Lullism (combinatorial art)

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Lullism is the tradition descended from the Art (Ars) of Ramon Llull, the Majorcan philosopher, missionary, and writer who died around 1316. The Art was a method for finding and proving truth by combination: a small set of fundamental concepts, fixed in lettered figures and rotating concentric wheels, that could be turned against one another to yield every legitimate statement a subject allowed. Llull built it across many works and several revisions, from the early Ars compendiosa inveniendi veritatem to the late Ars generalis ultima, refining the apparatus for decades without ever abandoning the core idea. What he made on a Majorcan mountain his successors would read, copy, annotate, condemn, expand, and finally rebuild into something he could not have foreseen — a current that ran for four centuries under his name.

The instrument across its revisions

The Art was never one machine but a sequence of them. Bonner’s reconstruction divides the corpus into two great phases, the quaternary and the ternary, named for the number-bases on which each turns. The first, running from the illumination around 1274 to about 1289 and anchored in the Ars compendiosa inveniendi veritatem and the later Ars demonstrativa, worked with sixteen of nearly everything and a set of figures lettered with the upper alphabet — A, S, T, V, X, Y, Z — each carrying its dense column of meanings. The early Art was powerful and nearly unreadable; its critics complained, with some justice, that learning the apparatus cost more than learning the subjects it promised to master. The second phase, from about 1290 through the late summaries — the Ars generalis ultima and its pocket digest the Ars brevis — reduced the machine to a cleaner and more general form: four figures, an alphabet of nine letters running B through K, and nine of each kind of principle. The reduction was a refinement, not a retreat. The late Art does more with less, and it is these last summaries, above all the Ars brevis, that carried the method to later readers, who most often knew it simply as the Ars magna, the great art.

The architecture, in its mature form, is a layering of correspondences. At the base stand the absolute principles, the dignities; above them a set of relative principles — difference, concordance, contrariety, beginning, middle, end, majority, equality, minority — and a set of standing questions: whether, what, of what, why, how much, of what kind, when, where, with what. Each is mapped onto a letter, so that the alphabet becomes a compression of the whole field of inquiry. The figures then put the letters into motion. The first figure rings the dignities in a circle and joins every term to every other, so that the eye reads off each pairing in turn. A second figure carries the relations; a third lays out the binary combinations in a triangular half-table. The fourth is the famous one: concentric paper disks, lettered alike and mounted on a common pin, the inner wheels turning against the fixed outer ring so that every combination of principles comes into alignment as the disk is rotated, each alignment a question to be opened and a small demonstration to be drawn out. This is the image that fixed itself in the European imagination — the volvelle, the revolving wheel of words — and that every later Lullist would inherit, simplify, or multiply.

The theological core: the dignities

That core was theological before it was logical. The dignities are the divine attributes — in the mature ternary Art, nine of them: goodness, greatness, eternity (or duration), power, wisdom, will, virtue, truth, and glory — which Llull held to be common ground, more or less, among Christians, Muslims, and Jews. They are not for him mere names of God but the active structure of reality itself: every created thing exists as a likeness of them, so that to reason rightly about goodness or greatness anywhere is to reason about the perfections of their source. The Art is the formal expression of a double movement down and up the ladder of being — from the Creator through the orders of creation to the elements, and back again — and the wheels are the engine that runs the dignities through every legitimate combination, so that conclusions may be demonstrated rather than merely asserted.

The purpose was conversion by reason. Llull’s hope was that an argument built only from premises all three faiths of the Book already granted could compel assent without appeal to scripture, which an opponent could simply refuse. He set this combinatorial logic explicitly against the syllogism of the schools, which he judged able only to unfold what its premises already contained, never to discover anything genuinely new. The Llibre del gentil e dels tres savis — the Book of the Gentile and the Three Wise Men — stages the dream as a courteous fiction: a Christian, a Jew, and a Muslim reason together by the common method, and the book closes before the inquiring gentile says which faith he has chosen, so that the three resolve to keep disputing. The missionary purpose and the combinatorial machinery were, for Llull, one project. Later ages would keep the machinery and quietly retire the purpose — and this severance is the whole story of Lullism, which is the afterlife of a method whose original end fell away from it.

