MENTAL vs. LULLY'S ARS MAGNA

"A project of spiritual hermeneutics with universal projection" (Amador Vega)

"A relational system of concepts of universal character" (Thomas le Myésier).

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The Ars Magna of Raymond Lully
Raymond Lully −in Spanish, Raimundo Lulio; in Latin, Raimundus Lullus− was a multifaceted and universalist character. He was a prolific writer, poet, kabbalist, scientific disseminator, missionary, philosopher, theologian, Franciscan monk, mystic and alchemist. One of the most important figures of the Middle Ages, today he is considered one of the most influential thinkers in history. He was known as Doctor Iluminatus (Illuminated Doctor) and Doctor Inspiratus (Inspired Doctor). He was born in Mallorca (in 1232 or 1235), shortly after the conquest of the island by Jaime I. His youth was quite mundane, but around the age of 30 he had a mystical experience that made him change radically, launching himself to preach Christianity among the infidels.

Lully thought that the best way to spread his beliefs was to write a book that included a method aimed at rationally demonstrating the articles of faith. It is at the top of the mountain of Randa (in the center of the island of Mallorca) where the form and manner of writing the book is revealed to him. Lully wanted to write "the best book in the world", a book that would serve to find the "necessary reasons" to convince the infidels by demonstrating the truth in a clear and diaphanous way, and to unify the Christian, Jewish and Muslim religions. To this end, he sought the primary, essential and elementary notions that were common to these monotheistic religions. Although his initial intention was the rigorous demonstration of the truths of faith, his aim was considerably broadened to embrace the essential principles of philosophy and all the sciences, with the objective of "knowing the truth of all things."

Lully left an extensive body of work in Catalan, Latin and Arabic (he has 280 recognized works). By modernizing popular Catalan, he is considered the creator of true literary prose in this language. He was declared blessed. His feast day is celebrated on November 27.


The evolution of the method

Lully developed his method, called "Ars Magna", "Great Art", "Major Art", "General Art" and "Combinatorial Art". He made several improved versions over more than 30 years, the result of a process of progressive maturation of his ideas. Excessively complex at the beginning, he progressively simplified it. His method is set out successively in "Ars compendioso inveniendi veritatem" (1274), "Ars demostrativa " (1283-1289), "Ars scientiae" (1295), "Ars brevis" (1308) and "Ars generalis ultima" (1308). Apart from these works devoted to the method itself, much of his work revolves around his method, which he considered of great importance.


The principles and rules

Lully, in order to search for truth, relied on two key ideas:

1. He was convinced that all of reality could be explained on the basis of a few simple principles and that by combining them exhaustively all possible forms or structures of truth could be explored and thus universal knowledge could be achieved.
   
   
2. He believed in the existence of a realm of universals, whose manifestations gave rise to the particular or accidental, in the similarities or analogies between earthly things and divine realities. Philosophy, he said, depends on theology.

To this end, he established 18 universal principles: 9 absolute principles (or divine dignities), 9 relative principles and 9 rules, all named with the same letters: from A to K. Lully excluded J to avoid confusion with I in his manuscripts. He reserved the A to give it a central role (the Divine Unity), the source of absolute principles. The rules or questions of a general kind were oriented to cover all questions, issues or aspects that could be asked about anything.


By means of the combination of these (primary) concepts, all other (secondary) concepts that may appear in any reasoning would be founded in order to solve all kinds of questions with logical rigor. These principles are not equivalent to philosophical categories, since these refer to the physical and the metaphysical, and Lully's aim was to embrace all that is real, including all forms of thought: the actual and the potential, the true and the false, the possible and the impossible, the reasonable and the unreasonable, the logical and the contradictory.

Lully did not rely on any dogma, for he thought that reason was sufficient to attain the truth. Thomas Aquinas, his contemporary, distinguished between natural truths (those that could be established by reason) and the truths of theology (based on faith and revelation). Lully did not believe in such a distinction; he believed that all truths of faith could be demonstrated by irrefutable arguments.


The sensible and the intelligible

For the unification of the religious or theological aspects together with the philosophical and the scientific or logical, Lully also relied on two concepts, which he called the sensible and intelligible aspects of reality:

• The sensible corresponds to the particular, to the perception of sensible and visible things. For example, a stone, a vegetable, etc. It also includes the passive, the contemplative life.
  
