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Tag: 1875

Eco: The Last Flowering of Philosophic Languages, 2

Giovan Giuseppe Matraja, Genigrafia italiana, 1831

Giovanni Giuseppe Matraja, Genigrafia italiana, 1831. Original held at the University of Illinois at Urbana-Champaign, with a glorious eBook format posted by the Hathitrust and GoogleBooks among others. 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. 

Vismes was not the only one to fall foul of this seemingly elementary snare. In 1831 Father Giovan Giuseppe Matraja published his Genigrafia italiana, which is nothing other than a polygraphy with five (Italian) dictionaries, one for nouns, one for verbs, one for adjectives, one for interjections and one for adverbs.

Since the five dictionaries account for only 15,000 terms, Matraja adds another dictionary that lists 6,000 synonyms. His method managed to be both haphazard and laborious: Matraja divided his terms into a series of numbered classes each containing 26 terms, each marked by an alphabetical letter: thus A1 means “hatchet,” A2 means “hermit,” A1000 means “encrustation,” A360 means “sand-digger,” etc.

Even though he had served as a missionary in South America, Matraja was still convinced that all cultures used the same system of notions. He believed that western languages (all of which he seemed to imagine were derived from Latin grammar) might perfectly well serve as the basis for another language, because, by a special natural gift, all peoples used the same syntactic structures when speaking–especially American Indians.

In fact, he included a genigraphical translation of the Lord’s Prayer comparing it with versions in twelve other languages including Nahuatl, Chilean and Quechua.

In 1827 François Soudre invented the Solresol (Langue musicale universelle, 1866). Soudre was also persuaded that the seven notes of the musical scale composed an alphabet comprehensible by all the peoples of the world, because the notes are written in the same way in all languages, and could be sung, recorded on staves, represented with special stenographic signs, figured in Arabic numerals, shown with the seven colors of the spectrum, and even indicated by the touch of the fingers of the right and left hands–thus making their representation comprehensible even for the deaf, dumb and blind.

It was not necessary that these notes be based on a logical classification of ideas. A single note expresses terms such as “yes” (musical si, or B) and “no” (do, or C); two notes express pronouns (“mine” = redo, “yours” = remi); three notes express everyday words like “time” (doredo) or “day” (doremi).

The initial notes refer to an encyclopedic class. Yet Soudre also wished to express opposites by musical inversion (a nice anticipation of a twelve-tone music procedure): thus, if the idea of “God” was naturally expressed by the major chord built upon the tonic, domisol, the idea of “Satan” would have to be the inversion, solmido.

Of course, this practice makes nonsense of the rule that the first letter in a three-note term refers to an encyclopedic class: the initial do refers to the physical and moral qualities, but the initial sol refers back to arts and sciences (and to associate them with Satan would be an excess of bigotry).

Besides the obvious difficulties inherent in any a priori language, the musical language of Soudre added the additional hurdle of requiring a good ear. We seem in some way to be returning to the seventeenth century myth of the language of birds, this time with less glossolalic grace, however, and a good deal more pure classificatory pedantry.

Couturat and Leau (1903: 37) awarded to the Solresol the encomium of being “the most artificial and most impracticable of all the a priori languages.” Even its number system is inaccessible; it is based on a hexadecimal system which, despite its claims to universality, still manages to indulge in the French quirk of eliminating names for 70 and 90.

Yet Soudre labored for forty-five years to perfect his system, obtaining in the meantime testimonials from the Institut de France, from musicians such as Cherubini, from Victor Hugo, Lamartine and Alexander von Humboldt; he was received by Napoleon III; he was awarded 10,000 francs at the Exposition Universale in Paris in 1855 and the gold medal at the London Exposition of 1862.

Let us neglect for the sake of brevity the Système de langue universelle of Grosselin (1836), the Langue universelle et analytique of Vidal (1844), the Cours complet de langue universelle by Letellier (1832-55), the Blaia Zimandal of Meriggi (1884), the projects of so distinguished a philosopher as Renouvier (1885), the Lingualumina of Dyer (1875), the Langue internationale étymologique of Reimann (1877), the Langue naturelle of Maldant (1887), the Spokil of Dr. Nicolas (1900), the Zahlensprache of Hilbe (1901), the Völkerverkehrsprache of Dietrich (1902), and the Perio of Talundberg (1904).

We will content ourselves with a brief account of the Projet d’une langue universelle of Sotos Ochando (1855). Its theoretical foundations are comparatively well reasoned and motivated; its logical structure could not be of a greater simplicity and regularity; the project proposes–as usual–to establish a perfect correspondence between the order of things signified and the alphabetical order of the words that express them.

Unfortunately–here we go again–the arrangement is empirical: A refers to inorganic material things, B to the liberal arts, C to the mechanical arts, D to political society, E to living bodies, and so forth.

With the addition of the morphological rules, one generates, to use the mineral kingdom as an example, the words Ababa for oxygen, Ababe for hydrogen, Ababi for nitrogen, Ababo for sulphur.

If we consider that the numbers from one to ten are siba, sibe, sibi, sibo, sibu, sibra, sibre, sibri, sibro, and sibru (pity the poor school children having to memorize their multiplication tables), it is evident that words with analogous meanings are all going to sound the same.

This makes the discrimination of concepts almost impossible, even if the formation of names follows a criterion similar to that of chemistry, and the letters stand for the components of the concept.

The author may claim that, using his system, anyone can learn over six million words in less than an hour; yet as Couturat and Leau remark (1903: 69), learning a system that can generate six million words in an hour is not the same as memorizing, recognizing, six million meanings.

