Filum Cogitationis. Remarks on Leibnizian Projects of a Universal Language

Home , Louis Couturat

STUDIES IN LOGIC, GRAMMAR AND RHETORIC 62 (75) 2020 DOI: 10.2478/slgr-2020-0016 This work is licensed under a Creative Commons Attribution BY 4.0 License (http://creativecommons.org/licenses/by/4.0)

Halina Święczkowska University of Białystok e-mail: [email protected] ORCID: 0000–0002–8702–3760

FILUM COGITATIONIS. REMARKS ON LEIBNIZIAN PROJECTS OF A UNIVERSAL LANGUAGE

Abstract. This essay is an attempt to oﬀer at least a partial answer to the question concerning Leibniz’s motivation for the need to create a universal language. It is relevant, among other things, due to Leibniz’s claim which contradicts the idea of a universal language, in which he clearly stresses that “every language, even the poorest one, can express everything”, as well as owing to Leibniz’s historical contribution to the idea of formalization and to the mechanization of the reasoning processes. This paper is also an attempt to reconstruct the paradigm of language research pursued in a speciﬁc period of time in 17th century language theory. Keywords: G. W. Leibniz, the universal language, philosophy of language.

Leibniz as a philosopher of language is still only partially recognized in the history of philosophy. Sometimes, one can be under the impression that his contributions to research on language is either neglected or marked as insigniﬁcant (Guiraud, 1972, p. 100). Also, complete silence about Leibniz’s linguistic theory in Chomsky’s (1966) works could be treated as surprising. Hence, it would certainly be more correct to label the Cartesian linguistics as Leibnizian. For several decades as evidenced by literature, there has been an increased interest in the 17th and 18th century linguistic development and research. Interestingly, polish literature relating to this period in the history of the philosophy of language is limited. Moreover, Leibniz is known for being a theoretician and a philosopher of language to a small group of “insiders”, to which undoubtedly belongs Professor Anna Wierzbicka. Wierzbicka in the mid-seventies of the 20th century pioneered in her research concerning the tradition of modern semantics by analyzing its Leibnizian roots (1975, pp. 108–126). Gottfried Wilhelm Leibniz, the creator of one of the largest modern philosophical systems, deserves our attention as a theoretician of language

ISSN 0860-150X 113 Halina Święczkowska for several reasons. To start, his studies on the cognitive aspects of the linguistic sign functions and his theories on the role of the sign in the reasoning process are milestones in the language philosophy and should be treated as such. It has to be highlighted, that the Leibnizian theory of cognition rests to a large extent on the linguistic foundation. Next, Leibniz is a representative of material linguistics. He is the author of many studies and dissertations in which he analyzes the origin of language and genealog- ical classification of world languages. By emphasizing the culture-forming nature of language, the philosopher investigated the functions of language in the life of an individual and society (Święczkowska, 2008; 2016). For the most part, Leibniz is recognized as one of the originators of the idea of a universal language, the idea that accompanied him since the very in- ception of his scientific pursuits. Undoubtedly, this idea was entrenched in the philosophical system the philosopher was building. It may be assumed that the successive Leibnizian projects that were aimed at implementing the idea specified above also resulted from the intensive research on existing language systems, which the philosopher considered broadly. Para- doxically, although Leibniz has been associated with the idea of the perfect language he never went beyond his preliminary sketches and tenta- tive comments on the project. Hence, it is worth inquiring into the reasons justifying the need for creating such a language and the goals that Leib- niz wanted to achieve with it. This essay is an attempt to offer at least a partial answer to the question concerning Leibniz’s motivation for the need to create a universal language as well as Leibniz’s claims contradict- ing the idea of a universal language. In said claims he clearly stresses that “every language, even the poorest one, can express everything” (C, 352)1. The paper also recognizes and highlights Leibniz’s historical contribution to the idea of formalization and to the mechanization of the reasoning processes (Marciszewski & Murawski, 1955, pp. 103–113). This paper is also an attempt to reconstruct the paradigm of the research into language as conducted in a specific period of time in the 17th century language theory.

1. Which came ﬁrst – the true language or true philosophy?

In a letter to M. Mersenne dated November 20th 1629, Descartes (AT, I, 76–82)2 provided comments on the project of a universal language by an individual later known as Hardy, who in a leaﬂet disseminated in Paris laid out six postulates on the structure of such language and the tasks

114 Filum cogitationis. Remarks on Leibnizian projects of a universal language it would complete. Descartes was not fully satisfied with the project, with his remarks being very critical. The author of the project intended the postulated language to be a quasi-natural language with a simplified regular grammar and a dictionary in which every word would form a true definition of things. This language, easy to master, would be a reference point for other languages in the sense that existing ethnic languages would become its dialects. It would also serve as a means to convey thoughts in both speech and writing which would be more effective as compared to other languages. It is noteworthy that although based on different principles than presented by Hardy, Descartes to some extent allowed the possibility of constructing a universal language. In sum, although Descartes remained in op- position to Hardy, his largely critical review also contained several positive aspects on the idea. According to Descartes, Hardy’s mistake boiled down to believing that an effective method of simplifying a language in order to learn it more easily, is to eliminate those elements that are not necessary for its functioning. However, the number of elements in the structure of a language is not in itself the sole difficulty which arises in the due process of learning a given language. Even a system rich in quantitative measures can be learnt if its elements are ordered and systematized in accordance with clear and transparent principles. As Descartes explains, such a system can be mastered in a very short time, precisely because of the transparency and order. It is the order between all thoughts that the human mind can contain and the one which by nature occurs between numbers. And so in one day one can learn to name all numbers up to infinity and note them down in a foreign language. Yet we are dealing here with an infinitely large number of different words, so that one could express all which enters the human mind (AT, I, pp. 80–81). Therefore according to Descartes, it is important to establish the very principle of constructing a universal language. However, such establishment depends on so the called true philosophy. As the philosopher claims, without true philosophy it is not possible to count, differentiate and order all human thoughts which should be considered the greatest mystery that needs to be discovered in order to possess knowledge. The creation of a universal language rests on the possibility of a proper explanation of the simplest ideas contained within human imagination, as well as on the acceptance of said explanation. Such universal language, according to the philosopher, should be easy to master, both in speech and in writing, and, most importantly, it should support people’s judgment (Jugement), so that no error could ever be possible (AT, I, p. 81).

