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Tag: 1684

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: Perfection and Secrecy

Kircher Athanasius, 1667 Magneticum naturae regnum, Frontispiece

Athanasius Kircher (1602-80), frontispiece, Magneticum naturae regnum, Rome, Ignati de Lazaris, 1667, held by the Linda Hall Library, LHL Digital Collections, call number Q155.K58 1667. This engraving is often referred to with the expression, “the world is bound in secret knots.” 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 might think it is a pity that the search for a language that was as perfect as it was universal should lead to such a conception of a tongue reserved for the “happy few.” But it is perhaps nothing more than our “democratic” illusion to imagine that perfection must imply universality.

In order to understand the cultural framework of both Kircher’s Egyptology and Rosicrucian holy languages, it must be remembered that for the Hermetic tradition truth was not usually regarded as accessible to the many. Indeed, there existed a marked tendency to believe that what is true is unknown and hardly knowable, if not to a restricted elite (cf. Eco 1990).

There is a radical difference between the gnostic and Neo-Platonist ideas of late antiquity (as well as their Renaissance versions–which survived in the Counter-Reformation Catholicism of Kircher) and the Christian message, as it was proclaimed throughout most of the Middle Ages.

For medieval Christianity, salvation was promised to the meek and humble in spirit, and did not require any special knowledge: everyone can understand what is required in order to deserve the kingdom of heaven.

Medieval teaching reduced the aura of mystery that accompanied the revelation–which was explained by formulae, parables and images that even the uneducated might grasp: truth was considered effable, therefore public.

For Hermetic thought, instead, the cosmic drama could only be understood by an aristocracy of wisdom, able to decipher the hieroglyphs of the universe; the main characteristic of truth was its ineffability: it could not be expressed in simple words, was ambiguous by nature, was to be found through the coincidence of opposites, and could be expressed only by initiatic revelations.

Within this tradition, public accessibility was simply not a criterion by which a perfect language was judged. If one does not understand this point, one cannot understand why the cryptographers of this period dedicated their ciphers to grand-dukes deep in military campaigns and political machinations, presenting them as arcane suggestions.

Perhaps this is all merely another manifestation of the natural hypocrisy of a century fascinated by dissimulation, a feature that constitutes the continuing charm of baroque civilization.

It remains uncertain if that celebrated book Breviarium politicorum secundum rubricas Mazarinicas (1684) really collects Mazarin’s political thoughts or is a libel invented to defame him: in whatever case, it certainly reflects the image of a man of politics in the 1600’s.

It is notable that in the chapter entitled “Reading and writing” it recommends that, if one needs to write in a public place, it is convenient to place upon a lectern several already written pages as if one intended to copy them out, letting them be visible and concealing under them the paper upon which one is really writing, guarded in such a way that no one who approaches you will be able to read it.

Resorting to ciphers is suggested, but in such a way that at first glance the message looks understandable and provides irrelevant information (the canonical reference is to Trithemius).

Not only must the message be translated in a secret writing, but this writing must also conceal its own secrecy, because a cipher that blatantly appears as such can arouse suspicion and encourage decipherment.

Thus on the one hand the mystic who writes about perfect and holy languages winks his eye at the politician who will use this language as his secret code; on the other hand the cryptographer sells to the politician a cipher (that is, an instrument of power and dominion) that for him, the Hermetic initiate, is also a key to supernatural truths.

Such a man was Johann Valentin Andreae, whom many have considered (and many still do consider) to be, if not the author, at least the inspirer of the Rosicrucian manifestos. Andreae was a Lutheran mystic and writer of utopian works, like the Christianopolis of 1619, similar in spirit to those of Bacon and Campanella.

Edighoffer (1982: 175ff) has noted that many of his authentic works, like the Chemical Weddings, abound with ciphered expressions, according to the expressed principle that “Arcana publicata vilescunt” and that one ought not to cast pearls before swine.

In the same vein Andreae used ciphered messages in his correspondence with Augustus, Duke of Brunswick. Edighoffer remarks that there is nothing surprising in this: it was a correspondence filled with political observations, one, moreover, that took place during the Thirty Years War, when the difference between political and religious comments was minimal and the risks in both were the same.

In the light of these, as it were, “private” practices of the Rosicrucians, their public appeals concerning the need to use a secret language to inaugurate a universal reform must seem even more ambiguous.

They are so to such an extent as to make credible what not only modern historians but even the supposed authors of the manifestos themselves had always claimed: the manifestos were nothing but a joke, a sophomoric game, an exercise in literary pastiche made up of all the buzz-topics of the day: the search for the language of Adam, the dream of a sensual language, glossolalic illusions, cryptography, kabbala . . . And since everything went into this pot au feu, anything could be fished out again.

Thus, as will always happen when the specter of mystery is raised, there were those who read the Rosicrucian manifestos “paranoiacally,” discovering in them what they wanted to believe anyway, and needed to rediscover continually.

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 190-3.

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.

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