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[1]Leibniz's rational grammar

G.W. Leibniz (1646-1716) is well-known as a mathematician and as a philosopher. He also famously envisaged the construction of what he often called a 'philosophical language' (and sometimes a 'characteristica universalis') - a miraculous tool not only for communication but also for thinking, enabling its users to find new insights and even to put an end to disputes.

One part of this grand project was the elaboration of 'rational grammar', which was to describe the basic patterns underlying all languages, and therewith the structure of human knowledge and thought. Carrying out this project, Leibniz undertook a painstaking analysis of the grammar and idioms of various languages, focusing however on Latin.

Although this type of analysis was a central element of Leibniz's linguistic work, it has not yet been subjected to thorough study. This is primarily due to the fact that, until recently, only a small selection of the relevant texts had been published. Fortunately, in the last decades a series of texts has become available in complete form for the first time, although a number of important texts are still accessible in manuscript form only.

I am currently writing a book which describes Leibniz's rational grammar project, and interprets it in the light of its intellectual background. Furthermore, the book contains annotated English translations of a number of key texts (which Leibniz wrote in Latin), so as to make them accessible to a wider audience.

[2]

Language and Mind

Some scholars have suggested that Leibniz should be regarded as one of the first thinkers to envision something like the idea of artificial intelligence (cf. Churchland 1984; Pratt 1987). Whether or not he should be regarded as such, it is clear that Leibniz, like contemporary cognitive scientists, saw an intimate connection between the form and content of language, and the operations of the mind. Indeed, according to his own testimony in the New Essays, he “really believe[s] that languages are the best mirror of the human mind, and that a precise analysis of the signification of words would tell us more than anything else about the operations of the understanding” (bk.III, ch.7, sec.6 (RB, 333)). This view of Leibniz's led him to formulate a plan for a “universal language,” an artificial language composed of symbols, which would stand for concepts or ideas, and logical rules for their valid manipulation. He believed that such a language would perfectly mirror the processes of intelligible human reasoning. It is this plan that has led some to believe that Leibniz came close to anticipating artificial intelligence. At any rate, Leibniz's writings about this project (which, it should be noted, he never got the chance to actualize) reveal significant insights into his understanding of the nature of human reasoning. This understanding, it turns out, is not that different from contemporary conceptions of the mind, as many of his discussions bear considerable relevance to discussions in the cognitive sciences.

According to Leibniz, natural language, despite its powerful resources for communication, often makes reasoning obscure since it is an imperfect mirror of intelligible thoughts. As a result, it is often difficult to reason with the apparatus of natural language, “since it is full of innumerable equivocations” (On the Universal Science: Characteristic (undated); G VII, 205 (S, 18)). Perhaps this is because of his view that the terms of natural language stand for complex, or derivative, concepts—concepts which are composed of, and reducible to, simpler concepts. With this “combinatorial” view of concepts in hand, Leibniz notices “that all human ideas can be resolved into a few as their primitives” (On the Universal Science: Characteristic; G VII, 205 (S, 18)). We could then assign symbols, or “characters,” to these primitive concepts from which we could form characters for derivative concepts by means of combinations of the symbols. As a result, Leibniz tells us, “it would be possible to find correct definitions and values and, hence, also the properties which are demonstrably implied in the definitions” (On the Universal Science: Characteristic; G VII, 205 (S, 19)). The totality of these symbols would form a “universal characteristic,” an ideal language in which all human concepts would be perfectly represented, and their constitutive nature perfectly transparent. Now it is true that Leibniz eventually came to doubt “whether any concept of this [primitive] kind appears distinctly to men, namely, in such a way that they know they have it” (An Introduction to a Secret Encyclopedia (1679?); C, 513 (MP, 7)). But it is also clear that he did not see this skepticism concerning our ability to reach the primitive concepts as much of a barrier to the project of a universal language. He writes in The Art of Discovery (1685) that “there are certain primitive terms which can be posited, if not absolutely, at least relatively to us” (C, 176 (W, 51)). The suggestion seems to be that even if we cannot provide a catalog of absolutely primitive concepts, we can nevertheless construct a characteristic based on concepts which cannot be further resolved by humans.

In addition to the resolution of concepts, and their symbolic assignments, Leibniz envisages the formulation of logical rules for the universal characteristic. He claims that “it is plain that men make use in reasoning of several axioms which are not yet quite certain” (The Method of Certitude and the Art of Discovery (undated); G VII, 183 (W, 49)). Yet with the explicit formulation of these rules for the logical manipulation of the symbols—rules which humans use in reasoning—we would be in possession of a universal language which would mirror the relations between the concepts used in human reasoning. Indeed, the universal characteristic was intended by Leibniz as an instrument for the effective calculation of truths. Like formal logic systems, it would be a language capable of representing valid reasoning patterns by means of the use of symbols. Unlike formal logic systems, however, the universal language would also express the content of human reasoning in addition to its formal structure. In Leibniz's mind, “this language will be the greatest instrument of reason,” for “when there are disputes among persons, we can simply say: Let us calculate, without further ado, and see who is right” (The Art of Discovery (1685); C, 176 (W, 51)).

Judging from Leibniz's plans for a universal language, it is clear that Leibniz had a specific view about the nature of human cognitive processes, particularly about the nature of human reasoning. According to this view, cognition is essentially symbolic: it takes place in a system of representations which possesses language-like structure. Indeed, it was Leibniz's view that “all human reasoning uses certain signs or characters,” (On the Universal Science: Characteristic; G VII, 204 (S, 17)) and “if there were no characters, we could neither think of anything distinctly nor reason about it” (Dialogue (1677); G VII, 191 (A&G, 271)). Add to this conception Leibniz's view that human cognitive processes follow determinable axioms of logic, and the picture that emerges is one according to which the mind operates, at least when it comes to intelligible reasoning, by following implicit algorithmic procedures. Regardless of whether or not Leibniz should be seen as the grandfather of artificial intelligence, he did conceive of human cognition in essentially computational terms. In fact, as early as 1666, remarking favorably on Hobbes' writings, Leibniz wrote: “Thomas Hobbes, everywhere a profound examiner of principles, rightly stated that everything done by our mind is a computation” (On the Art of Combinations (1666); G IV, 64 (P, 3)).