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Having had a copy of the before mentioned letter to M. Mersenne, Leibniz commented on Descartes’s statement. He said that although the universal language depends on true philosophy, it does not depend on the perfection thereof. In other words the language can still be established even without the perfection of both philosophy and our knowledge. The philosopher was also of the opinion that the language would be extremely helpful in storing what we know and reviewing our deﬁciencies. However he highlighted that it would be most helpful in resolving doubts when it comes to properly reasoning about something (C, p. 28).

2. De arte combinatoria

It is not known whether Leibniz knew Descartes’s letter as discussed above when he created one of the most important works from his youth, namely Dissertiato de arte combinatoria. Nonetheless, the logical and mathematical results of this dissertation laid the foundation for his further philosophical pursuits. In De arte combinatoria, Leibniz, referring to the work of modern mathematicians and philosophers as well as to the method described in the writings of the Catalan encyclopaedist Raymond Lullus, developed the idea of creating the alphabet of human thoughts. Leibniz believed that all notions were only combinations of simple basic notions, just like words constituted infinitely diverse combinations of letters of the alphabet. He expressed the idea in the following way: Let us break any given term into its formal components, i.e. let us define it. Then let us break these components down into their own parts, i.e. let us provide definitions of terms (first definition) until we reach simple parts, or undefinable terms (GP, IV, pp. 65–67)3. These simple, undefinable parts would give rise to the alphabet of human thought, which means that by comparing them one could discover all the truths that the connections express. A starting point for this idea was in fact a traditional definition system through a closer genus (genus proximum) and a species differentia (differentia specifica). This approach, derived from Plato and Aristotle holds that the proper method of defining classes of things is to start with the most general class and divide it into two smaller mutually exclusive classes. The effective- ness of this method was further augmented by the belief that the defined concept must be more complex than the concept used in the definiens. This means that if the concept of ‘man’ is a combination of the concept of ‘animal’ and ‘rational’, then these components should be more basic, or at least simpler than the concept consisting of them.

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This implied the assumption of the existence of absolutely simple atomic concepts – otherwise the division would be infinite. By analyzing this system of definitions of concepts, Leibniz reached the conclusion that the process of division into species ends only when a complete description of an individual has been produced. This means that it is the individual concept that constitutes the concept of the lowest species. It follows that each of the lowest species cannot have more than one subordinate specimen (MacDonald Ross, 1984, pp. 51–52). In the dissertation entitled De principio individui, Leib- niz, adopting Suarez’s nominalist position that there are no entities other than those of an individual nature (and further that they cannot exist), established the principle of the identity of indistinguishable things, according to which there cannot be two identical individuals (D, II, pp. 11–14)4. The principle played a significant role in Leibniz’s philosophy. It was first and foremost associated with the concept of universal harmony, implying the systematic and harmonious unity of individual entities, of which any two differ internally from each other, even in the case of the elusiveness of the difference. Leibniz, assuming the existence of elementary concepts that would constitute the alphabet of human thought, assumed that they could be compared with each other in an unlimited way. The idea was therefore in accordance with the idea of the calculus. He illustrated it with an example in which the numbers 3, 6, 7, and 9 represent four basic concepts. They constitute the first class of concepts. The second class of new concepts is formed by combining successive pairs of basic concepts: 3 x 6,3x7,3x9, 6 x 7, 6 x 9, 7 x 9. Likewise, thanks to the combination of triples, the third class and subsequent ones are formed. One of them is 3 x 6 x 9, which is also 1/2 x 9 or 2/3 x 6, where m/n indicates the m-term of the nth class. There are, then, many expressions of the same thing, with the equivalence of the expressions being verified by the process of breaking them down into elementary factors (GP, IV, p. 65). Let us note that apart from the set of elementary concepts, the rules for compiling these concepts here bear significance. In De arte combinatoria Leibniz presents an outline of combinatorics, setting forth the rules of numerical calculus of relations between objects, while at the same time making an attempt to put these relationships in a perspective far beyond the calculus itself. Combinatorics was for the philosopher “the metaphysi- cal doctrine of the whole and part” (GP IV, p. 36). Leibniz held the view that because “everything that exists or can be thought of shall be composed of real or conceptual parts, whatever is different by nature, must necessarily differ in that it has different parts, and hence the usefulness

117 Halina Święczkowska of compounds; or by some different build-up, and hence the usefulness of decomposition. The first are adjudicated because of the diversity of mat- ter, the second because of the difference of form (GP, IV, p. 44). Accord- ing to Leibniz, on this ground one can discover not only types of things, but also their attributes, as the whole creative part of logic rests on the compounds. Leibniz, similarly as other logicians of his time, differentiated between the logic of discoveries and the logic of proof or judgment. Until then, the basic success of logic consisted in formulating the rules of proof, such as those employed in Aristotle’s syllogistics and in the axiomatic method of Euclid’s geometry. The main difficulty, however, lied in the lack of valid and reliable rules which could allow one to put forward revealing hypo- theses. Leibniz was totally overwhelmed by the vision of the logic of discoveries, a system which could prove the validity of the laws discovered. In addition, it was strengthened by the belief that the logic of discoveries and the logic of proof complement each other. Because true judgments are always analytical, the symmetry suggests that the process of discovery should be synthetic or, using a Leibnizian term, combinatorial5. This reflection reoccurs in many of his works. He presented it in inter alia a dissertation entitled De synthesi et analysi universalis eu arte inveniendi (GP, VII, p. 298). Leibniz explained that the process of synthesis began with the principles that led through successive truths to the discovering of new strings, arranging tables and for- mulas from them that can be used to find the solutions and problems that would emerge in due time. In fact, the very selection of primary concepts becomes a problem here because it occurs in a purely arbitrary manner. By analyzing this problem, Leibniz indicates the need to deploy the criteria of clarity which, to his mind, save against the adoption of contradictory concepts. The very process of synthesis of concepts is not arbitrary because every complex concept that has been created anew must be a possible concept. In the discussed work, Leibniz regards the so-called alphabet of thinking as a catalog of the highest types, the combinations of which would give rise to concepts of lower order. These concepts, more specific by their nature, would form species of lower order, including those that are possible (GP, VII, pp. 292–298). Leibniz considered combinatorics to be a science of possible forms or subject structures. In this sense it was a general science (science generale). General science should, according to the philosopher, “provide a way of using not only the knowledge that has already been possessed, but also methods of judging and discovering, so that one could make further advances and

