concept would be represented by the combination of signs that expressed its simple elements. As the simple concepts would be of a fairly small number, it would be enough to know the logical alphabet by heart in order to be able to read and understand at first sight a text written in this system without a dictionary.16
Thus, from the age of twenty, Leibniz had clearly conceived the plan of a universal and genuinely philosophical language that would surpass all the projects of which he knew, in that it was not only a stenography or cryptography but a logical pasigraphy and ideography.17
3. In the following years, Leibniz refined and developed his plan by comparing it and contrasting it with other contemporary projects that were somewhat more complete. This genre of invention appears to have been very much in vogue in the period. The plan of establishing a universal language that would replace all national languages, both in commerce between different nations and especially in the relations between the learned of Europe, clearly proceeds from the intellectual movement of the Renaissance, which in renewing philosophy and the sciences had revealed the fundamental unity of the human mind and had given birth to the idea of the international unity of all thinkers, so well captured in the expression "republic of letters." Furthermore, by freeing thought from the authority of the ancients and especially from the yoke of Aristotle, whose logic had reigned throughout the Middle Ages and still reigned in the Schools,18 the Renaissance had provided the stimulus for scientific investigations and consequently had given birth to the desire for a new logic, better suited to the needs of the new sciences.19 Reason became aware of its force and independence and strained to liberate itself from all the shackles of tradition and routine; men began to recognize that antiquity could be surpassed in its knowledge of the universe and to glimpse the possibility of an indefinite progress.20 The human mind finally became aware of its own unity and the unity of science. This whole great movement of ideas—this renewal of the sciences and the reform of logic that was both its condition and its consequence—must naturally have suggested the creation of a philosophical and scientific language more logical than ordinary languages, one that would be shared by all thinkers in every country.
4. We know that Descartes, having been informed by Mersenne of a plan for a universal language, gave his opinion on the matter in a famous letter. While criticizing the plan that had been submitted to him, he declared himself favorable in principle to the invention of a universal language and judged it possible. He even proposed adopting a logical principle for the creation of the vocabulary that closely resembles that of Leibniz: it would be necessary to set up a list of simple concepts, arrange them in order, and ascribe signs to them. Such a language would be at the same time a sort of logical instrument; however, its establishment "depends on the true philosophy," and that is one of the reasons Descartes believed it to be unrealizable in practice.21
It is unlikely that Leibniz knew of Descartes's letter when he wrote On the Art of Combinations, but he certainly was aware of it later (although we cannot ascertain precisely when), for among his manuscripts there is a copy (in a secretary's hand) of the part of the letter in which Descartes points to the logical foundation on which the universal language would have to be erected. Leibniz adds a personal remark to this copy in which he maintains that if the establishment of this language depends on the true philosophy, it does not depend on its completion or perfection; in other words, it rests on the first principles of the sciences but does not presuppose their completion.22 On the contrary, it will be developed and perfected along with the sciences, whose instrument it will be. With this, Leibniz answers in advance the main objection that might have been made at any time to philosophical languages based on the analysis of concepts. In any case, despite the similarity of Leibniz's project to that outlined by Descartes, it does not appear to have been derived from it. It seems rather that the two philosophers may have been in agreement, and such an accord is all the more remarkable.
5. The inspiration that led Leibniz to refine and develop the system sketched in On the Art of Combinations came from another source. Projects for a universal language seem to have especially flourished at this time in England, in the circle of learned men who founded the Royal Society of London. One of them, John Wilkins,23 had already published a work entitled Mercury, which appears to have been no more than a handbook for secret correspondence.24 But this work then suggested to George Dalgarno a better and more philosophical system.25 In theory, this system consisted of distributing every concept into one of 17 basic classes or categories, each of which was designated by a letter that served as an initial for the corresponding words. Each class was then divided into subclasses designated by the same initial letter and distinguished from each other by the addition of a second letter. Finally, in each subclass there were gathered a number of words characterized by the same letters and distinguished by variations in a final letter.26 This was, in short, a logical classification of concepts expressed by words that were formed systematically, in an arbitrary order, and which played the role of conventional indices or markers.27
It is evident that Dalgarno's plan constituted not only a system of correspondence and translation but a complete and universal language and system of writing. Wilkins in turn responded to this system and improved on it in a new work.28 In place of the 17 first-order classes, he counted 40, but instead of designating them by letters, he represented them by conventional symbols and expressed the subdivisions (differences and divisions) by marks added to the left and right of the symbol for the class.29 Leibniz preferred a language that could be written with ordinary letters. He thus found Wilkins's signs useless and tedious.30
6. Leibniz learned of Wilkins's new book at the beginning of 1671,31 and he appears to have found it much to his liking, for he repeatedly expressed his desire to see it translated into Latin.32 Nevertheless, while approving of the systems of Dalgarno and Wilkins, which had in his eyes the advantage of being at the same time spoken and written languages,33 he indicated clearly what he thought they lacked in a note inscribed in his copy of Ars Signorum.34 He criticizes these systems for focusing on practical uses rather than scientific utility, that is, for being chiefly artificial languages intended for international communication and not philosophical languages that would express the logical relations of concepts. He favors, and opposes to them, the true "real characteristic," which would express the composition of concepts by the combination of signs representing their simple elements, such that the correspondence between composite ideas and their symbols would be natural and no longer conventional.
He further defined his project and intentions in a letter to Oldenburg, composed during his sojourn in Paris (1673-1676).35 He elevates his "rational writing" well above previous attempts, saying that the least of its advantages would be to underwrite commerce between nations; thus he subordinates its practical utility to its logical utility as the "instrument of reason."36 He next explains what he understands by a real characteristic,37 offering as examples Egyptian and Chinese hieroglyphics38 and chemical signs.39 This shows that the real characteristic was for him an ideography, that is, a system of signs that directly represent things (or, rather, ideas) and not words, in such a way that each nation could read them and translate them into its own language. It would be at once a system of writing and a language, each sign being given a unique conventional name,40 yet this writing also could be read in different languages, just as Chinese can.41
7. Such were the ideas Leibniz had about the universal language during his stay in Paris and which he announced to Oldenburg and his colleagues at the Royal Society of London. In May 1676, he once again identified the universal language with the characteristic and dreamed of a language that would also be a calculus—a sort of algebra of thought.42 For this, he had only to develop the principle laid down in On the Art of Combinations. Since all concepts are combinations of simple ideas, and the composition of concepts analogous to the composition of numbers from prime factors, it was natural to take the prime factors as symbols for the simple ideas and numerical multiplication as a symbol for the combination of concepts (that is, for the adjunction of their contents). This analogy was familiar to Leibniz and he developed it freely. The prime numbers are, so to speak, categories in relation to their multiples: the multiples of 2 are the binaries, the multiples of 3 the ternaries, the multiples of 6 the senaries, and so on. Since every multiple of 6 is also a multiple of 2 and 3, every senary is a binary-ternary, just as 6 is the product of 2 and 3.43 In order to express that man is a rational animal, one would represent (for example) animal by 2, rational by 3, and man by 6, giving the numerical equality 6 = 2 x 3, which corresponds to the logical equality Man = animal x rational.
