Characteristica Universalis - More Recent Projects

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.

• Raymond F. Piper (1957; 432–433) claimed that O.L. Reiser's Unified Symbolism for World Understanding in Science (1955), an expansion of his A Philosophy for World Unification (1946), was inspired by Leibniz's Characteristica Universalis, and believed necessary for world understanding and unbiased communications so that "war may eventually be eliminated and that a worldwide organism of peaceful human beings may gradually be established" (Piper Ibid.).

• The study of Boolean algebras and group theory in the 19th century proved correct Leibniz's intuition that algebraic methods could be used to reason about qualitative and non-numerical phenomena. Specifically, the members of the universal set of a Boolean algebra or group need not be numbers. Moreover, a fair bit of philosophy and theoretical science can be formalized as axiomatic theories embodying first-order logic and set theory. Note also how model theory has been employed to formalize and reason about such emphatically nonnumerical subjects as semantics and pragmatics of natural languages. But these approaches have yet to result in any pictographic notations.

• Fearnley-Sander (1986) went one step further, defining 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 suggested that this combination had "come to pass" with the rise of universal algebra. Some people other than Fearnley-Sander working in the area of "universal algebra," the study of the mathematical and logical properties of algebraic structures generally, do not believe that universal algebra has anything to do with the characteristica.

• Palko, Gy Bulcsu (1986) considered structured analysis for analyzing and designing hierarchic systems by using an iconic language, and suggested that such was an application of the universal characteristics Leibniz's project to the language of structured analysis and the formalization of an iconic control system.

• Kluge (1980) argued that Frege's landmark Begriffsschrift was consciously inspired by the characteristica universalis.

• Even though Charles Sanders Peirce, a founder of semiotics, believed that all reasoning was diagrammatic, the relation, if any, of the characteristica to his existential graphs and to semiotics has yet to be explored in the English literature.

• Several aspects of logical positivism, specifically:
  • The first-order theories of Rudolf Carnap's Aufbau (1928, English translation 1967) and of its successor, Goodman (1977), are Leibnizian in their sweep and ambition, although Leibniz would have taken strenuous exception to Carnap's resolute hostility to all metaphysics.
  • The unification of science movement of the 1930s, led by Otto Neurath, Rudolf Carnap, and Charles W. Morris, and later by Edward Haskell et al., bears comparison with the characteristica.
  • Otto Neurath's isotype pictogram system, and "international picture language."

• The following attempts to recast parts of theoretical science as axiomatic first-order theories can be viewed as attempts to develop parts of the characteristica:
  • Special relativity, by Hans Reichenbach, Rudolf Carnap, and others during the 1920s (Carnap 1958: 197–212);
  • Biology, by Joseph Woodger (1937), also during the 1930s (Carnap 1958: 213–20):
  • Mechanics, by Suppes (1957: 291–305) and others during the 1950s.

• The objectives of the 'Symbolator' or 'idea-computer' (Goppold 1994) resemble in some respects a less ambitious version of the characteristica universalis.

• Connections with the Jewish Cabbala, and the International auxiliary language policy of the Bahá'í Faith have also been made.

• The characteristic has also been claimed as an ancestor of the pictographic Energy Systems Language and associated Emergy Synthesis of Odum's Systems Ecology (Cevolatti and Maud, 2004). The Energy Systems Language combines lines and points with "a kind of pictures" manipulated by means of digital computers and software packages like EXTEND(tm) (Odum, Odum, and Peterson 1995), and Valyi's Emergy Simulator. It was designed to provide a general systems language affording quantitative accounting and mathematical simulation of qualitative energy relationships between ecological entities: "that science in which are treated the forms or formulas of things in general, that is, quality in general". A general algebra known as the emergy algebra emerged out of the repeated use of this language in modelling and simulating the energetic principles of ecological relations. In particular it afforded the discovery and demonstration of the maximum power principle, suggested as the fourth law of thermodynamics. If this ancestral claim is granted, then simulation software like EXTEND(tm) and Valyi's Emergy Simulator can be seen as combining the characteristica and the Calculus ratiocinator, if and only if the digital computer is interpreted as a physical embodiment of the calculus ratiocinator.

• The work of Mario Bunge on the border of physics and metaphysics seems grounded in metaphysical presuppositions similar to those of Leibniz's characterisitica.

• Lojban (and its older version Loglan) are both artificial languages derived from predicate logic, and intended for use in human communication.

• Charles K. Bliss's Blissymbolics, presently used as an 'alternative and augmentative language' for disabled people but originally intended as an International 'Auxlang', is said to be in the mold of the Characteristica.