118 Filum cogitationis. Remarks on Leibnizian projects of a universal language complement what one needs to know” (C, p. 228). The language of this science should be a system of signs that could unequivocally map all the areas of this science – characteristica generalis. Commenting on Descartes, Leibniz was convinced that the language was almost within reach. Part of the work was already done, as he already thought of an excellent linguistic structure. By virtue of the assumption that the primary components of reality were substances and their properties, Leibniz reached the conclusion that the most appropriate linguistic structure, reflecting the process of including properties within substance, was a subject-predicate form; and combinatorics, which, when generalized, constituted a pattern of general science based on logical and mathematical theory. The combinatorial approach was connected with the vision of the invariability of a set of initial concepts which constituted the entire human knowledge. The whole cognitive enterprise of combinatorics was based on finding collates of these concepts that form true judgments. Leibniz’s Prin- ciple of Identity was the key to the procedure. The Principle holds that a given judgment is a true judgment if it is an identity judgment or can be reduced to it. The identity judgment is the judgment in which the predicate is identical to the subject or is contained within this subject, for example: a is a or ab is a. Therefore, it can be said that every true judgment is true by virtue of its form, and as such, shall be considered an analytical statement. Leibniz made a clear distinction between truths of reasoning and factual truths. The former are necessary propositions in the sense that they are either obvious propositions or can be reduced to them. All truths of reasoning are necessarily true, and their truth is based on the law of non-contradiction – or the principle of identity which, in his opinion, turns out to be the same (Czeżowski, 1969, p. 154). Factual truths, however, are not necessary propositions, but they are also analytical in a sense. For Leibniz “individuality involves infinity, and only someone who was ca- pable of grasping the infinite could know the principle of individuation of a given thing . . .” (NE, III ii, § 6)6. No finite mind is able to make this analysis, and therefore “certainty and the perfect right of casual truths is known only to God, who embraces the infinity with one act of intuition” (GP VII, p. 309). Therefore it can be said, that the difference between the truths of reasoning and factual truths referred essentially in Leibniz to the question of human cognition. Leibniz gave expression to his belief that the analysis of primary concepts whose collates would form the basis for em- bracing all of the human knowledge. One can here ask a question about the nature of this list, namely whether there are infinitely many or end- lessly many of the basic concepts. Leibniz, unfortunately, did not refer to

119 Halina Święczkowska this issue in a precise manner. The collation of primary concepts with in- teger numbers indicates that there are infinitely many of them in terms of calculations (C, p. 187); however, the definition of the set of these concepts as the “alphabet of human thought” (C, p. 430) allows to assume that Leibniz thought about a finite set, by virtue of the fact that the actual mind possesses the knowledge that contains a finite number of elementary components of thinking, and hypothetically speaking is able to develop it in an infinite manner. The key to improving the so called cognitive performance was the Leib- nizian postulate of cataloguing “all knowledge acquired, and yet dispersed and poorly systematized” (C, p. 229), or at least the one that seems to be the most important. The conclusive criterion for sentences belonging to such a set is the acceptance of only those whose truth has been proven because “true knowledge depends on proof” (C, p. 153). The problem here is the proof itself because it requires one to be familiar with the true method which according to Leibniz when “taken in its entirety”, is still “totally un- known” (C, p. 153). Undoubtedly, the foundation of the set of the sentences that form the catalogue of human knowledge are, for Leibniz, logical and mathematical truths. For “if the mathematicians’ method did not suffice to discover everything . . . then at least it managed to save them from mistakes; but if they did not say everything what they should have said, they likewise did not say everything they should have not” (C, pp. 153–154). According to Leibniz, mathematics was a model for other kinds of science. “If those who studied had imitated mathematicians . . . for a long time we would have had a safe metaphysics, as well as ethics on which everything depends . . . besides, the science of movements, which is key to physics, and therefore also to medicine”. The beauty of mathematics lies in the fact that, composed of clear symbols, in order to examine the evidence it does not have to go beyond its own sign system, and it can carry out its operation on those symbols and not on things. Mathematics describes certain subject areas, but due to the lack of ambiguity of the symbolic language imitating these subject areas, in its activities it can reduce itself to selected symbols. “If it were equally easy to detect . . . the truth of reasoning, there would not be so many incongruities within the sphere of beliefs”. It follows that “if it were possible to invent graphic or conventional signs (caracterès ou signes) which could be suitable for expressing our thoughts in as clear and concise way as arithmetic expresses numbers or as the geo- metric analysis expresses lines, one could do in any field – as long as it is subject to reasoning – everything which could ever be done in arithmetic or in geometry” (C, p. 155).

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3. Structural attempts

Inspired by mathematical symbolism, Leibniz made initial attempts to establish a set of initial concepts and the right notation for them. He ex- perimented with many systems. In one of his projects he proposed using prime numbers in order to denote primary concepts. Their ratio would give rise to complex concepts, such as: animal = 2, intelligent = 3, then human = 6 = 2 x 3 (Couturat, 1901, p. 62; GP, VII, p. 78). This language, however, did not satisfy Leibniz. It did not meet one of the most fundamental requirements; the structure of symbols should correspond to the structure of meanings; however, very large numbers do not reveal their components in a clear way, and so it is difficult to show in a comprehensible way the including of rulings in the subject, which is possible in the case of shorter collations. Likewise, it is also not clear which criteria Leibniz rested on to select primary concepts. It is also difficult to recognize them in the project as of 1678 (C, pp. 277–278). Leibniz himself, aware of practical difficulties in explaining the need to use a universal language to its potential users, intended to convince them with a system that would meet the requirements of elegance and simplicity. Therefore, the philosopher proposed the use of consonants that would correspond to nine digits, and it would proceed as follows:

123456789 BCDFGHLMN and the use of vowels that would express a decimal place for numbers:

1 10 100 1000 10000 AE I OU

Diphthongs could be employed to express higher powers of 10. For example, then, the number 81374 would mean mubodilefa. The rareness and beauty of this idea lied, according to Leibniz, in the phenomenon that the same number could be expressed also by the word bodifalemu, where the decimal place of a digit indicates vowels or famuledibo or lebomufadi. In fact, there are 120 permutations of this ﬁve-syllable word. This stunning selection of full synonyms gives rise to a multitude of possibilities for expression. It allows one to create the most subtle poems with the maintenance of the same meaning, which, according to Leibniz, constitutes one of the greatest advantages of the system (C, pp. 277–278, Couturat, 1901, pp. 62–62).

