Characteristica universalis

International communication

Many Leibniz scholars writing in English seem to agree that he intended his characteristica universalis or "universal character" to be a form of pasigraphy, or ideographic language. This was to be based on a rationalised version of the 'principles' of Chinese characters, as Europeans understood these characters in the seventeenth century. From this perspective it is common to find the characteristica universalis associated with contemporary universal language projects like Esperanto, auxiliary languages like Interlingua, and formal logic projects like Frege's Begriffsschrift. The global expansion of European commerce in Leibniz's time provided mercantilist motivations for a universal language of trade so that traders could communicate with any natural language.

Others, such as Jaenecke, for example, have observed that Leibniz also had other intentions for the characteristica universalis, and these aspects appear to be a source of the aforementioned vagueness and inconsistency in modern interpretations. According to Jaenecke,

the Leibniz project is not a matter of logic but rather one of knowledge representation, a field largely unexploited in today's logic-oriented epistemology and philosophy of science. It is precisely this one-sided orientation of these disciplines, which is responsible for the distorted picture of Leibniz's work found in the literature.

As Couturat wrote, Leibniz criticized the linguistic systems of George Dalgarno and John Wilkins for this reason since they focused 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.

A universal language of science

Leibniz said that his goal was an alphabet of human thought, a universal symbolic language (characteristic) for science, mathematics and metaphysics. According to Couturat, "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" (1901, chp 3.). This characteristic was a universalisation of the various "real characteristics". Couturat wrote that Leibniz gave Egyptian and Chinese hieroglyphics and chemical signs as examples of real characteristics writing:

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.

In a footnote Couturat added:

Elsewhere Leibniz even includes among the types of signs musical notes and astronomical signs (the signs of the zodiac and those of the planets, including the sun and the moon). It should be noted that Leibniz sometimes employs planetary signs in place of letters in his algebraic calculations

Metaphysics

Hartley Rogers emphasised the metaphysical aspect of the characteristica universalis by relating it to the "elementary theory of the ordering of the reals," defining it as "a precisely definable system for making statements of science" (Rogers 1963: 934). Universal language projects like Esperanto, and formal logic projects like Frege's Begriffsschrift are not commonly concerned with the epistemic synthesis of empirical science, mathematics, pictographs and metaphysics in the way Leibniz described. Hence scholars have had difficulty in showing how projects such as the Begriffsschrift and Esperanto embody the full vision Leibniz had for his characteristica.

The writings of Alexander Gode suggested that Leibniz' characteristica had a metaphysical bias which prevented it from reflecting reality faithfully. Gode emphasized that Leibniz established certain goals or functions first, and then developed the characteristica to fulfill those functions.

Science

In the domain of science, Leibniz aimed for his characteristica to form diagrams or pictures, depicting any system at any scale, and understood by all regardless of native language. Leibniz wrote:

And although learned men have long since thought of some kind of language or universal characteristic by which all concepts and things can be put into beautiful order, and with whose help different nations might communicate their thoughts and each read in his own language what another has written in his, yet no one has attempted a language or characteristic which includes at once both the arts of discovery and judgement, that is, one whose signs and characters serve the same purpose that arithmetical signs serve for numbers, and algebraic signs for quantities taken abstractly. Yet it does seem that since God has bestowed these two sciences on mankind, he has sought to notify us that a far greater secret lies hidden in our understanding, of which these are but the shadows.

P. P. Weiner raised an example of a large scale application of Leibniz's characteristica to climatic science. A weather-forecaster invented by Athanasius Kircher "interested Leibniz in connection with his own attempts to invent a universal language" (1940).