  
• The intelligible corresponds to the universal, to the invisible. For example: God, angel, soul, etc. It also includes the active, the active life, as well as the faculties of memory, understanding and will.

According to Lully, between these two extremes are all the scales of reality: from the particular (the sensible) to the general and universal (the intelligible). In "De Ascensu et Descensu Intellectus" (1304), Lully expounds his "scalar" method or the scales of knowledge by which one can go up or down. One goes up when one passes from the sensible to the intelligible (from the particular to the general) and one goes down when one travels the opposite path.

For Lully, it is the imagination that has to act as a mediator or bridge between the sensible and the intelligible, to unite both aspects, in a "coincidentia oppositorum" (for Lully, the cross, as "axis mundi" is the symbol of truth, the ultimate symbol of contemplation, for in it the opposites converge and are reconciled). By means of the imagination we can intuit the invisible things, because in the created things there is the trace of the divinity, and thus reach the optimal sensibility, which is the one that brings us closer to God. It is to elevate sensibility (the particular) towards intelligibility (the universal) and from this to the "pure intellect", the knowledge of God. The "pure knowledge" to which Lully refers today can be identified as "pure consciousness", self-consciousness or consciousness of being. Lullyian metaphysics attempts to arrive at God from things, the sensible.

Lully believed that the intellect is powerful enough to know all of reality. Reality is intelligible and the human understanding can reach it.


The correlatives

For Lully, everything contains three intrinsic principles: the active subject, the passive object and the functional act. It is a universal characteristic, applicable to everything, for example: the one who loves (lover), the beloved and (between the two) love. Another example is: the observer, the observed and the observation. This is what Lully called "correlatives". To ask about the essence of something is the same as asking about its correlatives.

There are essential or universal (necessary) correlatives and accidental or particular (contingent) correlatives.


The act as unifying element

Lully applies the theory of correlatives to found all entities from the perspective of the act, since the essence of being is the act. In every act there is an agent and a patient. The act falls on an object and is executed by a subject, forming act, object and subject three inseparable aspects and a single essence. Everything that exists, exists by its acts. The essence of everything is based on the act. Without activity neither God nor any creature would have nature.

For Lully, knowledge is also an act. Whenever we know something, we know it by means of an act. Physical and metaphysical forms, words, concepts, etc., everything we know are acts. Lully thus unifies all knowledge from the perspective of the act and, from this same perspective, unifies the world of thought and the world of the real, the abstract and the concrete. With this method it is possible to reach the transcendent, God, which is the pure act of being, the pure intellect.

In each universal principle there also converges an active property, a passive property and the act that connects them. These three elements together constitute the essence of each principle. The principles are real because, although they can be thought, their being is active and they are independent of thought. Absolute principles (or dignities) are active, for through them God knows himself. The dignities are the constitutive principles of all entities. By the dignities everything existing is constituted in activity.


The logic of logics

On the other hand, any act is intelligible and therefore logical. But there are many logics: there is a logic of physical entities, of metaphysical entities, of God, of human acts, of words, of names, and so on.

Lully proposes a logic of "first intention," that is, a logic for philosophizing about divine truth. Instead of connecting ideas in chains of cause-effect, he bases them on their common origin. The purely formal logic of human reason, independent of theology, like Aristotelian logic, is a logic of "second intention" and is not part of Metaphysics. True logic must be at the service of the transcendent and be an instrument of faith. Aristotelian logic is mental. Lullian logic transcends thought, but it also has deductive power, so that, in theory, it includes Aristotelian logic.

For Lully, the Ars is the logic of all logics, a logic of first intention, a universal logic that covers all reality and serves to discover "the real truth of things". It is a Logos, a logic based on the act of entities that embraces all that is real, for the real, being an act, is intelligible.

For Lully, "weak" thought is that which lacks God, which always provides a false vision of things because it lacks the true foundation. Therefore, science for science's sake, pure scientism, only leads to fragmentation and what is needed is a unified vision of reality. What is real and true is the divine. The rest are particular manifestations or reflections of the divine.