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Focusing on the aesthetic criterion, Leibniz also considered the possibility of applying musical notation (C, p. 280). The project has never been realized, though, which is evidenced by the author’s comment as found in New Essays..., namely that one could speak – i.e. make oneself understood by sounds from one’s mouth – without forming ‘articulate sounds’, instead employing musical tones for this purpose (NE, III, i, § 1). Although the majority of Leibniz’s experiments seem to be fragmen- tary and not conforming to the ideology of the entire pursuit whose aim was the perfect universal language, the system presented in Generales inquisitiones de Analysi Notionum et Veritatum (C, pp. 356–399), which is an algebraic framework of the relations between concepts, deserves our attention. This system, referred to by Leibniz as the calculus of concepts (calculus ratiotinator, calculus universalis) is a formal deductive system consti- tuting a part of general science (scientia universalis). Leibniz noticed that logic is all about classes of things or concepts. The difference between the subject and the predicate, however important from a grammatical point of view, does not bear much significance in logic. The subject may as well appear as the predicate, and vice versa; e.g. instead of Every human being is rational, it can be said that rationality is a constitutive characteristic of humanity. This leads, however, as Leibniz noted, to significant differences in the way the relationship between the subject and the predicate is addressed, depending on whether they are considered to be denoting classes or, perhaps, concepts. If we consider the scheme of the general sentence Each S is P, then when interpreted intensionally (i.e. conceptually) it means that the concept S includes the concept P. When, however, considered extensionally (or by means of ranges) it means that the class S is a subclass of the class P. When choosing the intensional interpretation, Leibniz focused on certain philosophical assumptions, as he claimed that the subjects of sentences are, in reality, highly complex predicates, contain- ing in itself all possible predicates that can be uttered about the subject. We will not delve into the technical details of the system as delineated in Generales inquisitiones; however, it is worth to pay attention to Leib- niz’s consistent use of variables in a way that allows one to refer them to objects of any kind, and above all, to an algebraic interpretation of the relationship between general sentences and their translation into existential sentences. By introducing the following terms: est ens (exists) and non est ens (does not exist), Leibniz used them in a sense which, as many researchers posit, anticipates Boolean algebra – for ‘est ens’ is equivalent to ‘=6 0’, and ‘non est ens’ can be understood as ‘= 0’ (Marciszewski & Mu- rawski, 1995, pp. 81–82).

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4. Reconstruction of the Latin Language

Perhaps the lack of any marked progress in the process of forming a language from the basics, a language that would be a creative tool for the development of human knowledge and would also fulfill the aesthetic criteria made Leibniz decide to address the problem from another perspective and pay attention to Latin – the international language of science. He believed that the reform of the existing language would allow it to become rid of all the phenomena characteristic of all the other languages. Characteristics leading to errors in a vocal formulation of thoughts: amphibolias, equivocations, etc., and would also eliminate all irregularities. The first step of such a reform would be the simplification of the grammar. Leibniz referred here to certain models provided by the language used in the Mediterranean trade and based on Italian – lingua franca, as well as the simplified language as presented by the Italian Jesuit Philippe Labbéin a work titled Grammatica linguae universalis published in 1667. In New Essays... he also mentioned a simplified system of the Latin language of a Jakobin whom he met during his stay in Paris (NE, III, ii, § 1). The argument for reducing the grammatical system was, undoubtedly, the ease of mastering it; however it seems that Leibniz’s motives had a deeper philosophical background. If the real world consists of accidents, then it can be described by means of a set of sentences of the following form: A est B, where A is a complete individual concept of a given substance, while B is its accident. Therefore, all judgments that have a different form should be reduced to this scheme. The simplification of grammar was to rely on the lack of inflection. For Leibniz, the model here comprised of the so-called analytical languages, i.e. languages in which all words were not subject to inflection. Leibniz proved that inflection was redundant in a language that had particles, such as prepositions, conjunctions and pronouns (Couturat, 1901, pp. 67–68; Walker, 1972, p. 298). For example cases correspond to prepositions, and through them there is often a preposition contained in a noun, absorbed in it so to speak” (NE, III, vii, § 3). The number of parts of speech should also be reformed (Couturat, 1901, pp. 67–68). Leibniz postulated, among others, the reduction of nouns to adjectives defining the being or the thing (Ens or Res): Idem est homo quod ens humanum; adverbs to adjectives (participles of gerunds (instead of valde potio, sum magnus potator) and all verbs to the verb est (C, p. 281). As a re- sult of this reduction, what we obtain is a dictionary consisting of one noun meaning a thing, one verb and a list of adjectives. Leibniz adds also particles to this set of expressions. Thanks to this class of expressions, especially