This was the principle of the first logical calculus Leibniz conceived.44 He stated it in February 1678 in a fragment entitled A General Language,45 and he took it as the basis of a plan for a universal language.46
In order to transform this characteristic into a spoken and written language, it would suffice to translate the numbers into words by a method similar to that of Dalgarno. The method of translation envisaged by Leibniz is as follows: The first nine consonants (b, c, d, f, g, h, l, m, n) would represent the nine significant digits, and the five vowels (a, e, i, o, u) would represent powers of 10 in ascending order (1, 10, 100, 1,000, 10,000). One could if necessary extend the series by means of diphthongs (again following the example of Dalgarno). In order to state or write a number, it would be enough to take the consonants that correspond to its successive digits, following each by the vowel which indicates its power of 10. Thus the number 81,374 would be written and pronounced mubodilefa.
The advantage of this notation over Dalgarno's lay in the fact that each syllable signifies (through its vowel) its power of ten, so that its value is independent of its position in the word, which can be easily altered. Thus the same number would be expressed just as well by the word bodifalemu, which literally signifies 1000 + 300 + 4 + 70 + 80000 = 81374.
Leibniz found great satisfaction in the possibility of rearranging all the syllables of a word; in his view this would render the artificial language more agreeable and harmonious and would offer marvelous opportunities for poetry and music. He even showed how one could translate it into music, using intervals.47 He believed one could compose "very beautiful" poems and chants in the language by an infallible and quasi-demonstrative method, with everything determined.48 We see that from here on, Leibniz borrowed his ideal of logic and even his aesthetic from mathematics.
8. He soon perceived, however, that the problem was more difficult and more complex than he initially believed. As an alternative to creating a priori and out of nothing a purely conventional language, he adopted a less arbitrary and more measured a posteriori method. He took as a point of departure living languages and extracted from them by logical analysis, on the one hand, simple ideas to express and combine, and on the other, a rational grammar, by simplifying, regularizing, and blending together the grammars of different languages. He set to work in April 1678, intending to reduce speech to the terms strictly necessary for the expression of thought, in order to discover the simple and primitive elements of thought itself.49 He outlined his plan in a fragment dated 11 September 1678:50 his aim was still the analysis of thought, but this analysis could be facilitated and even replaced by the analysis of characters, that is, the sensible signs of thought, of which the principal one is language. The analysis of language consists of resolving all the elements of speech into simpler terms by means of definitions; when these terms can be decomposed no further, one explains them, indicating their sense by means of equivalent terms. These irreducible terms are, in general, all the elements of speech that cannot be defined by decomposition: namely, words (with the exception of compound words), colloquial expressions, and those sentences and formulas, like proverbs, whose sense is established by use and cannot be explained by grammatical analysis. Next, one studies the syntax, that is, the different ways of assembling and combining the elements of speech, and consequently inflections (declensions and conjugations) and particles. One also must submit inflections and particles to analysis by reducing them to the simplest elements possible. It is necessary to define and distinguish with care their different senses, as there are homonyms among the inflections and particles, so that each inflection and each particle of the universal language has a unique and determinate sense. One must likewise reduce anomalies (grammatical and syntactical irregularities) to standard forms, thereby constructing a rational grammar that is absolutely regular and free of exceptions.51
9. Yet, as the establishment of a rational grammar must necessarily precede that of the universal language to which it is destined to be applied,52 Leibniz needed an auxiliary idiom that would provisionally play the role of a universal language and serve as an intermediary between living languages and the future rational language.
Latin was the obvious choice for this role, since it was the common language of the learned and consequently the idiom most suited to the sciences and philosophy.53 Leibniz planned first to construct a universal Latin grammar that would unite all the resources and advantages of other languages, notably genders, cases, moods and tenses, so as to provide every distinction and nuance that any language can express.54 At the same time, this philosophical grammar would be purged of every irregularity and exception that taints actual grammars, with the result that it would be both simpler and richer than any other. In this way, each of these grammars, including that of Latin, would be only a part of the philosophical grammar, at least insofar as they are regular. As we have said, this grammar would be applied provisionally to Latin and would constitute an absolutely regular Latin grammar.55 One would likewise first apply to Latin the method of analysis and reduction described above. For example, intransitive verbs would be replaced by paraphrases. In place of "the Lord needs these things," one would say, "the Lord wants to have these things, since without them he cannot bring about something that is necessary," which gives the definition of the verb "to need." In general, one would translate or paraphrase every complex locution, every indirect expression, and every idiom in order to reduce them to simple and direct terms (for example, active verbs).56 In doing so, one would even simplify the vocabulary by suppressing all words having a complicated or opaque meaning.
10. This was still only the first step in the simplification of grammar. Leibniz regarded the plurality of declensions and conjugations as superfluous, even when reduced to regular types. Therefore, the rational language would contain only one declension and one conjugation, both completely uniform.57 Likewise, the distinction of gender is useless and can be dropped without inconvenience.58 These suppressions leave the rational language much easier to comprehend than actual languages, whose principal difficulty consists in the diversity of genders, declensions, and conjugations.59 Conjugation itself can be simplified considerably, for distinctions of person and number are unnecessary: they are adequately shown by the subject.60 These sorts of pleonasms seem to be designed to remedy the inattention of listeners by repeating the same meaning twice.61 As for nouns, Leibniz goes so far as to deprive them of the distinction of number, no doubt believing that it can be shown by an article or adjective (e.g., some, several, all).62 With greater reason, he strips adjectives of inflection, since they serve only to repeat the inflections of the corresponding noun.63
11. The only inflections that remain are case for nouns and tense and mood for verbs. However, in general, inflections and particles play the same role in grammar and can be substituted for one another, since both express the coordination of words and sentences, the relations of concepts and propositions.64 Synthetic languages tend to employ inflections, whereas analytic languages use particles. Initially, Leibniz seems to have hesitated between these two systems: one either translates all the inflections of Latin by analogous inflections of the rational language or, carrying the analysis of grammatical relations to its conclusion, reduces all inflections to particles (for example, cases would be replaced by the nominative preceded by different prepositions). Later, however, he inclined toward the latter course, which is more in keeping with the analytic ideal of the rational language, and he preferred an analytic language like French to a synthetic language like Latin.65
Leibniz therefore attempted to do away with inflections wherever possible. He first noted that prepositions govern cases, just as conjunctions govern moods. Again, there are two options: either the cases and moods allow us to dispense with prepositions and conjunctions, or prepositions and conjunctions render cases and moods useless. Leibniz preferred the second alternative, for the reason that there are many more prepositions than cases and many more conjunctions than moods; consequently, one cannot render by inflections the variety of relations that can be expressed by particles.66 For example, what good is the distinction between the indicative and subjunctive governed by quod and ut respectively, given that these two conjunctions differ like the intellect and the will, the one signifying what is, the other what one wishes may be?67 Thus Leibniz appears to want to suppress any distinction of mood, as well as any distinction of case.68 Nevertheless, he does preserve a single oblique case elsewhere. It seems that this would have to be the accusative, the only case that cannot be replaced by a preposition. But this case itself is reduced to the genitive when the verb is converted into a verbal noun by grammatical analysis: "I praise Titus" becomes "I am a praiser of Titus."69
In verbs, there remains only the distinction of tense, which is essential to them. Nevertheless, Leibniz was not afraid to criticize the traditional definition of the verb, which goes back to Aristotle—"The verb is a word that signifies time"—by showing that nouns too can signify time: for example, participles, which are nouns (or adjectives) derived from verbs.70 The distinction of tense can also be applied to nouns,71 adjectives, and even adverbs.72 As a consequence, Leibniz rejected the Aristotelian distinction between nouns and verbs and very sensibly replaced it with the following: a noun expresses an idea; a verb expresses a proposition (an affirmation or negation).73 Into the class of nouns are drawn not only nouns and adjectives but also pronouns, particles, and adverbs.