The Figures

Lully uses geometric figures and colors as sensitive elements to aid the imagination. Lully's use of circular figures may have its origin in the contemplation of the sky in the starry nights of Randa. In any case, the circle is a universal symbol that represents God, totality and eternity (since it has neither beginning nor end).


Figure 1

It represents the absolute. It is a circle with a crown in which there are 9 compartments (or "chambers") and an inscribed enneagon. There is a letter A at its center, and each chamber contains a letter, from B to K, representing the 9 absolute principles, divine dignities or essential attributes of God. They are the "keys" for God to reach our intellect.

Figure 1

God is a single essence with multiple attributes. The letter A represents the Divine Unity in the center of the circle, a center that is projected (expressed) on the periphery, where the absolute principles, the attributes of the divine essence, are distributed. Lully believed that with these divine attributes all believers in monotheistic religions would agree, providing him with a firm basis on which to argue.

By means of the binary combinations of the absolute principles, represented by the diagonals of the enneagon, "compound principles" are generated, with which "the knowledge of God" can be obtained. The combinatorial consists in taking one of the principles as the subject and using any other as the predicate, because these absolute principles are defined circularly, they are interchangeable (or "mutually convertible"), for example: Goodness is great, Goodness is eternal, Goodness is powerful, Greatness is good, Greatness is eternal, etc. According to Lully, this figure serves to help the intellect discern between what is convertible and what is not. For example, God and Goodness are convertible, but in creatures the principles are finite and cannot be converted among themselves.

The figure contains 36 diagonals, which correspond to the 72 possible binary combinations, since each diagonal can be traversed in two directions. Implicit in the figure and its combinations are the syllogisms or automatic deductions. For example, from the premises "Goodness is great" and "Greatness is eternal" it follows that "Goodness is eternal", a conclusion that can also be obtained by direct combinatorics.


Figure 2

Represents the relative. It is a circle showing the letter T in the center, with a crown divided into 9 chambers (also represented by the same 9 letters), and in which 3 triangles are inscribed, forming 9 small external triangles corresponding to the relative principles. The chambers and the triangles establish fixed relations, that is to say, this figure does not contemplate any combinatory, because it is only a visual artifice to better remember the fixed relations between the relative principles and the chambers.

Figure 2

Relative principles are universal, that is, they are applicable to all things. They come in triads. There are 3 types (represented by the 3 triangles) and they are, together with the associated chambers (which also come in triads), as follows:

• Difference, Concordance and Opposition. Difference is more general than Concordance and Opposition, for there are more things different than concordant or opposite. Difference causes plurality. Concordance causes unity. Opposition "corrupts and dissolves things".
  
  This triplet relates to two sensible entities (as stone and plant), one sensible and one intelligible entity (as body and soul), and to two intellectual entities (as soul and angel).
  
  
• Beginning, Middle and End. A beginning is something that is followed by something else. An agent starts something, in the middle several entities come together (there is continuity), and at the end there is a "rest", a stop.
  
  Beginning points to Cause, Quantity and Time. There are three types of beginning.
  
  Means points to Conjunction, Measurement and Extremity. This indicates three types of means: a means of conjunction (e.g., a nail joining two boards), a means of measurement (e.g., the center of a circle), and a means between extremes (e.g., a line between two points).
  
  Final points to Deprivation, Completion and Perfection. This indicates three types of end: end of deprivation (e.g., death), end of termination (e.g., the boundary of a field), and end of perfection (e.g., God).
  
  
• Majority, Equality, Minority. The intellect ascends and descends through these scales to approach truth, in substance and in accident. For example, substantial goodness is associated with majority, while accidental goodness is associated with minority. There is a maximal majority that is above all particular majorities.
  
  This triplet relates to Substance-Substance (e.g., "human substance is greater in goodness, virtue, etc. than the substance of stones"), Substance-Accidental (e.g., "the substance of a man is greater than his height"), and Accidental-Accidental (e.g., "understanding is greater than sensation").

Figure 3

This figure is composed of the first and second figures. It considers all possible combinations of the 9 letters, giving rise to 36 two-letter chambers, where each letter refers to the two figures.