Leibniz talked about his dream of a universal scientific language at the very dawn of his career, as follows:

We have spoken of the art of complication of the sciences, i.e., of inventive logic... But when the tables of categories of our art of complication have been formed, something greater will emerge. For let the first terms, of the combination of which all others consist, be designated by signs; these signs will be a kind of alphabet. It will be convenient for the signs to be as natural as possible—e.g., for one, a point; for numbers, points; for the relations of one entity with another, lines; for the variation of angles and of extremities in lines, kinds of relations. If these are correctly and ingeniously established, this universal writing will be as easy as it is common,and will be capable of being read without any dictionary; at the same time, a fundamental knowledge of all things will be obtained. The whole of such a writing will be made of geometrical figures, as it were, and of a kind of pictures — just as the ancient Egyptians did, and the Chinese do today. Their pictures, however, are not reduced to a fixed alphabet... with the result that a tremendous strain on the memory is necessary, which is the contrary of what we propose.

Nicholas Rescher, reviewing Cohen's 1954 article, wrote that:

Leibniz's program of a universal science (scientia universalis) for coordinating all human knowledge into a systematic whole comprises two parts: (1) a universal notation (characteristica universalis) by use of which any item of information whatever can be recorded in a natural and systematic way, and (2) a means of manipulating the knowledge thus recorded in a computational fashion, so as to reveal its logical interrelations and consequences (the calculus ratiocinator).

Near the end of his life, Leibniz wrote that combining metaphysics with mathematics and science through a universal character would require creating what he called:

... a kind of general algebra in which all truths of reason would be reduced to a kind of calculus. At the same time, this would be a kind of universal language or writing, though infinitely different from all such languages which have thus far been proposed; for the characters and the words themselves would direct the mind, and the errors — excepting those of fact — would only be calculation mistakes. It would be very difficult to form or invent this language or characteristic, but very easy to learn it without any dictionaries.

The universal "representation" of knowledge would therefore combine lines and points with "a kind of pictures" (pictographs or logograms) to be manipulated by means of his calculus ratiocinator. He hoped his pictorial algebra would advance the scientific treatment of qualitative phenomena, thereby constituting "that science in which are treated the forms or formulas of things in general, that is, quality in general" (On Universal Synthesis and Analysis, 1679, in Loemker 1969: 233).

His diagrammatic reasoning

Since the characteristica universalis is diagrammatic and employs pictograms (below left), the diagrams in Leibniz's work warrant close study. On at least two occasions, Leibniz illustrated his philosophical reasoning with diagrams. One diagram, the frontispiece to his 1666 De Arte Combinatoria (On the Art of Combinations), represents the Aristotelian theory of how all material things are formed from combinations of the elements earth, water, air, and fire.

These four elements make up the four corners of a diamond (see picture to right). Opposing pairs of these are joined by a bar labeled "contraries" (earth-air, fire-water). At the four corners of the superimposed square are the four qualities defining the elements. Each adjacent pair of these is joined by a bar labeled "possible combination"; the diagonals joining them are labeled "impossible combination". Starting from the top, fire is formed from the combination of dryness and heat; air from wetness and heat; water from coldness and wetness; earth from coldness and dryness. This diagram is reproduced in several texts including Saemtliche Schriften und Briefe (Saemtliche Schriften und Briefe, Reihe VI, Band 1: 166, Loemker 1969: 83, 366, Karl Popp and Erwin Stein 2000: 33).

Leibniz loses will

Leibniz rightly saw that creating the characteristica would be difficult, fixing the time required for devising it as follows: "I think that some selected men could finish the matter in five years" (Loemker 1969: 224), later remarking: "And so I repeat, what I have often said, that a man who is neither a prophet nor a prince can ever undertake any thing of greater good to mankind of more fitting for divine glory" (Loemker 1969: 225). But later in life, a more sober note emerged. In a March 1706 letter to the Electress Sophia of Hanover, the spouse of his patron, he wrote:

It is true that in the past I planned a new way of calculating suitable for matters which have nothing in common with mathematics, and if this kind of logic were put into practice, every reasoning, even probabilistic ones, would be like that of the mathematician: if need be, the lesser minds which had application and good will could, if not accompany the greatest minds, then at least follow them. For one could always say: let us calculate, and judge correctly through this, as much as the data and reason can provide us with the means for it. But I do not know if I will ever be in a position to carry out such a project, which requires more than one hand; and it even seems that mankind is still not mature enough to lay claim to the advantages which this method could provide.