12. Leibniz attempted to reduce still further the parts of speech by seeking to replace some with others. First, adjectives are only distinguished from nouns because their gender can change, but if one does away with this difference, they are identical.74 Nor do degrees of comparison define adjectives, for they are equally applicable to nouns, pronouns,75 and even verbs.76 The only possible logical difference between adjectives and nouns is that the latter imply the idea of substance or being; therefore, any noun is equivalent to an adjective accompanied by the word "being" or "thing."77 On the other hand, all verbs can be reduced to the single substantive verb "to be" and adjectives: "Peter writes, that is: is writing."78 Likewise, adverbs can be reduced to adjectives, since in a way they are to verbs what adjectives are to substantives, and serve to qualify the verb.79 Instead of saying, "I drink deeply," one may say: "I am a great drinker," in which the verb is replaced by a substantive and the adverb by an adjective.80
In the end, all speech can be reduced to the single substantive noun "being" or "thing," the substantive verb "is," adjectival nouns (expressing qualities), and particles, which serve to join all the preceding words together and to indicate their relations.81 One could therefore form every noun and verb derivatively from roots that indicate simple ideas, either substantival or verbal. Hebrew employs verbs as roots; Leibniz preferred nouns, undoubtedly because they naturally give rise to verbs.82 In order to establish the vocabulary it would suffice, on the one hand, to form a lexicon of the roots, and on the other, to draw up a list of endings that would serve to form the derivatives, each of which would have a unique and well-defined sense.83
13. This is the method for forming words in the strictest sense (nouns and verbs); it remains to consider the particles, to determine their number and their sense. This is not the least critical phase in the establishment of a language, for Leibniz regarded particles as playing an extremely important role in language: they constitute the form of a language,84 and determine its syntax, operation, and physiognomy. They are the frames or molds into which the variable matter of discourse, represented by words, comes to be cast. Thus Leibniz exercised an uncommon care in the analysis of particles and of their sense and function.85 These particles include not only prepositions and conjunctions but also many words classified without reason among the adverbs, notably adverbs of time, place, and interrogation, which have nothing in common with genuine qualifiers, such as adverbs of manner.86 Leibniz has an ingenious theory concerning prepositions.87 According to him, all prepositions primitively signify some relation of place, and it is by metaphor that they subsequently come to designate relations of every sort. This principle or hypothesis provided him with a method for classifying and logically defining all prepositions in terms of whether they do or do not involve the idea of movement.
Again, Leibniz added to this a priori method for constructing particles an a posteriori method, by enumerating the various Latin particles, analyzing them, defining them, and classifying them.88 It is likely that he did not see an essential difference between prepositions and conjunctions,89 any more than between prepositions and adverbs of place and time, which differ only in their lack of an explicit antecedent.
14. An analysis of inflections obviously must be added to the analysis of particles, since these play the same syntactical role. Thus Leibniz attempted to analyze the various cases and replace them with paraphrases from which they would be excluded. He was chiefly concerned with analyzing the genitive, to which, as we have seen, he rigorously reduced all the other cases; it was for him the paradigm of obliquity, since it appeared to him to express the simplest relation.90 This relation consists of uniting one substantive with another in order to determine it, that is, to make its sense precise and specific. The sword of Evander is the sword that Evander possesses; the reading of poets is the act by which one reads poets. But this inversion does not succeed everywhere: "Paris is the lover of Helen" means "Paris is a lover insofar as Helen is loved"; likewise, "This sword is the sword of Evander" means "This sword is an instrument insofar as Evander is an owner."91 Leibniz discovered in this way that the genitive in fact expresses very different relations: relations of whole to part ("the man's hand"); of cause to effect ("the man's son"); of possesser to possessed ("the man's horse"); and of subject to predicate ("the man's title").92 It is the same for the dative and the ablative. Thus in order to express the different cases and eliminate their obliquity, one must break the proposition up into two others related by a conjunction such as "insofar as."
Using the same method, Leibniz also attempted to analyze judgments of comparison. Consider, for example, the proposition "Titus is wiser than Caius." It is analyzed as follows: "Insofar as Titus is wise and Caius is wise, Titus is superior and Caius inferior"; or better still, "Titus is wise and as such superior, insofar as Caius is wise and as such inferior."93
15. This grammatical analysis of inflections and particles had, as we have seen, a logical significance, especially since Leibniz thought that certain inferences (from the direct to the oblique), which Jungius had shown not to be reducible to syllogisms, could not be demonstrated in any other way.94 This is why he always considered grammatical analysis (or characteristic) as an indispensable prelude to logical analysis (or characteristic).95 Among the oblique inferences, which depend on grammar rather than logic,96 Leibniz cites the inversion of relations, which Jungius had catalogued in his Tabula de Dianoea,97 and of which he gives the following examples: "David is the father of Solomon, and therefore Solomon is the son of David"98; "Peter is similar to Paul, and therefore Paul is similar to Peter."99 All of these non-syllogistic consequences, which can only be demonstrated in ordinary languages by the analysis of terms and the substitution of the definition for the defined, would become demonstrable in an immediate and intuitive way through the very composition of the words used to express the relations.100 This is the ideal of the universal language: to express concepts by characters that render their composition and their relations manifest and transparent[/b].101
16. This brings us to the establishment of the vocabulary of the universal language, to which the rules of the philosophical grammar must at last be applied. We have seen how Leibniz sought to simplify grammar and syntax as much as possible, in order to render them truly logical and hence universal. One would first translate the sentences of any language into a simplified and standardized Latin, and then from this Latin into the rational language. Undoubtedly the paraphrases that would have to be given for complex thoughts would entail the elimination of certain nuances and would render speech prolix and often flat, but Leibniz deliberately sacrificed the elegance and brevity of language for precision and conciseness of thought.102
Just as the analysis of particles and inflections by means of paraphrases uncovers the primitive logical relations, so the analysis of concepts by means of the definition of words reduces them to simple notions; just as the first is the indispensable basis for the grammar and syntax of the philosophical language, so the second serves as the logical foundation for its vocabulary. It is not a question, as it was in the attempts of Leibniz's predecessors, of assigning to each word a conventional and arbitrary substitute, but of finding a natural expression for each idea that conveys its logical composition and constitutes, so to speak, its formula. This is what we arrive at by means of definition, for to define an idea is to reduce it to simpler ideas and, finally, to absolutely simple and irreducible ideas, if we can continue the reduction by substituting in every case a new definition in place of the defined. With this done, we form the "character" of each idea from the characters that designate each of its elements.