A general science of knowledge

Across the later Middle Ages the Art was read less as a tool of conversion than as a general science — a key that, rightly used, might unlock any field at once. The immediate reception was fought over: a fourteenth-century Lullism, traced in detail by J. N. Hillgarth, took root in the schools and courts of France and Catalonia, where it drew both disciples and inquisitorial suspicion. The Aragonese inquisitor Nicolau Eymeric attacked the Art and secured a papal condemnation of Llull’s writings in 1376 — a bull whose authenticity Llull’s defenders disputed for centuries, and which the cult of the Doctor Illuminatus on Majorca eventually outlasted. Lullist chairs and academies persisted nonetheless, on Majorca and at Barcelona, and the manuscript copies multiplied across Europe.

The decisive turn came with the men who read the Art as philosophy rather than weapon. Nicholas of Cusa owned and heavily annotated a collection of Llull’s works — his library at Kues preserves the volumes in his own hand — and absorbed from them the impulse to give theology a quasi-mathematical machinery, an impulse that runs straight into his doctrine of learned ignorance and his geometry of the infinite. In the high Renaissance the Art passed into the orbit of the Florentine Platonists and the new Christian Kabbalah: Pico della Mirandola counted a Lullian ars combinandi among the disciplines that could be set beside the combinatory of the Hebrew letters, folding Llull’s wheels into the wider search for a single hidden grammar beneath all knowledge. In the sixteenth century Cornelius Agrippa wrote a commentary on the Ars brevis that was printed some fifteen times between 1531 and the mid-seventeenth century, fixing the Art firmly within the canon of occult philosophy.

It was the Strasbourg printer Lazarus Zetzner who gave Lullism its early-modern shape. In 1598 he gathered Llull’s logical works together with the commentaries of Agrippa and Giordano Bruno into a single anthology — reprinted through the seventeenth century, a copy reaching the library of Isaac Newton — and it was in this Zetzner collection, far more than in any medieval manuscript, that the later world met the Art. The book made Lullism a printed, portable tradition: a self-contained school of combinatorial reasoning that one could buy, study, and extend without ever having seen the Majorcan originals.

Bruno and the memory-machine

Giordano Bruno is the hinge between the medieval Art and its modern descendants. The Nolan devoted five works to Llull, four of them to the Art, and in De umbris idearum (Paris, 1582) and the works that followed he fused Llull’s lettered wheels with the classical art of memory — the technique of placing images in remembered architecture — into revolving systems of vast ambition. Where Llull’s fourth figure turned three concentric disks, Bruno multiplied the wheels and loaded them with magical and astral images, building mnemonic engines meant not merely to store knowledge but to hold the whole intelligible order in a single rotating mind, and to generate from it. In Bruno’s hands the combinatory became cosmological: the same impulse that drove his vision of an infinite universe of innumerable worlds drove his appetite for a memory that could mirror that infinity. He is, at once, the most extravagant Lullist and the figure through whom the Art entered the seventeenth century as a living technique rather than an antiquarian curiosity.

Bruno’s Lullism also fed the encyclopedic dream of the baroque. The Jesuit polymath Athanasius Kircher built his Ars Magna Sciendi sive Combinatoria (1669) as an explicit expansion of Llull’s ars combinatoria, attempting to classify all knowledge under a set of divine attributes and to generate notions by combinatorial wheels — the Art turned into a universal taxonomy of everything, of a piece with Kircher’s lifelong project of a single key to all languages and sciences. The seventeenth century is thick with such schemes; the Art had become the common ancestor of every plan to mechanize the whole of learning.

The alchemist who never was

Alongside the genuine line ran a counterfeit one. From the 1330s — the earliest, the Testamentum, written in Catalan around 1332, well after Llull was in his grave — a large body of alchemical writing began to circulate under his name, growing over the centuries into a corpus of perhaps a hundred and forty texts on transmutation, the philosophers’ stone, and the distillation of a quintessence as universal medicine. None of it is his. The historical Llull condemned alchemy as a fraud in his authentic works, and not one of the pseudo-Lullian texts can be dated to his lifetime. The confusion was in part a pun on the ars — the combinatorial Art mistaken by later readers for the great work of the furnace — and it made Llull, for the esoteric tradition, a great adept whose laboratory reputation traveled quite independently of anything the real man had written. Michela Pereira’s inventory of the corpus established the disentanglement beyond doubt: the alchemical Llull and the missionary philosopher are different men, a generation apart. The genuine afterlife of the furnace belongs to Latin medieval alchemy, not to the Art — but the pseudo-Lullian writings are themselves a chapter of Lullism, the price a name paid for the prestige of its method.