The list could be continued, yet towards the end of the nineteenth century, news of the invention of a priori languages was becoming less a matter for scientific communications and more one for reports on eccentric fellows–from Les fous littéraires by Brunet in 1880 to Les fous littéraires by Blavier in 1982.

By now, the invention of a priori languages, other than being the special province of visionaries of all lands, had become a game (see Bausani 1970 and his language Markuska) or a literary exercise (see Yaguello 1984 and Giovannoli 1990 for the imaginary languages of science fiction).

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 305-8.

Eco: Blind Thought, 2

Wittgenstein, Ludwig

Ludwig Wittgenstein (1899-1951), portrait by Moritz Nähr (1859-1945), 1930, held by the Austrian National Library under Accession Number Pf 42.805: C (1). 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 70 years or less. 

“As Leibniz observed in the Accessio ad arithmeticum infinitorum of 1672 (Sämtliche Schriften und Briefen, iii/1, 17), when a person says a million, he does not represent mentally to himself all the units in that number. Nevertheless, calculations performed on the basis of this figure can and must be exact.

Blind thought manipulates signs without being obliged to recognize the corresponding ideas. For this reason, increasing the power of our minds in the manner that the telescope increases the power of our eyes, it does not entail an excessive effort.

“Once this has been done, if ever further controversies should arise, there should be no more reason for disputes between two philosophers than between two calculators. All that will be necessary is that, pen in hand, they sit down together at a table and say to each other (having called, if they so please, a friend) “let us calculate.” (In Gerhardt 1875: VII, 198ff).

Leibniz’s intention was thus to create a logical language, like algebra, which might lead to the discovery of unknown truths simply by applying syntactical rules to symbols. When using this language, it would no more be necessary, moreover, to know at every step what the symbols were referring to than it was necessary to know the quantity represented by algebraic symbols to solve an equation.

Thus for Leibniz, the symbols in the language of logic no longer stood for concrete ideas; instead, they stood in place of them. The characters “not only assist reasoning, they substitute for it.” (Couturat 1901: 101).

Dascal has objected (1978: 213) that Leibniz did not really conceive of his characteristica as a purely formal instrument apparatus, because symbols in his calculus are always assigned an interpretation. In an algebraic calculation, he notes, the letters of the alphabet are used freely; they are not bound to particular arithmetical values.

For Leibniz, however, we have seen that the numerical values of the characteristic numbers were, so to speak, “tailored” to concepts that were already filled with a content–“man,” “animal,” etc.

It is evident that, in order to demonstrate that “man” does not contain “monkey,” the numerical values must be chosen according to a previous semantic decision. It would follow that what Leibniz proposed was really a system both formalized and interpreted.

Now it is true that Leibniz’s posterity elaborated such systems. For instance, Luigi Richer (Algebrae philosophicae in usum artis inveniendi specimen primum, “Melanges de philosophie et de mathématique de la Societé Royale de Turin,” 1761: II/3), in fifteen short and extremely dry pages, outlined a project for the application of algebraic method to philosophy, by drawing up a tabula characteristica containing a series of general concepts (such as aliquid, nihil, contingens, mutabile) and assigning to each a conventional sign.

The system of notation, semicircles orientated in various ways, makes the characters hard to distinguish from one another; still, it was a system of notation that allowed for the representation of philosophical combinations such as “This Possible cannot be Contradictory.”

This language is, however, limited to abstract reasoning, and, like Lull, Richer did not make full use of the possibilities of combination in his system as he wished to reject all combinations lacking scientific utility (p. 55).

Towards the end of the eighteenth century, in a manuscript dating 1793-4, we also find Condorcet toying with the idea of a universal language. His text is an outline of mathematical logic, a langue des calculs, which identifies and distinguishes intellectual processes, expresses real objects, and enunciates the relations between the expressed objects and the intellectual operations which discover the enunciated relations.

The manuscript, moreover, breaks off at precisely the point where it had become necessary to proceed to the identification of the primitive ideas; this testifies that, by now, the search for perfect languages was definitively turning in the direction of a logico-mathematical calculus, in which no one would bother to draw up a list of ideal contents but only to prescribe syntactic rules (Pellerey 1992a: 193ff).

We could say that Leibniz’s characteristica, from which Leibniz had also hoped to derive metaphysical truths, is oscillating between a metaphysical and ontological point of view, and the idea of designing a simple instrument for the construction of deductive systems (cf. Barone 1964: 24).

Moreover, his attempts oscillate between a formal logic (operating upon unbound variables) and what will later be the project of many contemporary semantic theories (and of artificial intelligence as well), where syntactic rules of a mathematical kind are applied to semantic (and therefore interpreted) entities.

But Leibniz ought to be considered the forerunner of the first, rather than of the second, line of thought.

The fundamental intuition that lies behind Leibniz’s proposal was that, even if the numbers were chose arbitrarily, even if it could not be guaranteed that the primitives posited for the same of argument were really primitive at all, what still guaranteed the truth of the calculus was the fact that the form of the proposition mirrored an objective truth.

Leibniz saw an analogy between the order of the world, that is, of truth, and the grammatical order of the symbols in language. Many have seen in this a version of the picture theory of language expounded by Wittgenstein in the Tractatus, according to which “a picture has logico-pictorial form in common with what it depicts” (2.2).

Leibniz was thus the first to recognize that the value of his philosophical language was a function of its formal structure rather than of its terms; syntax, which he called habitudo or propositional structure, was more important than semantics (Land 1974: 139).

“It is thus to be observed that, although the characters are assumed arbitrarily, as long as we observe a certain order and certain rule in their use, they give us results which always agree with each other. (Dialogus in Gerhardt 1875: VII, 190-3).