Thus the name of each thing (or, rather, of each idea) would express its definition, and as all the properties of a thing follow logically from its definition, the name of a thing will be the key to all its properties.103 This does not prevent the same thing from having several other names, insofar as it possesses different properties.104 However, there will be one that is the key to all the others: the one that expresses the complete reduction of the idea into simple elements.105 All this is explained by the combinatory, which always serves as a basis for the characteristic: the formula of a concept that is in any way complex can be reduced to "factors" in a variety of ways, but there is only one reduction to "prime factors," that is, to simple elements, and it is the latter that serve as the foundation and explanation of the others.
Such a nomenclature, in which the name of each thing (or idea) would be an adequate and transparent symbol for it and, as it were, its description or logical portrait, would clearly constitute a sort of natural language, such as Plato dreamed of in the Cratylus. It would be the Adamic language, as it was called by mystics,106 that is, the nomenclature that, according to Hebraic legend, the first man established in the terrestrial paradise and which men spoke until the confusion of languages at the Tower of Babel.107
17. We have seen how the idea of a universal language was developed and elaborated as Leibniz investigated its details more deeply. It was no longer a question of a kind of disguised arithmetic whose use would require constant mental calculation,108 but of a genuine spoken and written language, with sentences formed from nouns, verbs, and particles as in ordinary languages and capable of being written with ordinary letters.109 Thus, when in 1680 Leibniz planned to present a fragment of his philosophical language by applying it to geometry, he announced that he would employ the inflections, particles, and constructions of Latin and would be content to invent new names to express the generation of figures and hence their construction or definition.110 And he was so far from conceiving of this language as a sort of calculus that he expressly declared, "But I will mix nothing of calculus in this." He excludes all considerations of magnitude, equality, and proportion, which are common to arithmetic and geometry, and limits himself to the study of points, lines, angles, intersections, contacts, and movements, in a word, what are today called the projective properties of figures.111 He thus hoped to be able to carry out all geometrical reasoning without figures and without calculation, using only the logical connections of concepts and the corresponding words. Such is the character of the universal language. Without a doubt it is always a logical and "rational" language, which serves as an aid and instrument for thought. However, it is no longer a logical algebra, and the proof of this is that the calculus ratiocinator is henceforth developed in parallel, yet in an absolutely independent manner, in the guise of a genuine algebra and not a spoken and written language.112
18. Leibniz was therefore led by the very progress of his project for a universal language, or rather by the development of the idea that was its principle, to surpass it. In order to construct the "alphabet of human thoughts" that was to be the foundation of the vocabulary, it would be necessary to analyze every concept and to reduce them to their simplest elements by means of definition.113 But this would amount to making an inventory of human knowledge or even, as the analysis of concepts is at the same time the analysis of truths, to demonstrating all known truths by reducing them to simple and self-evident principles, that is, to constructing a demonstrative encyclopedia. On the other hand, once the primitive concepts were tallied and classified, it would be necessary to represent them with appropriate characters and to invent signs to express their combinations and relations. This was properly the work of the universal characteristic.114
Thus the true universal, or rather philosophical, language presupposed at once this huge, twofold labor: the establishment of a characteristic and the elaboration of an encyclopedia. These two enterprises in turn involve one another and must be carried out in tandem, for the characteristic assumes that all scientific notions have been reduced to a logical system and brought under a small number of categories; it assumes, that is, that the encyclopedia has been completed or at least well advanced. The characteristic, on the other hand, appears indispensable to the establishment of the encyclopedia, for it serves to determine the logical connection of scientific truths and even the hierarchical order of the sciences.115 In order to escape this vicious circle, the characteristic and encyclopedia would have to be elaborated in parallel and at the same pace. Leibniz understood perfectly the necessary connection between the two parts of his project, which was not the least of its difficulties.116 For the moment it is enough to note this connection and to emphasize the comprehensive plan of this huge undertaking. For the sake of clarity in our exposition, we are obliged to study the characteristic and the encyclopedia separately and successively, not forgetting, however, the bond that unites them.
1. Leibniz did not initially conceive of his characteristic as an algebra or calculus—doubtless because he was still "a novice in mathematics"1—but rather as a universal language or writing. This, in fact, is the first application he makes of his logical invention in On the Art of Combinations.2 It was no doubt suggested to him by various contemporary projects for a universal or international language, which he enumerates following Caspar Schott. One of these projects was conceived by an anonymous Spaniard (also cited by Kenelm Digby3) who had been in Rome in 1653. He had organized "things" (that is, concepts) into several classes and had numbered the classes and the concepts in each of them. He then designated each concept by the number of its class and by its number in that class. It is interesting to note that he was obliged to add to this two-digit number certain signs that would replace grammatical inflections and serve as a syntax (just as Leibniz was obliged to employ articles and prepositions in his attempt at a geometrical characteristic4); this shows that he had not analyzed the relations of concepts and did not know how to translate them into symbols.
Another attempt at a universal language was made by Johann Joachim Becher, a physician from Mainz.5 He had simply numbered (in alphabetical order) all the words in a Latin dictionary and created dictionaries in different languages in which the words were arranged according to the order of their numbers. In this way he established a correspondence between the vocabularies of different languages, so that a text written in numbers could be read and translated at will into any language by means of the corresponding lexicon.6
Finally, the third attempt Leibniz cites is that of Athanasius Kircher7 who had already had the idea of employing the art of combinations in his plan, though (as we shall see) in a far cruder fashion. He had composed a double dictionary in five languages (Latin, Italian, French, Spanish, and German). The first dictionary was intended for composition: the words of each language were arranged in alphabetical order and opposite each was found its translation into numbers. The second dictionary was intended for translation: the corresponding words of the five languages (those having the same meaning) were arranged on the same line in five parallel columns (according to the alphabetical order of the Latin words); when the lines on each page and the pages themselves were numbered, each word (or concept) was designated by the number of its page (in Roman numerals) and the number of its line (in Arabic numerals).8 If necessary, a sign or letter indicating the inflection of the word (for nouns, the case and number; for verbs, the voice, mood, tense, number, and person) were added to these two numbers. By means of this system—analogous to that of the anonymous Spaniard but more artificial—a text from any one of the five languages could be translated into numbers and, conversely, a text written in numbers could be translated with equal ease into any of the five languages.9
In an unpublished fragment, Leibniz summarizes an earlier project of Kircher, which appears to have been an outline for the preceding one.10 The dictionary (in only one language) consists of nine folio pages; each of these contains six columns, yielding 54 columns in all. Each column bears a distinctive character or sign and contains 30 words numbered in order. (This is followed by a list of the titles of the 54 columns and their signs.11) In order to designate a word, it is enough to indicate its number in a column and the sign of its column. This project shows a greater similarity to that of the anonymous Spaniard, the concepts being distributed into natural classes or logical categories.