Leibniz and the dream of calculation

The most ambitious heir read the Art young. Gottfried Wilhelm Leibniz, barely twenty, encountered Llull’s logic in the Zetzner anthology and made it the occasion of his first published work, the Dissertatio de arte combinatoria (1666). From that seed grew the project of his life: a characteristica universalis, a symbolic language in which every concept would be analyzed into its primitive components and represented by a character, so that reasoning could become calculation — and disputes between honest men be settled, in his famous image, by their sitting down together to compute. Llull’s revolving disks stand at the head of that lineage. Both men begin from the same audacious premise: that the universe of true statements can be generated mechanically from a finite alphabet of simple notions, that thought has a combinatorial skeleton, and that exposing it would end disagreement.

How much credit Llull deserves for the descent is argued, and the argument is worth keeping precise. Bonner notes that the Art is generative not in Leibniz’s sense — building complex concepts out of simple ones — but in the narrower sense that a wide range of demonstrations can be drawn from a finite set of primitive principles. The dignities are not Leibniz’s atoms of meaning; the wheels do not compute. What passes from Llull to Leibniz is less a technique than a conviction: the dream that reasoning might be rendered mechanical, that there could be an alphabet of human thought and a calculus to run on it. Some historians of logic see in the wheels a genuine ancestor of the formal and symbolic systems that followed; others judge the resemblance loose and the debt overstated. The kinship is real and the inheritance indirect, both at once — the disputed descent is the liveliest part of the Art’s modern reputation.

Scholarship and the critical reconstruction

Lullism has its own modern science, built on a century of editorial and historical work that separated the genuine Art from its legends and reconstructed how the figures actually operate.

• Anthony Bonner, The Art and Logic of Ramon Llull: A User’s Guide (Leiden: Brill, 2007). The indispensable technical reconstruction of the figures, distinguishing the quaternary and ternary phases and tracing the line through Agrippa, Bruno, and Leibniz; the standard work on how the Art works rather than what it claimed. A freely hosted English supplement is published by the Llull database at the University of Barcelona, ub.edu/llulldb.

• R. D. F. Pring-Mill, El microcosmos lul·lià (Palma, 1961). The study that recovered the metaphysical architecture behind the diagrams — the dignities, the correlatives, the ladder of being — showing that the Art is a cosmology before it is a logic. Summarized for Anglophone readers in the Stanford Encyclopedia of Philosophy entry, plato.stanford.edu/entries/llull.

• J. N. Hillgarth, Ramon Lull and Lullism in Fourteenth-Century France (Oxford: Clarendon Press, 1971). The major reconstruction of the immediate reception — how the Art and its author were read, taught, and disputed in the generation after his death, including the Eymeric controversy.

• Michela Pereira, The Alchemical Corpus Attributed to Raymond Lull (London: Warburg Institute, 1989). The inventory that cataloged the pseudo-Lullian alchemical writings and established that none of them is by Llull, dating the corpus to the generations after his death.

• Frances A. Yates, The Art of Memory (London: Routledge & Kegan Paul, 1966) and her essays on Lull’s Art of Finding Truth, which set Bruno’s combinatorial memory-machines within the longer history of the Art and made the Lull–Bruno line a fixture of Renaissance studies.

• The Centre de Documentació Ramon Llull at the Universitat de Barcelona maintains the Llull DB, the working census of the authentic corpus, its manuscripts and editions — the instrument by which the genuine Art is now kept distinct from everything that accreted to the name.

What is not in doubt is the strangeness of the original conception — that turning a set of lettered disks could be a way of arguing toward God. The device was built to end disputation; it instead became one of the more fertile machines in the history of thought.

→ Related: Learned Ignorance Docta Ignorantia · Latin Platonism · Latin Medieval Alchemy · Ramon Llull · Nicholas Of Cusa · Giordano Bruno · Gottfried Wilhelm Leibniz · Giovanni Pico Della Mirandola · Art Of Memory Mnemonics · Scholasticism · The Renaissance · Middle Ages · Cornelius Agrippa