BC	CD	DE	EF	FG	GH	HI	IK
BD	CE	DF	EG	FH	GI	HK
BE	CF	DG	EH	FI	GK
BF	CG	DH	EI	FK
BG	CH	DI	EK
BH	CI	DK
BI	CK
BK

This figure indicates that each camera (e.g., the B) is combined with the others (C to K) in order to establish relationships between them to see the possible connections between them.

Once the combinatorics is done, we have to perform a "chamber evacuation", which consists of establishing relationships by means of the relative principles. For example, for chamber BC (combination of Goodness and Greatness), they are related (according to Figure 2) by means of the principles of Difference and Concordance, thus obtaining 4×3 = 12 properties (variations of 4 elements, taken 2 by 2):

1. Goodness is great
2. Difference is great.
3. Goodness is different.
4. The Difference is good.
5. Goodness is concordant.
6. The Difference is concordant.
7. Greatness is good.
8. Concordance is good.
9. Greatness is different.
10. Concordance is different.
11. Greatness is concordant.
12. Concordance is great.

From the 12 properties we obtain, in turn, 24 questions by applying to them the corresponding rules B (does it exist?) and C (what is it?). For example, "Does different Goodness exist?" and "What is a big Goodness?". Thus, the third Figure allows 36×12 = 432 propositions and 432×2 = 864 questions.


Figure 4

It is the key figure of the Ars and the most famous. It combines the 3 previous figures and produces the "combinatorial explosion". It consists of three crowns with the same 9 elements (from B to K), concentric and mobile around the common center, which produce by combination triplets (groups of 3 elements). The total number of combinations is C_9,3 = 84 (combinations of 9 elements taken 3 by 3).

Figure 4

Lully transforms the triplets into quadruplets, since he inserts the letter T as a separator or delimiter. The left part of the T refers to the absolute principles of Figure 1, and the right part refers to the relative principles of Figure 2. For example, in the quadrupole BCTC, B is Goodness and C Greatness, while the second C is Concordance, a quadrupole that can be interpreted as "If Goodness is Great (or Greatness is Good), it contains in itself concordant things."

Each triplet then generates a column of 20 combinations, which are the combinations of 6 elements taken 3 by 3 (C_6,3). The 6 elements come from the double value of each letter. If we capitalize the absolute principles and lowercase the relations, then, for example, BCTD would be equivalent in our notation to BCd. Since there are 84 triplets, the total number of combinations is 84×20 = 1680.

Quadruplets can be interpreted in many ways, like symbols in general, in such a way that multiple possible meanings can be discovered. A certain interpretation may be valid, while another interpretation would be rejectable. There are also combinations in which all possible interpretations are rejectable. From the combinatorics only those that correspond to the "real arrangement of the cosmos" have to be selected, i.e. there is an underlying cosmology that limits the valid combinations. In reality, combinatorics is an instrument for understanding, imagining and discovering the essence of things, exploring their possible connections and facilitating the creation of new ideas, arguments, relationships and truths.


The rules

• Rule B. It asks if the thing exists. There are 3 possible answers: doubt (there is possibility), affirmation and negation.
  
  
• Rule C. It is the rule oriented to define things, including definitions of principles. It has 4 forms (or "species"):
  
  
  1. Defines things so that the thing defined is convertible with its definition.
  2. Asks what the thing has as essence, without which it could not exist.
  3. Asks whether the thing is in other things, whether the thing adopts in other things different qualities.
  4. He asks whether the thing has something in other things.
  
  
• Rule D. Question about material consistency. It has 3 species:
  
  
  1. Question about its origin.
  2. Question what a thing is made of, what is its composition.
  3. Question about belonging.
  
  
• Rule E. Question why. It has 2 species:
  
  
  1. Question for the reason of its existence.
  2. It asks for action or movement toward a purpose.
  
  
• Rule F. Question about quantity, that is, about the measure and number of things. It has 2 species:
  
  
  1. Simple quantity.
  2. Compound quantity, that is, it asks about the composition of quantities.
  
  Lully recognizes that there are discrete and continuous quantities. For example, a stone is continuous in appearance, superficially, but discrete in its essential components.
  