It seems Kircher was not fully satisfied with either of these projects, for around 1670 he wrote to Leibniz that he was preparing a new work, to be entitled The Tower of Babel.12
2. On the whole, the various plans for a universal language with which Leibniz was acquainted at this time were fairly crude and scarcely merited the title of a language.13 They were, as we have seen, rather convention-based systems of writing, analogous to telegraphic codes or diplomatic ciphers, in which the correspondence between words and numbers was wholly arbitrary and artificial. Thus Leibniz clearly indicated the inadequacy of these systems, whose primary failing was the lack of any logical or philosophical basis and whose interest was merely practical. The ambiguity of the terms, which had several senses in each language; the lack of exact synonyms, so that the words of different languages never corresponded precisely with each other; the diversity of syntaxes, so that a sentence translated word for word became barbarous or unintelligible; and finally, the nuisance of constantly having to check a dictionary, the memory being unable to retain the numbers referring to all the words of a language—these were the principal shortcomings Leibniz rightly criticized in these ingenious, but in reality unworkable, projects.
The universal writing he envisioned would, on the contrary, be extremely simple to learn and easy to retain because it would rest on a logical foundation, namely, the complete analysis of concepts and their reduction to simple terms.14 Each simple term would be represented by a sign that was as natural and fitting as possible.15 In this way, one would construct a sort of ideographic alphabet, composed of as many symbols as there are elementary concepts or categories. Thereafter, each complex or derivative concept would be represented by the combination of signs that expressed its simple elements. As the simple concepts would be of a fairly small number, it would be enough to know the logical alphabet by heart in order to be able to read and understand at first sight a text written in this system without a dictionary.16
Thus, from the age of twenty, Leibniz had clearly conceived the plan of a universal and genuinely philosophical language that would surpass all the projects of which he knew, in that it was not only a stenography or cryptography but a logical pasigraphy and ideography.17
3. In the following years, Leibniz refined and developed his plan by comparing it and contrasting it with other contemporary projects that were somewhat more complete. This genre of invention appears to have been very much in vogue in the period. The plan of establishing a universal language that would replace all national languages, both in commerce between different nations and especially in the relations between the learned of Europe, clearly proceeds from the intellectual movement of the Renaissance, which in renewing philosophy and the sciences had revealed the fundamental unity of the human mind and had given birth to the idea of the international unity of all thinkers, so well captured in the expression "republic of letters." Furthermore, by freeing thought from the authority of the ancients and especially from the yoke of Aristotle, whose logic had reigned throughout the Middle Ages and still reigned in the Schools,18 the Renaissance had provided the stimulus for scientific investigations and consequently had given birth to the desire for a new logic, better suited to the needs of the new sciences.19 Reason became aware of its force and independence and strained to liberate itself from all the shackles of tradition and routine; men began to recognize that antiquity could be surpassed in its knowledge of the universe and to glimpse the possibility of an indefinite progress.20 The human mind finally became aware of its own unity and the unity of science. This whole great movement of ideas—this renewal of the sciences and the reform of logic that was both its condition and its consequence—must naturally have suggested the creation of a philosophical and scientific language more logical than ordinary languages, one that would be shared by all thinkers in every country.
4. We know that Descartes, having been informed by Mersenne of a plan for a universal language, gave his opinion on the matter in a famous letter. While criticizing the plan that had been submitted to him, he declared himself favorable in principle to the invention of a universal language and judged it possible. He even proposed adopting a logical principle for the creation of the vocabulary that closely resembles that of Leibniz: it would be necessary to set up a list of simple concepts, arrange them in order, and ascribe signs to them. Such a language would be at the same time a sort of logical instrument; however, its establishment "depends on the true philosophy," and that is one of the reasons Descartes believed it to be unrealizable in practice.21
It is unlikely that Leibniz knew of Descartes's letter when he wrote On the Art of Combinations, but he certainly was aware of it later (although we cannot ascertain precisely when), for among his manuscripts there is a copy (in a secretary's hand) of the part of the letter in which Descartes points to the logical foundation on which the universal language would have to be erected. Leibniz adds a personal remark to this copy in which he maintains that if the establishment of this language depends on the true philosophy, it does not depend on its completion or perfection; in other words, it rests on the first principles of the sciences but does not presuppose their completion.22 On the contrary, it will be developed and perfected along with the sciences, whose instrument it will be. With this, Leibniz answers in advance the main objection that might have been made at any time to philosophical languages based on the analysis of concepts. In any case, despite the similarity of Leibniz's project to that outlined by Descartes, it does not appear to have been derived from it. It seems rather that the two philosophers may have been in agreement, and such an accord is all the more remarkable.
5. The inspiration that led Leibniz to refine and develop the system sketched in On the Art of Combinations came from another source. Projects for a universal language seem to have especially flourished at this time in England, in the circle of learned men who founded the Royal Society of London. One of them, John Wilkins,23 had already published a work entitled Mercury, which appears to have been no more than a handbook for secret correspondence.24 But this work then suggested to George Dalgarno a better and more philosophical system.25 In theory, this system consisted of distributing every concept into one of 17 basic classes or categories, each of which was designated by a letter that served as an initial for the corresponding words. Each class was then divided into subclasses designated by the same initial letter and distinguished from each other by the addition of a second letter. Finally, in each subclass there were gathered a number of words characterized by the same letters and distinguished by variations in a final letter.26 This was, in short, a logical classification of concepts expressed by words that were formed systematically, in an arbitrary order, and which played the role of conventional indices or markers.27
It is evident that Dalgarno's plan constituted not only a system of correspondence and translation but a complete and universal language and system of writing. Wilkins in turn responded to this system and improved on it in a new work.28 In place of the 17 first-order classes, he counted 40, but instead of designating them by letters, he represented them by conventional symbols and expressed the subdivisions (differences and divisions) by marks added to the left and right of the symbol for the class.29 Leibniz preferred a language that could be written with ordinary letters. He thus found Wilkins's signs useless and tedious.30
6. Leibniz learned of Wilkins's new book at the beginning of 1671,31 and he appears to have found it much to his liking, for he repeatedly expressed his desire to see it translated into Latin.32 Nevertheless, while approving of the systems of Dalgarno and Wilkins, which had in his eyes the advantage of being at the same time spoken and written languages,33 he indicated clearly what he thought they lacked in a note inscribed in his copy of Ars Signorum.34 He criticizes these systems for focusing on practical uses rather than scientific utility, that is, for being chiefly artificial languages intended for international communication and not philosophical languages that would express the logical relations of concepts. He favors, and opposes to them, the true "real characteristic," which would express the composition of concepts by the combination of signs representing their simple elements, such that the correspondence between composite ideas and their symbols would be natural and no longer conventional.