123 Halina Święczkowska after the rejection of inflection, we gain the possibility of combining expressions into complex wholes. For the particles “bind not only parts of speech composed of sentences and parts of the sentence comprised of ideas, but also parts of the idea made up in many ways by combining other ideas with each other”. Although the particle belongs to the dictionary, the rules for using them, however, determine the grammar of such a simplified language. And Leibniz writes directly that words belong to the dictionary, and particles belong to grammar (Voces pertinet ad Dictionarium, particulae ad Grammaticam) (Dascal, 1990, p. 56). He explains the reform of grammar in the following way: Distinction of gender is not relevant to a rational grammar; neither do distinctions of declensions and conjugations have any use in philosophical grammar. For we vary genders. Declensions and conjugations without any benefit, without any gain in brevity-unless perhaps the variation pleases the ear; and this consideration does not concern philosophy, especially as we can give beauty to a rational language by another method, in such a way that it will not be necessary to think useless rules7. By virtue of the assumption that vocabula sunt voces aut particulae – words constitute the thing, particles – a form of discourse (C, 288) – the fundamental issue is to analyze and classify the expressions added to this class of expressions (McRae, 1988, pp. 155–163). Leibniz repeatedly emphasized the cognitive nature of this endeavor. If in previous works he treated particles as a form of discourse, then in New Essays... the particles became forms of thinking itself (NE, III, vii, § 3, 4). In the sketch Leibniz on Particles (Dascal, 1990, p. 35), Marcello Dascal reconstructed his research program, indicating, inter alia, that for Leibniz the principle of saving had remained the most important. The principle meant the reduction of multiplicity, chaos and complexity to redundancy, regularity and simplicity. It directly led to the directive of searching for regular meanings and the need to construct such definitions of particles that would reveal their mutual substitutability (NE, III, vii, § 4). Leibniz rejected the traditional morphological criterion for non-declin- ability that were used by grammarians, who were markedly guided by func- tional criteria. Particles were for the philosopher those expressions that per- formed the auxiliary function in all its entirety. However, he did not explain how to understand the nature of this function, which made the class of particles considerably heterogeneous. For instance, this class included the pronouns quis and ille, the verbs sum and habeo, the adverbs quomodo and sic, and, of course, articles and conjunctions, all performing the auxiliary function (Dascal, 1990, p. 39).

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Let us note, however, that although the criterion for fulfilling the auxiliary function does not differ considerably from the medieval division into categorematic and syncategorematic expressions, Leibniz modifies the range of this last class of expressions, adding to it those phrases that specula- tive grammar treated as independent in terms of meaning and necessary to form a sentence. The criterion indicated by Leibniz does not determine whether the expression is rid of any meaning. Additionally, the postulate of analyzing regular meanings implies that the particles perform certain semantic functions. The Leibnizian criterion for non-independence is close to the division of expressions into basic categories and categories of non- independent expressions, adopted in modern logical semiotics. There is a certain analogy here between the class of particles indicated by Leib- niz and the class of functors. He clearly underlines the differences between the prepositions that connect names and the conjunctions that connect sentences – Praepositiones jungunt nomina, conjunctions jungunt integras propositiones (Dascal, 1990, p. 54). According to Leibniz, the only class of expressions that are signs of concepts, are names, the ways of describ- ing things are the rest (this is the semantic criterion presented by Leib- niz in Characteristica verbalis (C, p. 434). The basis for all cognitive activities is the subject-predicative judgment. What arises here, therefore, is a proposal of a significant simplification of the language system, com- bined with an attempt to adjust semantic categories with grammatical categories. However, there appears some inconsistency. By analyzing the nature of the particle, Leibniz wrote that in the philosophical language, particles, affixes and endings were not specified, and so every part of the word would be a word (C, p. 433). This remark could be seen as surprising, since Leibniz, while accepting analytical languages as the starting model of the whole endeavor, simultaneously assumed that the reconstruction project of Latin would consist, at least in its initial phase, in removing redundant inflection in terms of the functioning of particles. It can be assumed that Leibniz, being influenced by the principle of economy, made the next stage of the reduction a whole set of auxiliary expressions, aspiring to replace all of them with the constructs that would be reducible to the subject-predicative form, for example: Titius est magis doctus Caio is equivalent, according to Leibniz, with the sentence: Quatenus Titius est doctus, et Caiues est doctus, eatenus Titius est superior et Caius est inferior, hence Titius est doctus, et qua talis est supeitor, quatenus inferior qua doctus est Caius (C, p. 280).

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Petrus scribit pulchre: Petrus scribit aliquid pulchrum < seu Petrus scribit (or Petrus est scribens), et quod Petrus scribit est pulchrum (C, p. 244). Paris est amator Helenae: Paris amat (et eo ipso) Helena amatur (C, p. 287). Homines scribunt: Titius est scribens, Caius est scribens. Titius est homo. Caius est Homo (C, p. 244). The term reduction was very broadly understood by Leibniz. Some- times he referred to the reduction of modes of one syllogism to another, or the reduction of a problem to others. This process also had to do with sentences. In addition to the above-mentioned attempts, Leibniz provided many examples of such transformations. And so we have: Petrus est similis Paulo. Ergo Paulus est similis Petro is reduced to the sentences: Petrus est A nunc et Paulus est A nunc (C, p. 224). Nullus homo est lapis: Omnes Homines non sunt lapid (C, p. 223). The main objective of these analyses was first and foremost to maintain the logical equivalence of the sentences subject to reduction with their equivalents. However, it is difficult to fulfill this requirement in other cases, for example what might be questionable is the equivalence of the sentence Homines scribunt with the one-sentence conjunction as pointed out by Leib- niz, due to its elliptical nature. For it can be interpreted as a general sentence: Omnes hominess scribunt, existential sentence: Quidam homines scribunt, or a sentence in which the name homines appears as the name of a species. It seems, however, that although the so called reductional analysis was for Leibniz one of the means leading to the creation of the grammar of a universal language, it just as well served as a method of seeking regu- larities of language structures in existing ethnic languages. This regularity is also referred to by Leibniz as universality or rationality (C, p. 35); it covers everything that is general in language (C, p. 353). In this sense, such reductional analysis does not always lead to the transformations that meet the criteria of logical equivalence, but instead allows one to discern the general nature of certain language forms, and as such, sets the foundation for searching for universal logical structures (Dascal, 1990, p. 49). It is also critical to mention Leibniz’s other sources of inspiration. Irre- spective of his individual constructional attempts, the philosopher remained under the influence of the hermetic tradition. He studied the works of al- chemists, Pythagorean numerology, and cabbalism (GP VII, p. 184). He was quite open with his fascination with ideograms and cryptograms. While conducting intensive research into the Chinese language, he hoped to dis-

126 Filum cogitationis. Remarks on Leibnizian projects of a universal language cover the key that would lead to the recognition of a real, natural relationship between signs and concepts. In one of his letters to Father Bouvet, a Jesuit missionary in China who provided Leibniz with research material, he wrote that the new language that he had planned as a wonderful calculus of mind, would be a continuation of the system of signs contained in the Book I – Ching, attributed to the legendary Emperor Fohi. It would also be a special language of the highest caste, of the most enlightened intellectuals (Merkel, 1952, p. 55).