  
• Rule G. Quality question. It has 2 species:
  
  
  1. Main qualities. For example, what are the qualities of heat? The answer is that the main quality of fire is heat.
  2. Secondary qualities. For example, the secondary quality of fire is dryness.
  
  
• Rule H. Ask about time. There are as many ways to ask as there are forms in Rules C, D and K. The reason for this is because "the essence of time is very difficult to understand". For example, on the question of its origin (C, species 1), the answer is that time is a primordial substance, not generated by any other.
  
  By the K rule of modality, time is understood to exist as a part of substance within another. By the rule K of instrumentality, time is an instrument of substance in movement and which allows the intellect to know its essence. Lully associates time with movement (like Aristotle) and affirms that in God there is neither time nor movement.
  
  
• Rule I. It asks about the location of things in space, although there are things that occupy neither place nor space. Like the previous rule, there are as many ways of asking as there are ways in rules C, D and K.
  
  
• Rule K of modality (K-1). It refers to the way in which things exist. It has 4 species:
  
  
  1. Question about how a thing exists in itself.
  2. It asks how the thing exists in other things and the other things in the thing.
  3. Question how the thing exists in its parts and its parts in the thing.
  4. It asks how the thing conveys its likeness externally.
  
  
• Rule K of instrumentality (K-2). Question: with what do things exist and with what do they act. It has 4 species, similar to the K-rule of modality. For example, applying them to the intellect:
  
  
  1. With what is the intellect a part of the soul?.
  2. By what does the intellect understand things distinct from itself?
  3. By what is the intellect universal and particular?
  4. By what does the intellect convey its likeness externally?
  
  There are instruments of various kinds: substantial (as the instrument of procreation) and accidental instruments (as fire); particular (as the different elements necessary to build a house); intrinsic (as the intelligible part of the intellect, which is its own essence); extrinsic, external to the intellect, which teachers use to teach science.

The functioning of the Ars Magna

Lully's method is rather ambiguous when it comes to its application. However, there are general criteria for its use:

1. Faced with the thing to be investigated, the first thing to do is to study its own activity, since through it we enter into its essence. As in every act there is a subject-object connection, to study its own activity is to identify the subject and the object.
   
   
2. Combine the object (obtained from the previous step) with each of the universal (absolute and relative) principles of all things and use the rules to: see whether the thing exists or not, what is substantial about it, what it exists for, etc. The result is an object of the highest possible universality (intelligibility).
   
   
3. The same is done as in the previous step, but with the subject obtained from the first step. The result is that the subject to be investigated is rectified, limited or conditioned.
   
   
4. Both knowledge or conclusions of the two previous steps are put together. And the rules are applied again to obtain the definitive conclusions or results.

The Ars does not work alone. It is a support system for human thought, an aid to formulate questions and search for answers or particular truths on the basis of universal truths. It is a matter of contemplating the particular in the light of the universal. The complete value of an entity is known to the extent that we discover the relations with the whole. But value, not in the psychological sense, but as a reflection of something superior: of divine perfection.

Lully recommended that the practitioner of the Ars should place himself as the object, in order to observe his act of knowing from the outside, and thus eliminate possible subjectivisms in order to better attain the truth.


The universalism of Ars Magna

LLull's fundamental trait was his passion for truth, truth that he believed he had found. He was convinced that his system was universal, that he had found the secret of existence, the foundation of everything, the hidden key to creation, the general or universal principles of all sciences, the essence or root of the universal science of man, nature and God, the philosophical categories, a system of discovery and investigation, a general system of interpretation of visible and invisible reality, and an instrument for the foundation of knowledge. Thus, the system was applicable to all fields of knowledge to solve and clarify all kinds of problems, not only in theology and metaphysics, but also in cosmology, law, medicine, astronomy, geometry and psychology. And it was also an art of asking questions, of posing questions and getting answers, about multiple earthly and heavenly matters.

Lully sought to unite or integrate into a single system:

• Faith and reason. For Lully, faith and reason complement each other. Faith is a "necessity of reason". Pure reason is materialism, and faith without knowledge is simply superstition.
  
  
• Theology and philosophy.
  
  
• Natural truth and supernatural truth.
  
