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Eco: The Encyclopedia and the Alphabet of Thought


Charles-Nicolas Cochin (1715-1790), Frontispiece of L’Encyclopédie ou Dictionnaire raisonné des sciences, des artes, et des métiers, abbreviated as L’Encyclopédie, or Encyclopedia. One source claims that this illustration was entitled Lycurgus blessé dans une sédition, while another states that it depicts la Raison et la Philosophie arrachant son voile à la Vérité rayonnante de lumière. Drawn by Cochin in 1764, it was engraved by Benoît-Louis Prévost (1735-1804) in 1765. 

“The idea of a universal encyclopedia was something that Leibniz was never to give up. Leibniz was, for a long period, a librarian; as such, and as a historian and érudit, he could not have failed to follow the pansophic aspirations and encyclopedic ferment that filled the closing years of the seventeenth century–tremors that would yield their fruits in the century to come.

For Leibniz, the interest in the idea of a universal encyclopedia grew less and less as the basis of an alphabet of primitive terms, and more and more as a practical and flexible instrument which might provide for everyone an access to and control over the immense edifice of human learning.

In 1703, he wrote the Nouveaux essais sur l’entendement humain (which did not appear until 1765, after Leibniz’s death). This book was a confutation of the doctrines of Locke, and ends with a monumental fresco of the encyclopedia of the future.

The point of departure was a rejection of Locke’s tripartite division of knowledge into physical, ethical and logical (or semiotic). Even such a simple classification was untenable, Leibniz argued, because every item of knowledge might reasonably be considered from more than one of the three divisions.

We might treat the doctrine of spirits either as a philosophical or as a moral problem, placing it in the province either of logic or of ethics. We might even consider that a knowledge of the spirit world might prove efficacious for certain practical ends; in which case we might want to place it in the physical province.

A truly memorable story might deserve a place in the annals of universal history; yet it might equally well deserve a place in the history of a particular country, or even of a particular individual. A librarian is often undecided over the section in which a particular book needs to be catalogued (cf. Serres 1968: 22-3).

Leibniz saw in an encyclopedia the solution to these problems. An encyclopedia would be a work that was, as we might now say, polydimensional and mixed, organized–as Gensini observes (Gensini 1990: 19)–more according to “pathways” than by a classification by subject matters; it would be a model of a practico-theoretical knowledge that invited the user to move transversally, sometimes following deductive lines, as mathematicians do, and sometimes moving according to the practical purposes of the human users.

It would be necessary also to include a final index that would allow the user to find different subjects or the same subject treated in different places from different points of view (IV, 21, De la division des sciences).

It is almost as if Leibniz intended here to celebrate as a felix culpa that monument of non-dichotomical incongruity that was the encyclopedia of Wilkins; as if he were writing a rough draft for the very project that d’Alembert was to set forth at the beginning of the Encyclopédie. Dimly shining from beneath the project of Wilkins, Leibniz has recognized the first idea of a hypertext.

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 278-9.

Eco: The Problem of the Primitives

Gottfried Wilhelm von Leibniz, Dissertatio de Arte Combinatoria, frontispiece

Gottfried Wilhelm von Leibniz (1646-1716), Dissertatio de Arte Combinatoria, frontispiece, Dissertation on the Art of Combinations or On the Combinatorial Art, Leipzig, 1666. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less.

“What did Leibniz’s ars combinatoria have in common with the projects for universal languages? The answer is that Leibniz had long wondered what would be the best way of providing a list of primitives and, consequently, of an alphabet of thoughts or of an encyclopedia.

In his Initia et specimina scientiae generalis (Gerhardt 1875: VII, 57-60) Leibniz described an encyclopedia as an inventory of human knowledge which might provide the material for the art of combination.

In the De organo sive arte magna cogitandi (Couturat 1903: 429-31) he even argued that “the greatest remedy for the mind consists in the possibility of discovering a small set of thoughts from which an infinity of other thoughts might issue in order, in the same way as from a small set of numbers [the integers from 1 to 10] all the other numbers may be derived.”

