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"We have seen that the characteristic was inseparable in Leibniz's mind from the encyclopedia. The former presupposed the latter, or at least had to be established at the same time and developed in parallel with it. Conversely, once established, the characteristic would be the instrument of the encyclopedia and the key to all the sciences." LEIBNIZ'S UNIVERSAL PICTOGRAPHIC 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. Firstly is the aspect of logic and language which is associated with analytic philosophy. Secondly is the aspect of science and engineering which is associated with synthetic philosophy. Either or both of these aspects Leibniz hoped would guide human reasoning like Ariadne's thread and thereby provide solutions to many of humanity's urgent problems. A universal language of logic and 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 based on a rationalised version of the 'principles' of Chinese Character s, 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 , 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 langugage. The mercantile motivation informed some of the research into universal characters, and has also been present in the association of universal language projects with Computer Metalanguage s like XML (Roy and Ramanujan 2000, Yen et. al 2002). However authors, like P. 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 afore mentioned 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; (Jaenecke 1996). 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 . The "representation" of knowledge would take place through a combination of lines and points with "a kind of pictures" ( Pictographs ) to be manipulated by means of his Calculus Ratiocinator . H.Rogers emphasised the metaphysical aspect of the ''characteristica universalis'' by relating it to the ''elementary theory of the ordering of the reals'', and defined it as, "a precisely defineable system for making statements of science" (1963, p.934). Universal language projects like Esperanto, and formal logic projects like the ''Begriffsschrift'' are not commonly concerned with the epistemic synthesis of empirical science, mathematics, pictographs and metaphysics in the way Leibniz described (below). Hence scholars have had difficulty in showing how such projects embody Leibniz's full vision for his "''characteristica''". Unfortunately there is no accessible explanation of this matter currently available in English language philosophy. In the domain of science, Leibniz aimed for his ''characteristica'' to form maps, 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." (Unless stated otherwise, all Leibniz quotations are from his ''On the General Characteristic'' as translated in Loemker 1969: 221-25. This passage is from p. 222.) P.P.Weiner raised an example of a large scale application of Leibniz's ''characteristica'' to climatic science. A weather-forecaster invented by Athanasius Kirchner apparently, "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 gave 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, someting 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 extrmities 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." (''On The Art of Combination'', 1666, translated in Parkinson 1966: 10-11) Writing in the Journal of Symbolic Logic, Nicholas Rechner, in a review of Cohen's article wrote that, "Lebiniz's program of a universal science (''scientea universalis'') for co-ordinating 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 sysetmatic 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 '').Rechner 1954. Reviewed Work(s): On the Project of a Universal Character. by Jonathan Cohen, The Journal of Symbolic Logic, Vol. 19, No. 2 (Jun., 1954), p. 133 Desmond Fearnley-Sander went one step further and defined Leibniz's ''characteristica'' as a combination of the algebra of logic (which Fearnley-Sander defined as the ''calculus ratiocinator'') and the algebra of geometry (defined as the ''characteristica geometrica'') (Fearnley-Sander 1986; p. 164. ref: Hermann Grassmann and the Prehistory of Universal Algebra, The American Mathematical Monthly, Vol. 89, No. 3 (Mar., 1982), pp. 161-166). Fearnley-Sander suggested that this combination had "come to pass" (ibid.) in the development of Universal Algebra . The "general algebra" Near the end of his life, he 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" (letter to Nicolas Remond, 10 January 1714, in Loemker 1969: 654. Translation revised.) 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 , the diagrams in Leibniz's work warrant close study. On at least two occasions, Leibniz illustrated his philosophical reasoning with diagrams (reproduced in Loemker 1969: 83, 366). 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, air, fire, and water. These four elements make up the four corners of a diamond. 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 more clearly reproduced in ''Saemtliche Schriften und Briefe'', Reihe VI, Band 1, p. 166. Leibniz loses heart 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 I once planned a new method of calculation proper to subjects having nothing in common with mathematics, and if this manner of Logic were put into practice, all reasoning, even analogical ones, would be carried out in a mathematical way. Then modest intellects could, with diligence and good will, not accompany but at least follow greater ones. For one could always say "let us calculate" and judge properly, insofar as reason and the data can furnish us the means to do so. But I do not know whether I will ever be able to execute such a project, one requiring more than one hand, and it would even seem that humanity is not yet sufficiently mature to pretend to the advantages to which this method could lead." (translation of a passage reproduced in Couturat 1901: 118, fn 2) In an 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 dicussions with men who could stimulate and help me in work of this nature." (Loemker 1969: 656) THREE CRITERIA 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. (Lewis 1960: 3. Also see pp. 7-9) Following from this Cohen stipulated that the universal character would have to serve as a:
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 . 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..." (Parkinson 1973: ix ) 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 apparently had failed to appreciate the magnitude of the task facing the editors of Leibniz's manuscripts, given that Leibniz left about 15000 letters and 40000 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 unifing thread can be discerned among these projects.
SEE ALSO
REFERENCES On Leibniz's lifelong interest in the ''characteristica'' and the like, see the following texts in Loemker (1969): 165-66, 192-95, 221-28, 248-50, and 654-66. On the ''characteristica'', see Rutherford (1995) and the still-classic discussion in Couturat (1901: chpts. 3,4). Also relevant to the ''characteristica'' is Mates's (1986: 183-88) discussion of what he called the ''lingua philosophica''.
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