Characteristica universalis


The Latin term characteristica universalis, commonly interpreted as universal characteristic, or universal character in English, is a universal and formal language imagined by Gottfried Leibniz able to express mathematical, scientific, and metaphysical concepts. Leibniz thus hoped to create a language usable within the framework of a universal logical calculation or calculus ratiocinator.
The characteristica universalis is a recurring concept in the writings of Leibniz. When writing in French, he sometimes employed the phrase spécieuse générale to the same effect. The concept is sometimes paired with his notion of a calculus ratiocinator and with his plans for an encyclopaedia as a compendium of all human knowledge.

A universal pictographic language: the key to all the sciences

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

A universal language of science

Leibniz said that his goal was an alphabet of human thought, a universal symbolic language 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". 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:
In a footnote Couturat added:

Metaphysics

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". 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:
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".
Leibniz talked about his dream of a universal scientific language at the very dawn of his career, as follows:
Nicholas Rescher, reviewing Cohen's 1954 article, wrote that:
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:
The universal "representation" of knowledge would therefore combine lines and points with "a kind of pictures" 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".

His diagrammatic reasoning

Since the characteristica universalis is diagrammatic and employs pictograms, 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, 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. Opposing pairs of these are joined by a bar labeled "contraries". 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.

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", 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". 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:
In another 1714 letter to Nicholas Remond, he wrote:

Three criteria

C. J. Cohen 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:
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

, 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:
The logician Kurt Gödel, on the other hand, believed that the characteristica universalis was feasible, and that its development would revolutionize mathematical practice. 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, and an "algebra of thought," allowing rule-based manipulation. The philosophers and linguists who undertook such projects often belonged to pansophical 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.