It was in this same work that Leibniz first made hints about the combinational possibilities of a binary calculus.

In the Consilium de Encyclopedia nova conscribenda methodo inventoria (Gensini 1990: 110-20) he outlined a system of knowledge to be subjected to a mathematical treatment through rigorously conceived propositions. He proceeded to draw up a plan of how the sciences and other bodies of knowledge would then be ordered: from grammar, logic, mnemonics topics (sic) and so on to morals and to the science of incorporeal things.

In a later text on the Termini simpliciores from 1680-4 (Grua 1948: 2, 542), however, we find him falling back to a list of elementary terms, such as “entity,” “substance” and “attribute,” reminiscent of Aristotle’s categories, plus relations such as “anterior” and “posterior.”

In the Historia et commendatio linguae characteristicae we find Leibniz recalling a time when he had aspired after “an alphabet of human thoughts” such that “from the combination of the letters of this alphabet, and from the analysis of the vocables formed by these letters, things might be discovered and judged.”

It had been his hope, he added, that in this way humanity might acquire a tool which would augment the power of the mind more than telescopes and microscopes had enlarged the power of sight.

Waxing lyrical over the possibilities of such a tool, he ended with an invocation for the conversion of the entire human race, convinced, as Lull had been, that if missionaries were able to induce the idolators to reason on the basis of the calculus they would soon see that the truths of our faith concord with the truths of reason.

Immediately after this almost mystical dream, however, Leibniz acknowledged that such an alphabet had yet to be formulated. Yet he also alluded to an “elegant artifice:”

“I pretend that these marvelous characteristic numbers are already given, and, having observed certain of their general properties, I imagine any other set of numbers having similar properties, and, by using these numbers, I am able to prove all the rules of logic with an admirable order, and to show in what way certain arguments can be recognized as valid by regarding their form alone.” (Historia et commendatio, Gerhardt 1875: VII, 184ff).

In other words, Leibniz is arguing that the primitives need only be postulated as such for ease of calculation; it was not necessary that they truly be final, atomic and unanalyzable.

In fact, Leibniz was to advance a number of important philosophical considerations that led him to conclude that an alphabet of primitive thought could never be formulated. It seemed self-evident that there could be no way to guarantee that a putatively primitive term, obtained through the process of decomposition, could not be subjected to further decomposition.

This was a thought that could hardly have seemed strange to the inventor of the infinitesimal calculus:

There is not an atom, indeed there is no such thing as a body so small that it cannot be subdivided [ . . . ] It follows that there is contained in every particle of the universe a world of infinite creatures [ . . . ] There can be no determined number of things, because no such number could satisfy the need for an infinity of impressions.” (Verità prime, untitled essay in Couturat 1903: 518-23).

If no one conception of things could ever count as final, Leibniz concluded that we must use the conceptions which are most general for us, and which we can consider as prime terms only within the framework of a specific calculus.

With this, Leibniz’s characteristica breaks its link with the research into a definitive alphabet of thought. Commenting on the letter to Mersenne in which Descartes described the alphabet of thoughts as a utopia, Leibniz noted:

“Even though such a language depends upon a true philosophy, it does not depend upon its perfection. This is to say: the language can still be constructed despite the fact that the philosophy itself is still imperfect.

As the science of mankind will improve, so its language will improve as well. In the meantime, it will continue to perform an admirable service by helping us retain what we know, showing what we lack, and inventing means to fill that lack.

Most of all, it will serve to avoid those disputes in the sciences that are based on argumentation. For the language will make argument and calculation the same thing.” (Couturat 1903: 27-8).

This was not only a matter of convention. The identification of primitives cannot precede the formulation of the lingua characteristica because such a language would not be a docile instrument for the expression of thought; it is rather the calculating apparatus through which those thoughts must be found.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 275-7.

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