He further defined his project and intentions in a letter to Oldenburg, composed during his sojourn in Paris (1673-1676).35 He elevates his "rational writing" well above previous attempts, saying that the least of its advantages would be to underwrite commerce between nations; thus he subordinates its practical utility to its logical utility as the "instrument of reason."36 He next explains what he understands by a real characteristic,37 offering as examples Egyptian and Chinese hieroglyphics38 and chemical signs.39 This shows that the real characteristic was for him an ideography, that is, a system of signs that directly represent things (or, rather, ideas) and not words, in such a way that each nation could read them and translate them into its own language. It would be at once a system of writing and a language, each sign being given a unique conventional name,40 yet this writing also could be read in different languages, just as Chinese can.41
7. Such were the ideas Leibniz had about the universal language during his stay in Paris and which he announced to Oldenburg and his colleagues at the Royal Society of London. In May 1676, he once again identified the universal language with the characteristic and dreamed of a language that would also be a calculus—a sort of algebra of thought.42 For this, he had only to develop the principle laid down in On the Art of Combinations. Since all concepts are combinations of simple ideas, and the composition of concepts analogous to the composition of numbers from prime factors, it was natural to take the prime factors as symbols for the simple ideas and numerical multiplication as a symbol for the combination of concepts (that is, for the adjunction of their contents). This analogy was familiar to Leibniz and he developed it freely. The prime numbers are, so to speak, categories in relation to their multiples: the multiples of 2 are the binaries, the multiples of 3 the ternaries, the multiples of 6 the senaries, and so on. Since every multiple of 6 is also a multiple of 2 and 3, every senary is a binary-ternary, just as 6 is the product of 2 and 3.43 In order to express that man is a rational animal, one would represent (for example) animal by 2, rational by 3, and man by 6, giving the numerical equality 6 = 2 x 3, which corresponds to the logical equality Man = animal x rational.
This was the principle of the first logical calculus Leibniz conceived.44 He stated it in February 1678 in a fragment entitled A General Language,45 and he took it as the basis of a plan for a universal language.46
In order to transform this characteristic into a spoken and written language, it would suffice to translate the numbers into words by a method similar to that of Dalgarno. The method of translation envisaged by Leibniz is as follows: The first nine consonants (b, c, d, f, g, h, l, m, n) would represent the nine significant digits, and the five vowels (a, e, i, o, u) would represent powers of 10 in ascending order (1, 10, 100, 1,000, 10,000). One could if necessary extend the series by means of diphthongs (again following the example of Dalgarno). In order to state or write a number, it would be enough to take the consonants that correspond to its successive digits, following each by the vowel which indicates its power of 10. Thus the number 81,374 would be written and pronounced mubodilefa.
The advantage of this notation over Dalgarno's lay in the fact that each syllable signifies (through its vowel) its power of ten, so that its value is independent of its position in the word, which can be easily altered. Thus the same number would be expressed just as well by the word bodifalemu, which literally signifies 1000 + 300 + 4 + 70 + 80000 = 81374.
Leibniz found great satisfaction in the possibility of rearranging all the syllables of a word; in his view this would render the artificial language more agreeable and harmonious and would offer marvelous opportunities for poetry and music. He even showed how one could translate it into music, using intervals.47 He believed one could compose "very beautiful" poems and chants in the language by an infallible and quasi-demonstrative method, with everything determined.48 We see that from here on, Leibniz borrowed his ideal of logic and even his aesthetic from mathematics.
8. He soon perceived, however, that the problem was more difficult and more complex than he initially believed. As an alternative to creating a priori and out of nothing a purely conventional language, he adopted a less arbitrary and more measured a posteriori method. He took as a point of departure living languages and extracted from them by logical analysis, on the one hand, simple ideas to express and combine, and on the other, a rational grammar, by simplifying, regularizing, and blending together the grammars of different languages. He set to work in April 1678, intending to reduce speech to the terms strictly necessary for the expression of thought, in order to discover the simple and primitive elements of thought itself.49 He outlined his plan in a fragment dated 11 September 1678:50 his aim was still the analysis of thought, but this analysis could be facilitated and even replaced by the analysis of characters, that is, the sensible signs of thought, of which the principal one is language. The analysis of language consists of resolving all the elements of speech into simpler terms by means of definitions; when these terms can be decomposed no further, one explains them, indicating their sense by means of equivalent terms. These irreducible terms are, in general, all the elements of speech that cannot be defined by decomposition: namely, words (with the exception of compound words), colloquial expressions, and those sentences and formulas, like proverbs, whose sense is established by use and cannot be explained by grammatical analysis. Next, one studies the syntax, that is, the different ways of assembling and combining the elements of speech, and consequently inflections (declensions and conjugations) and particles. One also must submit inflections and particles to analysis by reducing them to the simplest elements possible. It is necessary to define and distinguish with care their different senses, as there are homonyms among the inflections and particles, so that each inflection and each particle of the universal language has a unique and determinate sense. One must likewise reduce anomalies (grammatical and syntactical irregularities) to standard forms, thereby constructing a rational grammar that is absolutely regular and free of exceptions.51
9. Yet, as the establishment of a rational grammar must necessarily precede that of the universal language to which it is destined to be applied,52 Leibniz needed an auxiliary idiom that would provisionally play the role of a universal language and serve as an intermediary between living languages and the future rational language.
Latin was the obvious choice for this role, since it was the common language of the learned and consequently the idiom most suited to the sciences and philosophy.53 Leibniz planned first to construct a universal Latin grammar that would unite all the resources and advantages of other languages, notably genders, cases, moods and tenses, so as to provide every distinction and nuance that any language can express.54 At the same time, this philosophical grammar would be purged of every irregularity and exception that taints actual grammars, with the result that it would be both simpler and richer than any other. In this way, each of these grammars, including that of Latin, would be only a part of the philosophical grammar, at least insofar as they are regular. As we have said, this grammar would be applied provisionally to Latin and would constitute an absolutely regular Latin grammar.55 One would likewise first apply to Latin the method of analysis and reduction described above. For example, intransitive verbs would be replaced by paraphrases. In place of "the Lord needs these things," one would say, "the Lord wants to have these things, since without them he cannot bring about something that is necessary," which gives the definition of the verb "to need." In general, one would translate or paraphrase every complex locution, every indirect expression, and every idiom in order to reduce them to simple and direct terms (for example, active verbs).56 In doing so, one would even simplify the vocabulary by suppressing all words having a complicated or opaque meaning.