5. The idea of a universal language in the 17th century

While analyzing the Leibnizian idea of a universal language one must remember the 17th century European civilization and cultural context it grew out of. Geographic discoveries, economic development and ensuing a lively trade exchange, the need for linguistic communication between Europe and the rest of the world, as well as the development of national languages are only a few of the reasons that had an impact on the researchers’ engage- ment with the construction of a language that would meet both the needs of everyday life – as an international communication system – and would fulfill the requirements that the language of science had to meet. Within this field Leibniz competed with many others, and it must be clearly said that fathering being a precursor or having an exceptional role in this field upon Leibniz is at least disputable if not totally unfounded. The 17th century can be called, without too gross an exaggeration, the epoch of universal language projects (Jurkowski, 1982). Searches and constructional attempts went in different directions: some focused on research and comparisons of the existing languages to indicate the most perfect system, some were projects that aimed at simplifying selected ethnic languages, and others were ambitious plans to build a language anew. Leibniz tried each of these. Comparative studies of ethnic languages made the philosopher reach the conclusion that they must have originated from some primary language with properties that could, perhaps, meet the requirements of a universal language, a language called by some the Adamic language, but with the view that its reconstruction was not possible in any way (C, p. 151). However, it is difficult to maintain consistency here because Leibniz sometimes claimed that this language reflected only the state of cognitive advancement of primitive societies, and the barbarians had more instinct than reason. In the discussion about the historical and cultural primacy of languages, he let emotions be involved and argued that German re-

127 Halina Święczkowska mained closest to the Adamic language, and that the German language met the criteria of the language of philosophy (Święczkowska, 2016, pp. 94–95). Such a radical position on this issue was weakened due to his contact with the civilization of Far East. Leibniz even assumed that Chinese hid the whole truth about things. And he was not the only one to believe in that concept. A similar opinion was expressed much earlier by Francis Bacon, who claimed that the ideograms of this language were “Characteres real, which express neither letters nor words in gross, but Things or Notions” (Bacon, 1905, p. 121). F. Bacon was one of the first to consider the project of building a universal language and which, according to him, would be an ideographic system. He wrote about this question in The Advancement of Learning (1605), as well as in a dissertation titled The Augumentis Scientiarum (1623), which was published later. Although Bacon saw some advantages of implementing his idea – “any book written in characters of this kind can be read off by each nation in their own language”, the very difficulty concerned with it would be to learn such a language, as it would contain “a vast multitude of characters; as many, I suppose, as radical words” (Bacon, 1905, p. 522). However, Bacon’s idea had itself such resonance that numerous attempts appeared to make it be implemented. It is worth mentioning here the joint project of William Bedell, the Bishop Kilmore and Reverend Jonston as of 1633, the project of Herman Hugo, Philipe Labbéand Edward Somer- set. In 1657, Cave Beck published in Ipswich the grammar and dictionary of such language titled The Universal Character, By which all the nations in the world may understand one another’s Conceptions, reading out of one Common writing their own Mother Tonques. Similar writings were also published by J. J. Becher in Frankfurt in 1661 (Character, pronotitia linguarum universali), and by Athanasius Kircher Rome in 1663 (Polygraphia Nova et Universalis) (Cohen, 1954, p. 54). The difficulties that Bacon underlined seemed to be overcome by the program outlined by Descartes in the aforementioned letter to Mersenne. Descartes himself, although he was convinced of the theoretical possibility of constructing a universal language whose structure would reflect the structure of thinking, never made an attempt to implement it, claiming that first of all the so called “true philosophy” must be discovered. Moreover, despite recognizing the cognitive value of such a language, he was essentially skeptic about practical possibilities (AT I, pp. 81–82). The Cartesian program became a challenge for other researchers, and it was Mersenne, who mentions his project in a letter from 1636 or 1637, who undertook it as one of the first among those others interested in this idea (AT I, p. 572). The Cartesian ideas

128 Filum cogitationis. Remarks on Leibnizian projects of a universal language was mentioned in the project of Lodowick as presented in a book from 1647 titled A Common Writing, whereby two, although not understanding on the other’s language yet by the help thereof may communicate their minds one to another, and improved in a work from 1652 titled The Groundwork, or foundation laid (or so intended) for the framing of a new perfect language and an universal or common writing. Lodowick’s universal language was an ideographic system. The only project based on phonograms was the system presented by Sir Thomas Urquhart in 1651 (Cohen, 1954, p. 55). The idea of a universal language as presented by Seth Ward in 1654 deserves special attention. In a work titled Vindiciae Academiarum he wrote: “because all dissertations are established within sentences, and those sentences in words, and words, in turn, mean simple concepts or are reducible to them, it indicates that if all possible kinds of simple concepts are discovered, and symbols, which will be, in comparison to others, very few, become assigned to them, and therefore the rules for assembling them will be easily recognizable, hence the most complex wholes will be immediately understandable and will, additionally, present directly in a visible way all elements of the assemblies and, as such, will direct themselves to the nature of things” (Ward, 1654, p. 21). Although Ward’s idea was not implemented, the conception as presented by the author ﬁtted within the Cartesian model of language, and what is more, it corresponded to a large extent to Leib- niz’s later projects. Leibniz did not refer to Ward’s work; however, he was familiarized with other English projects – the work of George Dalgarno published in 1661 and titled Ars Signorum, vulgo Character Universalis et Lingua Philosophica, and Essay towards a Real Character and a Philosoph- ical Language (1668) authored by John Wilkins. According to Leibniz, however, neither Dalgarno nor Wilkins had addressed enough the signiﬁcance of things, and their languages had achieved only one thing: they were useful as a communication tool, “because the real Characteristica realis which I imagine shall be included among the most useful tools of the human mind, as naturally possessing invincible strength to discover and to preserve, and to judge” (GP VII, p. 7).