Something can be called an “expression” of something else whenever the structure [habitudines] subsisting in the expression corresponds to the structure of that which it wishes to express [ . . . ].

From the sole structure of the expression, we can reach the knowledge of the properties of the thing expressed [ . . . ] as long as there is maintained a certain analogy between the two respective structures.” (Quid sit idea in Gerhardt 1875: VII, 263-4).

What other conclusion could the philosopher of preestablished harmony finally have reached?”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 281-4.

Eco: Blind Thought


Johann Heinrich Lambert (1728-1777), Neues Organon, Leipzig, Johann Wendler, 1764. 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. 

“We have seen that Leibniz came to doubt the possibility of constructing an alphabet that was both exact and definitive, holding that the true force of the calculus of characteristic numbers lay instead in its rules of combination.

Leibniz became more interested in the form of the propositions generated by his calculus than in the meaning of the characters. On various occasions he compared his calculus with algebra, even considering algebra as merely one of the possible forms that calculus might take, and thought more and more of a rigorously quantitative calculus able to deal with qualitative problems.

One of the ideas that circulated in his thought was that, like algebra, the characteristic numbers represented a form of blind thought, or cogitatio caeca (cf. for example, De cognitione, veritate et idea in Gerhardt 1875: IV, 422-6). By blind thought Leibniz meant that exact results might be achieved by calculations carried out upon symbols whose meanings remained unknown, or of which it was at least impossible to form clear and distinct notions.

In a page in which he defined his calculus as the only true example of the Adamic language, Leibniz provides an illuminating set of examples:

“All human argument is carried out by means of certain signs or characters. Not only things themselves but also the ideas which those things produce neither can nor should always be amenable to distinct observation: therefore, in place of them, for reasons of economy we use signs.

If, for example, every time that a geometer wished to name a hyperbole or a spiral or a quadratrix in the course of a proof, he needed to hold present in his mind their exact definitions or manner in which they were generated, and then, once again, the exact definitions of each of the terms used in his proof, he would be likely to be very tardy in arriving at his conclusions. [ . . . ]

For this reason, it is evident that names are assigned to the contracts, to the figures and to various other types of things, and signs to the numbers in arithmetic and to magnitudes in algebra [ . . . ]

In the list of signs, therefore, I include words, letters, the figures in chemistry and astronomy, Chinese characters, hieroglyphics, musical notes, steganographic signs, and the signs in arithmetic, algebra, and in every other place where they serve us in place of things in our arguments.

Where they are written, designed, out sculpted, signs are called characters [ . . . ]. Natural languages are useful to reason, but are subject to innumerable equivocations, nor can be used for calculus, since they cannot be used in a manner which allows us to discover the errors in an argument by retracing our steps to the beginning and to the construction of our words–as if errors were simply due to solecisms or barbarisms.

The admirable advantages [of the calculus] are only possible when we use arithmetical or algebraic signs and arguments are entirely set out in characters: for here every mental error is exactly equivalent to a mistake in calculation.

Profoundly meditating on this state of affairs, it immediately appeared as clear to me that all human thoughts might be entirely resolvable into a small number of thoughts considered as primitive.

If then we assign to each primitive a character, it is possible to form other characters for the deriving notions, and we would be able to extract infallibly from them their prerequisites and the primitive notions composing them; to put it in a word, we could always infer their definitions and their values, and thereby the modifications to be derived from their definitions.

Once this had been done, whoever uses such characters in their reasoning and in their writing, would either never make an error, or, at least, would have the possibility of immediately recognizing his own (or other people’s) mistakes, by using the simplest of tests.” (De scientia universalis seu calculo philosophico in Gerhardt 1875: VII, 198-203).

This vision of blind thought was later transformed into the fundamental principle of the general semiotics of Johann Heinrich Lambert in his Neues Organon (1762) in the section entitled Semiotica (cf. Tagliagambe 1980).

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 279-81.

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.

Eco: Characteristica and Calculus

Gottfried Wilhelm von Leibniz, Dissertatio de Arte Combinatoria

Gottfried Wilhelm von Leibniz (1646-1716), Dissertatio de Arte Combinatoria, an excerpt from his first doctoral dissertation, Dissertation on the Art of Combinations, 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. 

“The theme of invention and discovery should remind us of Lull; and, in fact, Lull’s ars combinatoria was one of Leibniz’s first sources. In 1666, at the age of twenty, Leibniz composed his own Dissertatio de arte combinatoria (Gerhardt 1875: IV, 27-102). But the dream of the combinatoria was to obsess him for the rest of his life.

In his short Horizon de la doctrine humaine (in Fichant 1991), Leibniz dealt with a problem that had already troubled Father Mersenne: how many utterances, true, false or even nonsensical, was it possible to formulate using an alphabet of 24 letters?

The point was to determine the number of truths capable of expression and the number of expressions capable of being put into writing. Given that Leibniz had found words of 31 letters in Latin and Greek, an alphabet of 24 letters would produce 2432 words of 31 letters.

But what is the maximum length of an expression? Why should an expression not be as long as an entire book? Thus the sum of the expressions, true or false, that a man might read in the course of his life, imagining that he reads 100 pages a day and that each page contains 1,000 letters, is 3,650,000,000.

Even imagining that this man can live one thousand years, like the legendary alchemist Artephius, it would still be the case that “the greatest expressible period, or the largest possible book that a man can read, would have 3,650,000,000,000 [letters], and the number of truths, falsehoods, or sentences expressible–that is, readable, regardless of pronounceability or meaningfulness–will be 24365,000,000,001 – 24/23 [letters].”