10. This was still only the first step in the simplification of grammar. Leibniz regarded the plurality of declensions and conjugations as superfluous, even when reduced to regular types. Therefore, the rational language would contain only one declension and one conjugation, both completely uniform.57 Likewise, the distinction of gender is useless and can be dropped without inconvenience.58 These suppressions leave the rational language much easier to comprehend than actual languages, whose principal difficulty consists in the diversity of genders, declensions, and conjugations.59 Conjugation itself can be simplified considerably, for distinctions of person and number are unnecessary: they are adequately shown by the subject.60 These sorts of pleonasms seem to be designed to remedy the inattention of listeners by repeating the same meaning twice.61 As for nouns, Leibniz goes so far as to deprive them of the distinction of number, no doubt believing that it can be shown by an article or adjective (e.g., some, several, all).62 With greater reason, he strips adjectives of inflection, since they serve only to repeat the inflections of the corresponding noun.63
11. The only inflections that remain are case for nouns and tense and mood for verbs. However, in general, inflections and particles play the same role in grammar and can be substituted for one another, since both express the coordination of words and sentences, the relations of concepts and propositions.64 Synthetic languages tend to employ inflections, whereas analytic languages use particles. Initially, Leibniz seems to have hesitated between these two systems: one either translates all the inflections of Latin by analogous inflections of the rational language or, carrying the analysis of grammatical relations to its conclusion, reduces all inflections to particles (for example, cases would be replaced by the nominative preceded by different prepositions). Later, however, he inclined toward the latter course, which is more in keeping with the analytic ideal of the rational language, and he preferred an analytic language like French to a synthetic language like Latin.65
Leibniz therefore attempted to do away with inflections wherever possible. He first noted that prepositions govern cases, just as conjunctions govern moods. Again, there are two options: either the cases and moods allow us to dispense with prepositions and conjunctions, or prepositions and conjunctions render cases and moods useless. Leibniz preferred the second alternative, for the reason that there are many more prepositions than cases and many more conjunctions than moods; consequently, one cannot render by inflections the variety of relations that can be expressed by particles.66 For example, what good is the distinction between the indicative and subjunctive governed by quod and ut respectively, given that these two conjunctions differ like the intellect and the will, the one signifying what is, the other what one wishes may be?67 Thus Leibniz appears to want to suppress any distinction of mood, as well as any distinction of case.68 Nevertheless, he does preserve a single oblique case elsewhere. It seems that this would have to be the accusative, the only case that cannot be replaced by a preposition. But this case itself is reduced to the genitive when the verb is converted into a verbal noun by grammatical analysis: "I praise Titus" becomes "I am a praiser of Titus."69
In verbs, there remains only the distinction of tense, which is essential to them. Nevertheless, Leibniz was not afraid to criticize the traditional definition of the verb, which goes back to Aristotle—"The verb is a word that signifies time"—by showing that nouns too can signify time: for example, participles, which are nouns (or adjectives) derived from verbs.70 The distinction of tense can also be applied to nouns,71 adjectives, and even adverbs.72 As a consequence, Leibniz rejected the Aristotelian distinction between nouns and verbs and very sensibly replaced it with the following: a noun expresses an idea; a verb expresses a proposition (an affirmation or negation).73 Into the class of nouns are drawn not only nouns and adjectives but also pronouns, particles, and adverbs.
12. Leibniz attempted to reduce still further the parts of speech by seeking to replace some with others. First, adjectives are only distinguished from nouns because their gender can change, but if one does away with this difference, they are identical.74 Nor do degrees of comparison define adjectives, for they are equally applicable to nouns, pronouns,75 and even verbs.76 The only possible logical difference between adjectives and nouns is that the latter imply the idea of substance or being; therefore, any noun is equivalent to an adjective accompanied by the word "being" or "thing."77 On the other hand, all verbs can be reduced to the single substantive verb "to be" and adjectives: "Peter writes, that is: is writing."78 Likewise, adverbs can be reduced to adjectives, since in a way they are to verbs what adjectives are to substantives, and serve to qualify the verb.79 Instead of saying, "I drink deeply," one may say: "I am a great drinker," in which the verb is replaced by a substantive and the adverb by an adjective.80
In the end, all speech can be reduced to the single substantive noun "being" or "thing," the substantive verb "is," adjectival nouns (expressing qualities), and particles, which serve to join all the preceding words together and to indicate their relations.81 One could therefore form every noun and verb derivatively from roots that indicate simple ideas, either substantival or verbal. Hebrew employs verbs as roots; Leibniz preferred nouns, undoubtedly because they naturally give rise to verbs.82 In order to establish the vocabulary it would suffice, on the one hand, to form a lexicon of the roots, and on the other, to draw up a list of endings that would serve to form the derivatives, each of which would have a unique and well-defined sense.83
13. This is the method for forming words in the strictest sense (nouns and verbs); it remains to consider the particles, to determine their number and their sense. This is not the least critical phase in the establishment of a language, for Leibniz regarded particles as playing an extremely important role in language: they constitute the form of a language,84 and determine its syntax, operation, and physiognomy. They are the frames or molds into which the variable matter of discourse, represented by words, comes to be cast. Thus Leibniz exercised an uncommon care in the analysis of particles and of their sense and function.85 These particles include not only prepositions and conjunctions but also many words classified without reason among the adverbs, notably adverbs of time, place, and interrogation, which have nothing in common with genuine qualifiers, such as adverbs of manner.86 Leibniz has an ingenious theory concerning prepositions.87 According to him, all prepositions primitively signify some relation of place, and it is by metaphor that they subsequently come to designate relations of every sort. This principle or hypothesis provided him with a method for classifying and logically defining all prepositions in terms of whether they do or do not involve the idea of movement.
Again, Leibniz added to this a priori method for constructing particles an a posteriori method, by enumerating the various Latin particles, analyzing them, defining them, and classifying them.88 It is likely that he did not see an essential difference between prepositions and conjunctions,89 any more than between prepositions and adverbs of place and time, which differ only in their lack of an explicit antecedent.
14. An analysis of inflections obviously must be added to the analysis of particles, since these play the same syntactical role. Thus Leibniz attempted to analyze the various cases and replace them with paraphrases from which they would be excluded. He was chiefly concerned with analyzing the genitive, to which, as we have seen, he rigorously reduced all the other cases; it was for him the paradigm of obliquity, since it appeared to him to express the simplest relation.90 This relation consists of uniting one substantive with another in order to determine it, that is, to make its sense precise and specific. The sword of Evander is the sword that Evander possesses; the reading of poets is the act by which one reads poets. But this inversion does not succeed everywhere: "Paris is the lover of Helen" means "Paris is a lover insofar as Helen is loved"; likewise, "This sword is the sword of Evander" means "This sword is an instrument insofar as Evander is an owner."91 Leibniz discovered in this way that the genitive in fact expresses very different relations: relations of whole to part ("the man's hand"); of cause to effect ("the man's son"); of possesser to possessed ("the man's horse"); and of subject to predicate ("the man's title").92 It is the same for the dative and the ablative. Thus in order to express the different cases and eliminate their obliquity, one must break the proposition up into two others related by a conjunction such as "insofar as."