6. The magical charm of the algorithm

Although Leibniz had many predecessors while searching for the perfect system of the representation of thoughts, there is something, however, that determines the unique nature of the Leibnizian idea of a universal language. Descartes, despite the fact that he pointed the direction of the

129 Halina Święczkowska search, rejected the need for establishing a universal language by question- ing the cognitive usefulness of any language system. Understanding the sign in a purely conventional manner, the philosopher claimed that the material side of the sign had no connection with meaning, which stood in stark contrast to the usefulness of linguistic expressions in the thinking processes. This meant that thinking, as an operation on ideas, could not be founded on anything material. The Cartesian methodology referred, then, to direct contact of the mind with the object of cognition. The methodology stated that the mind grasped a thing not through a word that could refer to it, but through its idea which it always had in itself and which it took into account at a given moment (Kopania, 1994, p. 155). The Leibnizian methodology indicated the indispensable nature of a different way of thinking, in which the contact of the mind with the object of cognition was not direct but took place by means of signs as those tools of thinking that represented the object assigned to them. Signs should, however, fulfill a certain requirement: according to the Leibnizian theory of representation, they should express this object (GP VII, pp. 263–264). This indirect way of thinking about things, where the idea of things does not reveal itself as an object of apperception, was called by Leibniz blind thinking (caeca cogitatio) (GP IV, p. 423). It is similar to operations conducted on large numbers, and, indeed, Leibniz often referred to examples of arithmetic calculations. The belief that every mental operation in fact consisted in counting, was, indeed, derived from Hobbes (GP IV, p. 64), but Leibniz gave a completely new dimension to it. Assuming that thinking leading to apperception was analogous to some kind of calculus, the philosopher concluded that the replacement of actions of the mind at each of its stages (with symbols reflecting these actions, would allow to recreate the wholeness of the cognitive process and put it in the right system of rules. For there was, as he posited, a natural order of ideas common to angels and people, and all intelligences in general (NE, III, i, § 5). Hence, the whole project of building a universal language was an attempt to recreate this natural order. Leibniz assumed that apperception, and thus thinking leading to ideas, was of an algorithmic nature (i.e. having to do with the calculus). It did not follow, however, that each thinking on the level of consciousness led to cognition, and it was also difficult to agree with the view that all thinking was of an algorithmic nature, although, undoubtedly, the actions of the mind taking place on the level of unconsciousness had such a character, according to Leibniz. Ethnic languages, as reflecting the order of our discoveries, allow to recreate all thoughts that remain in accordance with the internal

130 Filum cogitationis. Remarks on Leibnizian projects of a universal language order of ideas, but they also reflect those actions of the mind that lead to incorrect judgments and beliefs (GP VII, pp. 204–206). Therefore, these are not systems that allow to recreate the real structure of our cognition, although, undoubtedly, they allow to delve deep into those areas of consciousness that are possible to become verbalizable. Surely, it seems that it is possible to make an attempt to rebuild the languages so that the system resulting from it is isomorphic with the natural order of ideas; however, it is necessary to be familiarized with the order beforehand. The attempt made by Leibniz to rebuild the Latin language indicates that adjusting the ready language system to even clear assumptions concerning the structure of our cognition is an extremely difficult task in practical implementation, if not totally impossible. One should remember, however, that the vision of a perfect language did not completely cover the cognitive usefulness of the existing languages. Each language, as Leibniz claimed, was suitable for recording discoveries, and each language, even the poorest, could express everything (C, p. 352). If we are not yet able to build a universal language, we should focus on becoming familiarized with and improving our own language – ethnic languages, as “the oldest monuments of peoples”, allow “to recreate the history of our discoveries” and progress in science depends on expressing our thoughts in a clear and precise manner (GP IV, p. 138). The assumption of the natural order of ideas, which is a system of intra-mind representation, results from one of the most basic assumptions of the Leibnizian metaphysics. The mind, as a monad, and closed to all external activities, finds the whole universe in itself. The natural order of ideas is isomorphic with the order of the universe. And this order is a consequence of the Creator’s action, who by choosing the best world among those possible, created it in accordance with the internal order of one’s own thought, for “when God calculates and reflects upon something, the world comes into existence” (GP VII, p. 191). For Leibniz, similarly as for many other thinkers, the world order is a mathematical order, and God himself is a mathematician. The eminent contemporary mathematician Stanisław Ulam draws attention to the fact that every formalism and every algorithm has a certain magical charm (Ulam, 1996, p. 305). Leibniz, fascinated by the beauty of mathematics, was undoubtedly attracted to algorithmic procedures. Filum cogitationis, caeca cogitatio or calculus are all expressions that directly refer to the idea of the algorithm (Marciszewski & Murawski, 1995, p. 76). At the core of algorithmic procedures lies a language defined in a purely formal way, i.e., referring only to the physical shape of expressions and their combinations. Undoubtedly, this language was the ideal at which Leibniz

131 Halina Święczkowska aimed. “The progress of the art of intellectual invention depends to a large extent on the art of marking. . . . If either some exact language (called by some Adamic), or at least some kind of truly philosophical writing, was created, with the help of which the concepts would be reduced to some alphabet of human thoughts, then everything that can be achieved by means of reason on the basis of data, could be obtained through a certain calculus in the very way in which arithmetic or geometrical problems are solved” (GP VII, pp. 198–199). The system obtained in this way would become “a certain sensual and somewhat mechanical guide of the mind, understandable even to those who are the most stupid. Since following the text and thinking will proceed in a gradual manner, it means that the written text will be a thread for thought” (GP VII, p. 14). Moreover, it would allow one to determine the issue of truth in a purely mechanical way, so that “visible truth would be just as in the picture, as if it were printed by a machine. It would be so because the criterion that would create truth would be established in a mechanical manner, making it visible” (GP VII, p. 10). Historians of science indicate that the Leibnizian project of a universal language anticipated both the program of the formalization of the language of mathematics announced in 1900 by David Hilbert, during the Second Congress of Mathematics in Paris, as well as the modern program of Ar- tificial Intelligence, due to the belief that every creative manifestation of human thinking is, in fact, a calculus (Marciszewski, 1994). With the right symbolism it could be possible to do everything in any field that could be done in arithmetic and geometry – as long as it is subject to the reasoning processes. The object of Leibniz’s unattainable dreams, a new language expressing all our thoughts, difficult to build but easy to master “because of its enor- mous usefulness and amazing ease will be shortly accepted by everyone and will be marvelously useful for the communication of many nations, and that will prompt its acceptance. Those who will be writing in this language will not make any mistake unless they avoid errors of a calculative nature, bar- barisms, solecisms and other mistakes as present within grammatical forms and syntactical build-up. This language will also have a unique property: it will shut the mouths of those who are ignorant. For one will be able to speak or write in this language only with regard to those topics one understands himself. Because, in reality, those who count, learn by writing, and those who speak, often encounter something they did not think about, lingua praecur- rante mentem. And particularly this will happen in this language because