We can imagine even larger numbers. Imagine our alphabet contained 100 letters; to write the number of letters expressible in this alphabet we would need to write a 1 followed by 7,300,0000,000,000 (sic) zeros. Even to write such a number it would take 1,000 scribes working for approximately 37 years.

Leibniz’s argument at this point is that whatever we take the number of propositions theoretically capable of expression to be–and we can plausibly stipulate more astronomical sums than these–it will be a number that vastly outstrips the number of true or false expressions that humanity is capable of producing or understanding.

From such a consideration Leibniz concluded paradoxically that the number of expressions capable of formulation must always be finite, and, what is more, that there must come a moment at which humanity would start to enunciate them anew.

With this thought, Leibniz approaches the theme of the apochatastasis or of universal reintegration–what we might call the theme of the eternal return.

This was a line of speculation more mystical than logical, and we cannot stop to trace the influences that led Leibniz to such fantastic conclusions.

It is plain, however, that Leibniz has been inspired by Lull and the kabbala, even if Lull’s own interest was limited to the generation of just those propositions that expressed true and certain knowledge and he thus would never have dared to enlarge his ars combinatoria to include so large a number of propositions.

For Leibniz, on the contrary, it was a fascination with the vertiginous possibilities of discovery, that is of the infinite number of expressions of which a simple mathematical calculation permitted him to conceive, that served as inspiration.

At the time he was writing his Dissertatio, Leibniz was acquainted with Kircher’s Polygraphia, as well as with the work of the anonymous Spaniard, of Becher, and of Schott (while saying that he was waiting for the long-promised Ars magna sciendi of the “immortal Kircher“).

He had yet to read Dalgarno, and Wilkins had still not published his Essay. Besides, there exists a letter from Kircher to Leibniz, written in 1670, in which the Jesuit confessed that he had not yet read Leibniz’s Dissertatio.

Leibniz also elaborated in the Dissertatio his so-called method of “complexions,” through which he might calculate, given n elements, how many groups of them, taken t at a time, irrespective of their ordering, can be ordered.

He applied this method to syllogisms before he passed to his discussion of Lull (para. 56). Before criticizing Lull for limiting the number of his elements, Leibniz made the obvious observation that Lull failed to exploit all the possibilities inherent in his combinatorial art, and wondered what could happen with variations of order, which could produce a greater number.

We already know the answer: Lull not only limited the number of elements, but he rejected those combinations that might produce propositions which, for theological and rhetorical reasons, he considered false.

Leibniz, however, was interested in a logica inventiva (para. 62) in which the play of combinations was free to produce expressions that were heretofore unknown.

In paragraph 64 Leibniz began to outline the theoretical core of his characteristica universalis. Above all, any given term needed to be resolved into its formal parts, the parts, that is, that were explicitly entailed by its definition.

These parts then had to be resolved into their own components, and so on until the process reached terms which could not, themselves, be defined–that is, the primitives. Leibniz included among them not only things, but also modes and relations.

Other terms were to be classified according to the number of prime terms they contained: if they were composed from 2 prime terms, they were to be called com2nations; if from 3 prime terms, com3nations, and so forth. Thereby a hierarchy of classes of increasing complexity could be created.

Leibniz returned to this argument a dozen years later, in the Elementa characteristicae universalis. Here he was more generous with his examples. If we accept the traditional definition of man as “rational animal,” we might consider man as a concept composed of “rational” and “animal.”

We may assign numbers to these prime terms: animal = 2, and rational = 3. The composite concept of man can be represented as the expression 2 * 3, or 6.

For a proposition to be true, if we express fractionally the subject-predicate (S/P) relationship, the number which corresponds to the subject must be exactly divisible by the number which corresponds to the predicate.

Given the preposition “all men are animals,” the number for the subject (men), is 6; the number for animals is 2; the resulting fraction is 6/2 = 3. Three being an integer, consequently, the preposition is true.

If the number for monkey were 10, we could demonstrate the falsity of either the proposition “all men are monkeys” or “all monkeys are men:” “the idea of monkey does not contain the idea of man, nor, vice versa, does the idea of the latter contain the former, because neither can 6 be exactly divided by 10, nor 10 by 6” (Elementa, in Couturat 1903: 42-92). These were principles that had all been prefigured in the Dissertatio.

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 271-5.

Eco: From Leibniz to the Encyclopédie


Johann Friedrich Wentzel (1670-1729), Gottfried Wilhelm Leibniz (1646-1716), circa 1700. 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. 

“In 1678 Leibniz composed a lingua generalis (in Couturat 1903). After decomposing all of human knowledge into simple ideas, and assigning a number to each, Leibniz proposed a system of transcription for these numbers in which consonants stood for integers and vowels for units, tens and powers of ten:

Umberto Eco, The Search for the Perfect Language, p. 270

Umberto Eco, The Search for the Perfect Language, p. 270. 

In this system, the figure 81,374, for example, would be transcribed as mubodilefa. In fact, since the relevant power of ten is shown by the following vowel rather than by the decimal place, the order of the letters in the name is irrelevant: 81,374 might just as easily be transcribed as bodifalemu.

This system might lead us to suspect that Leibniz too was thinking of a language in which the users might one day discourse on bodifalemu or gifeha (= 546) just as Dalgarno or Wilkins proposed to speak in terms of nekpot or deta.

Against this supposition, however, lies the fact that Leibniz applied himself to another, particular form of language, destined to be spoken–a language that resembled the latino sine flexione invented at the dawn of our own century by Peano.