Using the same method, Leibniz also attempted to analyze judgments of comparison. Consider, for example, the proposition "Titus is wiser than Caius." It is analyzed as follows: "Insofar as Titus is wise and Caius is wise, Titus is superior and Caius inferior"; or better still, "Titus is wise and as such superior, insofar as Caius is wise and as such inferior."93
15. This grammatical analysis of inflections and particles had, as we have seen, a logical significance, especially since Leibniz thought that certain inferences (from the direct to the oblique), which Jungius had shown not to be reducible to syllogisms, could not be demonstrated in any other way.94 This is why he always considered grammatical analysis (or characteristic) as an indispensable prelude to logical analysis (or characteristic).95 Among the oblique inferences, which depend on grammar rather than logic,96 Leibniz cites the inversion of relations, which Jungius had catalogued in his Tabula de Dianoea,97 and of which he gives the following examples: "David is the father of Solomon, and therefore Solomon is the son of David"98; "Peter is similar to Paul, and therefore Paul is similar to Peter."99 All of these non-syllogistic consequences, which can only be demonstrated in ordinary languages by the analysis of terms and the substitution of the definition for the defined, would become demonstrable in an immediate and intuitive way through the very composition of the words used to express the relations.100 This is the ideal of the universal language: to express concepts by characters that render their composition and their relations manifest and transparent[/b].101
16. This brings us to the establishment of the vocabulary of the universal language, to which the rules of the philosophical grammar must at last be applied. We have seen how Leibniz sought to simplify grammar and syntax as much as possible, in order to render them truly logical and hence universal. One would first translate the sentences of any language into a simplified and standardized Latin, and then from this Latin into the rational language. Undoubtedly the paraphrases that would have to be given for complex thoughts would entail the elimination of certain nuances and would render speech prolix and often flat, but Leibniz deliberately sacrificed the elegance and brevity of language for precision and conciseness of thought.102
Just as the analysis of particles and inflections by means of paraphrases uncovers the primitive logical relations, so the analysis of concepts by means of the definition of words reduces them to simple notions; just as the first is the indispensable basis for the grammar and syntax of the philosophical language, so the second serves as the logical foundation for its vocabulary. It is not a question, as it was in the attempts of Leibniz's predecessors, of assigning to each word a conventional and arbitrary substitute, but of finding a natural expression for each idea that conveys its logical composition and constitutes, so to speak, its formula. This is what we arrive at by means of definition, for to define an idea is to reduce it to simpler ideas and, finally, to absolutely simple and irreducible ideas, if we can continue the reduction by substituting in every case a new definition in place of the defined. With this done, we form the "character" of each idea from the characters that designate each of its elements.
Thus the name of each thing (or, rather, of each idea) would express its definition, and as all the properties of a thing follow logically from its definition, the name of a thing will be the key to all its properties.103 This does not prevent the same thing from having several other names, insofar as it possesses different properties.104 However, there will be one that is the key to all the others: the one that expresses the complete reduction of the idea into simple elements.105 All this is explained by the combinatory, which always serves as a basis for the characteristic: the formula of a concept that is in any way complex can be reduced to "factors" in a variety of ways, but there is only one reduction to "prime factors," that is, to simple elements, and it is the latter that serve as the foundation and explanation of the others.
Such a nomenclature, in which the name of each thing (or idea) would be an adequate and transparent symbol for it and, as it were, its description or logical portrait, would clearly constitute a sort of natural language, such as Plato dreamed of in the Cratylus. It would be the Adamic language, as it was called by mystics,106 that is, the nomenclature that, according to Hebraic legend, the first man established in the terrestrial paradise and which men spoke until the confusion of languages at the Tower of Babel.107
17. We have seen how the idea of a universal language was developed and elaborated as Leibniz investigated its details more deeply. It was no longer a question of a kind of disguised arithmetic whose use would require constant mental calculation,108 but of a genuine spoken and written language, with sentences formed from nouns, verbs, and particles as in ordinary languages and capable of being written with ordinary letters.109 Thus, when in 1680 Leibniz planned to present a fragment of his philosophical language by applying it to geometry, he announced that he would employ the inflections, particles, and constructions of Latin and would be content to invent new names to express the generation of figures and hence their construction or definition.110 And he was so far from conceiving of this language as a sort of calculus that he expressly declared, "But I will mix nothing of calculus in this." He excludes all considerations of magnitude, equality, and proportion, which are common to arithmetic and geometry, and limits himself to the study of points, lines, angles, intersections, contacts, and movements, in a word, what are today called the projective properties of figures.111 He thus hoped to be able to carry out all geometrical reasoning without figures and without calculation, using only the logical connections of concepts and the corresponding words. Such is the character of the universal language. Without a doubt it is always a logical and "rational" language, which serves as an aid and instrument for thought. However, it is no longer a logical algebra, and the proof of this is that the calculus ratiocinator is henceforth developed in parallel, yet in an absolutely independent manner, in the guise of a genuine algebra and not a spoken and written language.112
18. Leibniz was therefore led by the very progress of his project for a universal language, or rather by the development of the idea that was its principle, to surpass it. In order to construct the "alphabet of human thoughts" that was to be the foundation of the vocabulary, it would be necessary to analyze every concept and to reduce them to their simplest elements by means of definition.113 But this would amount to making an inventory of human knowledge or even, as the analysis of concepts is at the same time the analysis of truths, to demonstrating all known truths by reducing them to simple and self-evident principles, that is, to constructing a demonstrative encyclopedia. On the other hand, once the primitive concepts were tallied and classified, it would be necessary to represent them with appropriate characters and to invent signs to express their combinations and relations. This was properly the work of the universal characteristic.114
Thus the true universal, or rather philosophical, language presupposed at once this huge, twofold labor: the establishment of a characteristic and the elaboration of an encyclopedia. These two enterprises in turn involve one another and must be carried out in tandem, for the characteristic assumes that all scientific notions have been reduced to a logical system and brought under a small number of categories; it assumes, that is, that the encyclopedia has been completed or at least well advanced. The characteristic, on the other hand, appears indispensable to the establishment of the encyclopedia, for it serves to determine the logical connection of scientific truths and even the hierarchical order of the sciences.115 In order to escape this vicious circle, the characteristic and encyclopedia would have to be elaborated in parallel and at the same pace. Leibniz understood perfectly the necessary connection between the two parts of his project, which was not the least of its difficulties.116 For the moment it is enough to note this connection and to emphasize the comprehensive plan of this huge undertaking. For the sake of clarity in our exposition, we are obliged to study the characteristic and the encyclopedia separately and successively, not forgetting, however, the bond that unites them.