132 Filum cogitationis. Remarks on Leibnizian projects of a universal language of its accuracy, all the more so that all equivocations and amphibols will disappear, and everything that will be uttered in a clear, understandable way, will be said just to the point” (C, p. 156). The natural order of ideas will be achieved thanks to the symbolism that recreates the alphabet of human thoughts. In this way, the language will find the transparency lost through the ages, enabling one to see the idea through its sign. It will be the system that connects all ethnic languages, since they should all be reducible to this common pattern. If the reason for the existence of all languages is the natural system of ideas, then, despite the differences between them, they form a harmonious whole because they express the same reality and refer to the same intra-mind order of thoughts. Each language grasps this reality from a different perspective, just as each monad perceives the world from its own point of view. Per- fect language is a physical representation of perceptions of every thinking mind. If that what distinguishes monads is the perspective of perceptions, it follows that the same rule applies in the case of the system that grasps the perceptions. In his confession of faith in the possibility of creating universal symbolism, Leibniz took care of the program’s compliance with the principle of individualization. This language would be a measure of the cognitive development of its users, which would be the degree of knowledge and efficiency of making use of the algorithm. By leading, or even by pre- ceding the thought, it would allow to accept only that what appears to be clear and what is expressible as such, just as it takes place in the process of apperception. The search for universal symbolism as the most powerful tool of reason is a great part of the European history of ideas, which is not only the attempt to develop a common tool of communication, but also the need to reach the fundamental common meanings that would enable us to overcome the consequences of the building of the Babel. The first attempts to find the perfect language is to reach the Hebrew Bible. The Middle Ages accepted the belief presented in the Holy Scriptures concerning the primary nature of the Hebrew language, which remained as a theologically grounded doctrine about the origin of language until the 18th century. In the treatise De vulgari eloquentia Dante Alighieri wrote that the Hebrew language “survived after Babylonian turmoil so that Jesus, the future Savior of the world, could speak the language of grace, not the language of confusion” (Heinz 1998, p. 81). Arguments in favor of the Hebrew monogenesis were also provided by Jew- ish mysticism. According to cabbalists, the written text of the Torah and Talmud contains the encrypted text of the eternal Torah that existed long before the Creation. Breaking the code would thus be the key to obtain-

133 Halina Święczkowska ing the ultimate wisdom. Leibniz was one of the first who questioned the primacy of the Hebrew language as the first language of mankind, pointing to the proto-language which sometimes he referred to, after Jacob Boehme, as lingua adamica. The sense of certainty and beauty carried across by mathematical symbolism became a source of inspiration for different projects of universal notation, in particular in the field of deductive sciences. The year 1897 is crucial here, as it was the time during which the German mathematician Gottlob Frege published a work entitled Begriffschrift, markedly influenced by the Leibnizian ouevre. This work opens a new era in formal logic and the whole mathematics. Its direct consequence is the aforementioned program of the formalization of mathematics announced by D. Hilbert in 19008. At the same time, the need for building one international common language is raised by the first publisher of Leibniz’s logical works, L. Couturat, who, together with L. Leau (Couturat & Leau, 1903), presents 38 aposteri- oric and mixed language systems, created only in the 19th century, in a 1903 work titled Histoire de la langue universelle. However, there is no universal perfect language which we use to communicate and write poetry, and which, at the same time, as Leibniz wanted, leads us by means of symbolism along the path of truth. There is, though, mathematics which is a concise way of formalizing rational thinking and is amazingly effective in explaining the secrets of the physical world. This relationship was very clearly indicated by the philosopher, who argued that the principles of mathematical order lie at the root of the diversity of phenomena (Davies, 1992).

NOTES

1 G.W. Leibniz, Opuscules et Fragments Inédites de Leibniz, ed. L. Couturat, Paris 1903, (repr Hildesheim1961), quoted as C, page. 2 R. Descartes, Oeuvres de Descartes. Publiées par Ch. Adam., P. Tannery, Paris 1974– 1983, v. I, p. 76–82, further quoted as AT. 3 G. W. Leibniz, Dissertatio de arte combinatoria, in: G. W. Leibniz, Die Philosophis- chen Schriften von G. W. Leibniz, VII vol., ed. C. I. Gerhard, 1849–1853 (repr. Hildesheim 1960), vol. IV, s. 64–65, further quoted as GP, volume, page. 4 G. W. Leibniz, Gothofiedi Guiliemi Leibnitii Opera Omnia, nunc primum par colleta... par Ludovitius Dudens, VI vol., Genève 1767, p. 11–14, quoted as D, volume, page. 5 Leibniz believed that both analytical and synthetic reasoning could be reduced to purely mechanical operations. Furthermore, he claimed that all combinatorial operations would have become analytical over time if all people had started using his method of collation, C, 168. (See MacDonald 1984, 61).

134 Filum cogitationis. Remarks on Leibnizian projects of a universal language

6 G. W. Leibniz, New Essays on Human Understanding, transl. and ed. by P. Remnant and J. Bennett, Cambridge, 1981, quoted as NE, book, chapter and section. 7 I quote after R. McRae, Locke and Leibniz on LinguisticParticles. Synthese, vol. 75, May 1988, No. 2, p. 158. The quotation does not overlap with the bibliographical data as pointed out by the author. 8 These issues were presented thoroughly by W. Marciszewski in his article entitled Does science progress towards ever higher solvability through feedbacks between insights and routines?, Studia Semiotyczne, vol. XXXII, no. 2.

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