This was a language whose grammar was drastically simplified and regularized: one declension for nouns, one conjunction for verbs, no genders, no plurals, adjectives and adverbs made identical, verbs reduced to the formula of copula + adjective.

Certainly, if my purpose were to try to delineate the entire extent of the linguistic projects undertaken by Leibniz throughout the course of his life, I would have to describe an immense philosophical and linguistically monument displaying four major aspects:

(1) the identification of a system of primitives, organized in an alphabet of thought or in a general encyclopedia;

(2) the elaboration of an ideal grammar, inspired probably by the simplifications proposed by Dalgarno, of which the simplified Latin is one example;

(3) the formulation of a series of rules governing the possible pronunciation of the characters;

(4) the elaboration of a lexicon of real characters upon which the speaker might perform calculations that would automatically lead to the formulation of true propositions.

The truth is, however, that by the end of his career, Leibniz had abandoned all research in the initial three parts of the project. His real contribution to linguistics lies in his attempts at realizing the fourth aspect.

Leibniz had little interest in the kinds of universal language proposed by Dalgarno and Wilkins, though he was certainly impressed by their efforts. In a letter to Oldenburg (Gerhardt 1875: VII, 11-5), he insisted that his notion of a real character was profoundly different from that of those who aspired to a universal writing modeled on Chinese, or tried to construct a philosophic language free from all ambiguity.

Leibniz had always been fascinated by the richness and plurality of natural languages, devoting his time to the study of their lineages and the connections between them. He had concluded that it was not possible to identify (much less to revive) an alleged Adamic language, and came to celebrate the very confusio linguarum that others were striving to eliminate (see Gensini 1990, 1991).

It was also a fundamental tenet of his monadology that each individual had a unique perspective on the world, as if a city would be represented from as many different viewpoints as the different positions of its inhabitants.

It would have been incongruous for the philosopher who held this doctrine to oblige everyone to share the same immutable grillwork of genera and species, without taking into account particularities, diversities and the particular “genius” of each natural language.

There was but one facet of Leibniz’s personality that might have induced him to seek after a universal form of communication; that was his passion for universal peace, which he shared with Lull, Cusanus and Postel.

In an epoch in which his english predecessors and correspondents were waxing enthusiastic over the prospect of universal languages destined to ease the way for future travel and trade, beyond an interest in the exchange of scientific information, Leibniz displayed a sensitivity towards religious issues totally absent even in high churchmen like Wilkins.

By profession a diplomat and court councillor, Leibniz was a political, rather than an academic, figure, who worked for the reunification of the church. This was an ecumenicism that reflected his political preoccupations; he envisioned an anti-French bloc of Spain, the papacy, the Holy Roman Emperor and the German princes.

Still, his desire for unity sprang from purely religious motives as well; church unity was the necessary foundation upon which a peaceful Europe could be built.

Leibniz, however, never thought that the main prerequisite for unity and peace was a universal tongue. Instead, he thought that the cause of peace might be better served by science, and by the creation of a scientific language which might serve as a common instrument in the discovery of truth.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 269-1.

Eco: Postel’s Universalistic Utopia

Guillaume Postel, The Great Key, Eliphas Levi, The Key of the Great Mysteries, 1861

Guillaume Postel (1510-81), The Great Key, in Eliphas Levi (1810-75), La Clef des Grands MystèresThe Key of the Great Mysteries, 1861.

“A special place in the story of the renewal of Hebrew studies belongs to the French utopian thinker and érudit, Guillaume Postel (1510-81). Councillor to the kings of France, close to the major religious, political and scientific personalities of his epoch, Postel returned from a series of diplomatic missions to the Orient, voyages which enabled him to study Arabic and Hebrew as well as to learn of the wisdom of the kabbala, a changed and marked man.

Already renowned as a Greek philologist, around 1539, Postel was appointed to the post of “mathematicorum et peregrinarum linguarum regius interpretes” in that Collège des Trois Langues which eventually became the Collège de France.

In his De originibus seu de Hebraicae linguae et gentis antiquitate (1538), Postel argued that Hebrew came directly from the sons of Noah, and that, from it, Arabic, Chaldean, Hindi and, indirectly, Greek had all descended as well.

In Linguarum duodecem characteribus differentium alphabetum, introductio (1538), by studying twelve different alphabets he proved the common derivation of every language. From here, he went on to advance the project of a return to Hebrew as the instrument for the peaceable fusion of the peoples of differing races.

To support his argument that Hebrew was the proto-language, Postel developed the criterion of divine economy. As there was but one human race, one world and one God, there could be but one language; this was a “sacred language, divinely inspired into the first man” (De Foenicum litteris, 1550).

God had educated Adam by breathing into him the capacity to call things by their appropriate names (De originibus, seu, de varia et potissimum orbit Latino ad hanc diem incognita aut inconsyderata historia, 1553).

Although Postel does not seem to have thought either of an innate faculty for languages or of a universal grammar, as Dante had done, there still appears in many of his writings the notion of an Averroist active intellect as the repository of the forms common to all humanity, in which the roots of our linguistic faculty must be sought (Les très merveilleuses victoires des femmes du nouveau monde together with La doctrine du siècle doré, both from 1553).

Postel’s linguistic studies were connected to his particular vision of a religious utopia: he foresaw the reign of universal peace.

In his De orbis terrae concordia (1544:I) he clearly states that his studies in language would help to lay the foundations upon which a universal concord could be created. He envisioned the creation of a linguistic commonwealth that would serve as living proof to those of other faiths that not only was the message of Christianity true, but equally it verified their own religious beliefs: there are some principles of a natural religion, or sets of innate ideas held by all peoples (De orbis, III).