In another 1714 letter to Nicholas Remond, he wrote:

I have spoken to the Marquis de l'Hôpital and others about my general algebra, but they have paid no more attention to it than if I had told them about a dream of mine. I should have to support it too by some obvious application, but to achieve this it would be necessary to work out at least a part of my characteristic, a task which is not easy, especially in my present condition and without the advantage of discussions with men who could stimulate and help me in work of this nature.

Three criteria

C. J. Cohen (1954) set out three criteria which any project for a philosophical language would need to meet before it could be considered a version of the characteristica universalis. In setting out these criteria, Cohen made reference to the concept of "logistic". This concept is not the same as that used in statistical analysis. In 1918, Clarence Irving Lewis, the first English-speaking logician to translate and discuss some of Leibniz's logical writings, elaborated on "logistic" as follows:

Logistic may be defined as the science which deals with types of order as such. It is not so much a subject as a method. Although most logistic is either founded upon or makes large use of the principles of symbolic logic, still as science of order in general does not necessarily presuppose or begin with symbolic logic.

Following from this Cohen stipulated that the universal character would have to serve as:

These criteria together with the notion of logistic reveal that Cohen and Lewis both associated the characteristica with the methods and objectives of general systems theory.

A common scientific language

Inconsistency, vagueness, and a lack of specifics in both English language translations and modern English language interpretations of Leibniz's writings render a clear exposition difficult. As with Leibniz's calculus ratiocinator two different schools of philosophical thought have come to emphasise two different aspects that can be found in Leibniz's writing. The first point of view emphasizes logic and language, and is associated with analytic philosophy and rationalism. The second point of view is more in tune with Couturat's views as expressed above, which emphasize science and engineering. This point of view is associated with synthetic philosophy and empiricism. Either or both of these aspects Leibniz hoped would guide human reasoning like Ariadne's thread and thereby suggest solutions to many of humanity's urgent problems.

Gödel alleges conspiracy

Because Leibniz never described the characteristica universalis in operational detail, many philosophers have deemed it an absurd fantasy. In this vein, Parkinson wrote:

Leibniz's views about the systematic character of all knowledge are linked with his plans for a universal symbolism, a Characteristica Universalis. This was to be a calculus which would cover all thought, and replace controversy by calculation. The ideal now seems absurdly optimistic..."

The logician Kurt Gödel, on the other hand, believed that the characteristica universalis was feasible, and that its development would revolutionize mathematical practice (Dawson 1997). He noticed, however, that a detailed treatment of the characteristica was conspicuously absent from Leibniz's publications. It appears that Gödel assembled all of Leibniz's texts mentioning the characteristica, and convinced himself that some sort of systematic and conspiratorial censoring had taken place, a belief that became obsessional. Gödel may have failed to appreciate the magnitude of the task facing the editors of Leibniz's manuscripts, given that Leibniz left about 15,000 letters and 40,000 pages of other manuscripts. Even now, most of this huge Nachlass remains unpublished.

Related 17th century projects

Others in the 17th century, such as George Dalgarno, attempted similar philosophical and linguistic projects, some under the heading of mathesis universalis. A notable example was John Wilkins, the author of An Essay towards a Real Character and a Philosophical Language, who wrote a thesaurus as a first step towards a universal language. He intended to add to his thesaurus an alphabet of human thought (an organisational scheme, similar to a thesaurus or the Dewey decimal system), and an "algebra of thought," allowing rule-based manipulation. The philosophers and linguists who undertook such projects often belonged to pansophical (universal knowledge) and scientific knowledge groups in London and Oxford, collectively known as the "Invisible College" and now seen as forerunners of the Royal Society.

More recent projects

A wide variety of constructed languages have emerged over the past 150 years which appear to support many of Leibniz's intuitions. If indeed they do support Leibniz's vision of unified science, then the remaining question is whether Ariadne's unifying thread can be discerned among these various projects, leading to their integration.