Here was the spirit that had inspired Lull and Nicholas of Cusa. Yet Postel was convinced that universal peace could only be realized under the protection of the king of France: among the world’s rulers the king of France alone held a legitimate claim to the title of king of the world.

He was the direct descendent of Noah, through Gomer, son of Japheth, founder of the Gallic and Celtic races (cf. particularly Les raisons de la monarchie, c. 1551). Postel (Trésor des propheties de l’univers, 1556) supported this contention with a traditional etymology (see, for example, Jean Lemaire de Belges, Illustration de Gaule et singularitez de Troye, 1512-3, fol. 64r): in Hebrew, the term gallus meant “he who overcame the waves;” thus the Gauls were the people who had survived the waters of the Flood (cf. Stephens 1989:4).

Postel first attempted to convert Francis I to his cause. The king, however, judged him a fanatic, and he lost favor at court. He went to Rome, hoping to win over to his utopian schemes Ignatius of Loyola, whose reformist ideals seemed kindred to his own.

It did not take Ignatius long, however, to realize that Postel’s ambitions were not identical to those of the Jesuits. Accepting Postel’s project might have placed their vow of obedience to the pope at risk.

Besides, Ignatius was a Spaniard, and the idea of turning the king of France into the king of the world would hardly have appealed to him. Although Postel continued long afterwards to look upon the Jesuits as the divine instrument for the creation of universal peace, he himself was forced to leave the company after a mere year and a half.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 75-7.

Kvanvig: Initiation is a Restriction of Marduk

“We think van der Toorn is right in taking this as a comment to the tendency present in the Catalogue. This is still no absolute chronology, since apkallus are listed as authors in III, 7; IV, 11; and VI, 11.

Nevertheless, the commentary seems to underscore three stages in the transmission of highly recognized written knowledge: it starts in the divine realm with the god of wisdom Ea; at the intersection point between the divine and the human stands Uanadapa; and as the third link in this chain stands (we must presuppose) an ummanu, “scholar.”

Tablet of Uruk. The ritual of daily sacrifices in the temple of the god Anu in Uruk.  Seleucid period, 3rd-2nd Centuries BCE, Hellenistic, from Uruk.  Baked clay, 22,3 x 10,4 cm  Louvre, AO 6451.

Tablet of Uruk. The ritual of daily sacrifices in the temple of the god Anu in Uruk.
Seleucid period, 3rd-2nd Centuries BCE, Hellenistic, from Uruk.
Baked clay, 22,3 x 10,4 cm
Louvre, AO 6451.

A. Lenzi has called attention to a colophon to a medical text which reveals a similar kind of transmission:

“Salves (and) bandages: tested (and) checked, which are ready at hand, composed by the ancient apkallus from before the flood, which in Šuruppak in the second year of Enlil-bani, king of Isin, Enlil-muballit, apkallu of Nippur, bequeathed. A non-expert may show an expert. An expert may not show a non-expert. A restriction of Marduk.”

(Medical Text, AMT 105, 1, 21-5. Lenzi, Secrecy and the Gods, p. 117.)

The models of transmission in the commentary of the Catalogue and in this colophon are not exactly the same, but the tendency is. In this text, an expert, possibly an āšipu, has in his hands a tablet of high dignity: it belongs to the secrets of the gods (cf. below).

AM-102 ; No. #1 (K4023) British Museum of London 

Tablet K.4023  COL. I  [Starting on Line 38] . . .  Root of caper which (is) on a grave, root of thorn (acacia) which (is) on a grave, right horn of an ox, left horn of a kid, seed of tamarisk, seed of laurel, Cannabis, seven drugs for a bandage against the Hand of a Ghost thou shalt bind on his temples.  FOOTNOTES:  [1] - The American Journal of Semitic Languages and Literatures, Vol. 54, No. 1/4 (Oct., 1937), pp. 12-40; Assyrian Prescriptions for the Head By R. Campbell Thompson

AM-102 ; No. #1 (K4023)
British Museum of London 

Tablet K.4023
[Starting on Line 38] . . .
Root of caper which (is) on a grave, root of thorn (acacia) which (is) on a grave, right horn of an ox, left horn of a kid, seed of tamarisk, seed of laurel, Cannabis, seven drugs for a bandage against the Hand of a Ghost thou shalt bind on his temples.
[1] – The American Journal of Semitic Languages and Literatures, Vol. 54, No. 1/4 (Oct., 1937), pp. 12-40; Assyrian Prescriptions for the Head By R. Campbell Thompson

Therefore, if somebody not belonging to the initiated by accident should have such a tablet, he may show it to the expert, but the expert should never show it to an uninitiated person. The content of the tablet was secret; it went back to the ancient apkallus from before the flood.

Afterwards a distinguished sage, an apkallu in Nippur, inherited it, and from this line of transmission it arrived to the scholar writing this colophon. The division between the apkallus before the flood and the postdiluvian apkallu in Nippur may here be similar to the division of the first group of apkallus of divine descent and the next group of four apkallus of human descent in Bīt Mēseri.

As we have seen, the Late Babylonian Uruk tablet also had a division between a group of seven “before the flood” and a group of ten afterwards, but here the first seven were apkallus, and the next group (with one or two exceptions) were ummanus.

What we observe here is confirmed by two independent contributions with different scope that we already have called attention to, K. van der Toorn, Scribal Culture and the Making of the Hebrew Bible, and A. Lenzi, Secrecy and the Gods.

They are both concerned with the transition from oral transmission of divine messages to written revelations, and they both use Mesopotamian sources from the first millennium as an analogy to what took place in Israel in the formation of the Hebrew Bible.

(van der Toorn, Scribal Culture, pp. 205-21; Lenzi, Secrecy and the Gods, pp. 67-122.)

Enuma Elish means “when above”, the two first words of the epic.  This Babylonian creation story was discovered among the 26,000 clay tablets found by Austen Henry Layard in the 1840's at the ruins of Nineveh.  Enuma Elish was made known to the public in 1875 by the Assyriologist George Adam Smith (1840-76) of the British Museum, who was also the discoverer of the Babylonian Epic of Gilgamesh. He made several of his findings on excavations in Nineveh.

Enuma Elish means “when above”, the two first words of the epic.
This Babylonian creation story was discovered among the 26,000 clay tablets found by Austen Henry Layard in the 1840’s at the ruins of Nineveh.
Enuma Elish was made known to the public in 1875 by the Assyriologist George Adam Smith (1840-76) of the British Museum, who was also the discoverer of the Babylonian Epic of Gilgamesh. He made several of his findings on excavations in Nineveh.

Van der Toorn is concerned about the broad tendency in Mesopotamian scholarly series from the end of the second millennium to classify these as nisirti šamê u erseti, “a secret of heaven and earth.” This expression, occurring in colophons and elsewhere, does two things to the written scholarly lore: on the one hand, it claims that this goes back to a divine revelation; on the other hand, it restricts this revelation to a defined group of scholars.

This tendency goes along with the tendency to date the written wisdom back to primeval time, or to the time before the flood. This also concerns the most well-known compositions from the end of the second millennium, Enuma Elish and the standard version of Gilgamesh.”

Helge Kvanvig, Primeval History: Babylonian, Biblical, and Enochic: An Intertextual Reading, Brill, 2011, pp. 149-51.

A Digression on Berossus and the Babyloniaca

“The books written by Berossus, priest of Marduk at Babylon in the early third century B.C., have been lost, and all that we know about them comes from the twenty-two quotations or paraphrases of his work by other ancient writers (so-called Fragmenta), and eleven statements about Berossus (Testimonia) made by classical, Jewish and Christian writers.

We learn that he wrote for Antiochus I (280-261 B.C.) a work generally referred to as the Babyloniaca, a work divided into three rolls, or books, of papyrus.

Ea, or Oannes, depicted as a fish-man.

Ea, or Oannes, depicted as a fish-man.

In the first book he told how a fish-like creature named Oannes came up from the Persian Gulf, delivered to mankind the arts of civilization, and left with them a written record of how their world had come into existence; according to this record, Berossus went on, Bel had created the world out of the body of a primeval female deity. This story of the creation of the world and mankind, otherwise familiar from Enūma eliš, filled out the first book of the Babyloniaca and ended with the statement that Bel established the stars, sun, moon and the five planets.

In book two Berossus (Frag. 3) described the 120-sar (432,000-year) rule of the ten antediluvian kings, and then the Deluge itself, with some detail on the survival of Xisuthros. The postdiluvian dynasties down to Nabonassar were baldly listed in the remainder of book two.

A prism containing the Sumerian King List. Borossus cites ten antediluvian rulers.

A prism containing the Sumerian King List. Borossus cites ten antediluvian rulers.

The third book, apparently beginning with Tiglath-Pileser III, presented the Late Assyrian, Neo-Babylonian and Persian kings of Babylon, and ended with Alexander the Great.

And that, according to Felix Jacoby’s edition of the Fragmenta and Testimonia is in sum what the Babyloniaca contained. There are eight quotations dealing with astronomical and astrological matters, but these he attributed not to our Berossus, but to Pseudo-Berossus of Cos.

It was to the latter, according to Jacoby, that Josephus referred as “well known to educators, since it was he who published for the Greeks the written accounts of astronomy and the philosophical doctrines of the Chaldaeans”; or who claimed, said Vitruvius, that by study of the zodiacal signs, the planets, sun and moon, the Chaldaeans could predict what the future held in store for man.

And it was Pseudo-Berossus, according to Jacoby, to whom Seneca referred in his discussion of world-floods:

Berosos, who translated Belus (qui Belum interpretatus est), says that these catastrophes occur with the movement of the planets. Indeed, he is so certain that he assigns a date for the conflagration and the deluge. For earthly things will burn, he contends, when all the planets which now maintain different orbits come together in the sign of Cancer, and are so arranged in the same path that a straight line can pass through the spheres of all of them. The deluge will occur when the same group of planets meets in the sign of Capricorn. The solstice is caused by Cancer, winter by Capricorn; they are signs of great power since they are the turning-points in the very change of the year.”

Pseudo-Berossus of Cos”, I believe, is not only an inconvenient but an utterly improbable scholarly creation. A century ago all of our fragments were assigned to one and the same Berossus, although those dealing with the stars were segregated from those of a mythological or historical characters.

Thus the notion was fostered that Berossus wrote two works, one on Babylonian history, another on astrology. By the turn of the century E. Schwartz found unlikely Vitruvius‘ statement that Berossus eventually settled on the Aegean island of Cos, where he taught the Chaldaean disciplina.”

Robert Drews, “The Babylonian Chronicles and Berossus,” Iraq, Vol. 37, No. 1 (Spring, 1975), pp. 50-2.

The Gods Fear Zu

“A long but broken text explains why it was that he had to take refuge in the mountain of ‘Sabu under the guise of a bird of prey.

We learn that Zu gazed upon the work and duties of Mul-lil;

“he sees the crown of his majesty, the clothing of his divinity, the tablets of destiny, and Zu himself, and he sees also the father of the gods, the bond of heaven and earth.

The desire to be Bel (Mul-lil) is taken in his heart; yea, he sees the father of the gods, the bond of heaven and earth; the desire to be Bel is taken in his heart:

‘Let me seize the tablets of destiny of the gods, and the laws of all the gods let me establish (lukhmum); let my throne be set up, let me seize the oracles; let me urge on the whole of all of them, even the spirits of heaven.’

So his heart devised opposition; at the entrance to the forest where he was gazing he waited with his head (intent) during the day.

When Bel pours out the pure waters, his crown was placed on the throne, stripped from (his head). The tablets of destiny (Zu) seized with his hand; the attributes of Bel he took; he delivered the oracles.

(Then) Zu fled away and sought his mountains. He raised a tempest, making (a storm).”

Then Mul-lil, “the father and councillor” of the gods, consulted his brother divinities, going round to each in turn. Anu was the first to speak. He

“opened his mouth, he speaks, he says to the gods his sons: ‘(Whoever will,) let him subjugate Zu, and (among all) men let the destroyer pursue him (?).

(To Rimmon) the first-born, the strong, Anu declares (his) command, even to him: …’0 Rimmon, protector (?), may thy power of fighting never fail! (Slay) Zu with thy weapon. (May thy name) be magnified in the assembly of the great gods. (Among) the gods thy brethren (may it destroy) the rival. May incense (?) (etarsi) be offered, and may shrines be built!

(In) the four (zones) may they establish thy strongholds. May they magnify thy fortress that it become a fane of power in the presence of the gods, and may thy name be mighty?’

(Rimmon) answered the command, (to Anu) his father he utters the word:

‘(0 my father, to a mountain) none has seen mayest thou assign (him); (never may) Zu play the thief (again) among the gods thy sons; (the tablets of destiny) his hand has taken; (the attributes of Bel) he seized, he delivered the oracles; (Zu) has fled away and has sought his mountains.'”

Rimmon goes on to decline the task, which is accordingly laid upon another god, but with like result.

George Rawlinson - Source: Seven Great Monarchies Of The Ancient Eastern World, Vol 1. (1875) The Chaldean god Nebo, from a statue in the British Museum.

George Rawlinson: Seven Great Monarchies Of The Ancient Eastern World, Vol 1. (1875)
The Chaldean god Nebo, from a statue in the British Museum.

Then Anu turns to Nebo:

“(To Nebo), the strong one, the eldest son of Istar, (Anu declares his will) and addresses him:  … ‘0 Nebo, protector (?), never may thy power of fighting fail! (Slay) Zu with thy weapon. May (thy name) be magnified in the assembly of the great gods! Among the gods thy brethren (may it destroy) the rival!

May incense (?) be offered and may shrines be built! In the four zones may thy strongholds be established! May they magnify thy stronghold that it become a fane of power in the presence of the gods, and may thy name be mighty!’

Nebo answered the command: ‘0 my father, to a mountain none hast seen mayest thou assign (him); never may Zu play the thief (again) among the gods thy sons! The tablets of destiny his hand has taken; the attributes of Bel he has seized; he has delivered the oracles; Zu is fled away and (has sought) his mountains.'”

Like Rimmon, Nebo also refused to hunt down and slay his brother god, the consequence being, as we have seen, that Zu escaped with his life, but was changed into a bird, and had to live an exile from heaven for the rest of time.”

A.H. Sayce, Lectures on the Origin and Growth of Religion as Illustrated by the Religion of the Ancient Babylonians, 5th ed., London, 1898, pp. 297-9.

Kabbalah as Metasystem

“The prime source for the precursors of the occult revival were without question Athanasius Kircher (1602-80), a German Jesuit whose Oedipus Aegyptiacus (1652) detailed Kabbalah amongst its study of Egyptian mysteries and hieroglyphics, and Cornelius Agrippa’s De Occulta Philosophia (1533).

Other works, such as those from alchemists including Khunrath, Fludd and Vaughan indicated that the Kabbalah had become the convenient metamap for early hermetic thinkers. Christian mystics began to utilise its structure for an explanation of their revelations, the most notable being Jacob Boeheme (1575-1624). However, the most notable event in terms of our line of examination is undoubtedly the publication of Christian Knorr von Rosenroth’s (1636-89) Kabbalah Denudata in Latin in 1677 and 1684, which provided translations from the Zohar and extracts from the works of Isaac Luria.”

“Another stream stemming from Rosenroth’s work came through Eliphas Levi (1810-75), who … ascribed to the Tarot an ancient Egyptian origin. From de Gebelin and Rosenroth, Levi synthesized a scheme of attribution of the Tarot cards to the twenty-two paths of the Tree of Life, a significant development in that it provided a synthetic model of processes to be later modified and used by the Golden Dawn as mapping the initiation system of psychological, occult, and spiritual development. Levi wrote, “Qabalah … might be called the mathematics of human thought.”

“It is said by traditional Kabbalists and Kabbalistic scholars that the occultist has an imperfect knowledge of the Tree, and hence the work of such is corrupt. It appears to me that the Kabbalah is a basic device whose keys are infinite, and that any serious approach to its basic metasystem will reveal some relevance if tested in the world about us, no matter how it may be phrased.

The first Kabbalists cannot be said to have had an imperfect knowledge because they did not understand or utilise information systems theory or understand modern cosmology. Indeed, their examination of themselves and the Universe revealed such knowledge many hundreds of years before science formalised it, in the same way that current occult thinking may be rediscovered in some new science a hundred or thousand years hence.”

–Frater FP, The Magician’s Kabbalah, pp.  5-7.