  
• Contemplative life and active life.
  
  
• The sensible and the intelligible.
  
  
• Lower order (terrestrial) and higher order (divine), where the order of creation is a reflection of the celestial order.
  
  
• The absolute and the relative.
  
  
• The visible and the invisible.
  
  
• The generic or universal and the specific or particular.
  
  
• The observer and the observed, the external experience and the internal knowledge. The two aspects are part of the same process, they cannot be separated.
  
  
• The possible and the impossible.
  
  
• Invention and discovery.
  
  
• Logic and metaphysics. In the introduction to the Ars demostrativa, Lully states that the Ars is both a logic and a metaphysics, but that it differs from both.
  
  
• The algebraic (the combinatorics of letters) and the geometric (the circle and polygon shapes). The algebraic is directed to the reason (the intelligible) and the geometric is directed to the sensible, as figures of contemplation.

It is also deduced from the exposition of Lullian art, that it is based on a triadic order, with which it tries to overcome duality:

• The 3 triangles of the relative principles.
• The structure of each triangle, which connects two opposite principles with their middle term.
• The correlatives are triads.
• The act (the unifying principle) unites subject and object. They form a triad.
• The sensible and the intelligible united by the imagination.
• The chambers of Figure 2 containing triads.
• The 3 circles of Figure 4.
• The symbol of the cross as a union of opposites that converge in the intersection (or center).

Actually, the Lullian method is a universal dialectic, for it teaches to formulate questions and discover answers about all things.

It has also been suggested that absurd relationships can be established. Lully also intended, like the koans of Zen, to overcome dualities, to transcend possible meanings in order to overcome them and to favor imagination, mystical experience and thus achieve a higher consciousness. Typical examples of koans are "What is the sound produced by clapping with one hand?" and "What was your real face before you were born?".


Lully, the pioneer

The figure of Lully has grown larger and larger, and awakened more and more interest, with the passing of time. Today he is recognized as a pioneer in many areas, among them:

• In the use of geometrical diagrams as an aid to the discovery of new truths. In particular, he was the first to use circles to represent concepts and relationships, which would later be used to represent classes (such as Euler and Venn diagrams).
  
  
• In the use of a mechanical device to facilitate the operation of a logical system. Figure 4 of the Ars can be considered a primitive logic machine for producing new ideas.
  
  
• Lully's symbolic language is considered a precursor system of many theoretical and technical topics that were developed many centuries later, such as: symbolic logic, mechanical calculus, combinatorial analysis, truth theory, generative grammars, graphs, semantic networks, heuristic methods of artificial intelligence and computer languages. In fact, since May 2001, Lully has been the patron saint of computer scientists in Spain.
  
  
• As a consequence of the two previous points, Lully can be considered a precursor of computer hardware and software. The hardware would correspond to the Figures, the operating system to the universal principles and the software to the rules.
  
  
• He pioneered the fusion of theology and philosophy, so that the Ars can be considered a precedent of theosophy.
  
  
• It has been suggested that Lully advanced the modern concept of fractal structural, because of these clues: 1) Because in every combinatorial form there are always the same principles; 2) Because of his use of recursive circles (circles within circles) in Figure 4; 3) Because in "The Tree scientae" (1295), a multi-volume encyclopedia devoted to the popularization of his art, he uses arboreal symbolism (a paradigmatic fractal) to represent unity in the diversity of knowledge; 4) Because of his conception of time as "something that contains itself."
  
  
• He was a pioneer in detecting the dualism between the sensible and the intelligible, which today we can identify as the two modes of consciousness corresponding to the two cerebral hemispheres (sensible or particular aspect: left hemisphere; intelligible or universal aspect: right hemisphere).
  
  
• He can also be considered a pioneer of the theory of unification through consciousness, consciousness as the foundation of everything. In Figure 1 of his Ars, the letter A in the center of the circle (God for Lully) can be considered as a symbol of consciousness, the connector of all things. Lully said that man's true quest should be the unity of Being, which comes from God.
  
  
• Even because of his universalistic vision, he can be considered as an antecedent of the modern "Theory of Everything", but "everything" in the literal sense −and not as the restricted concept applied in physics−, a "theory of everything" based on a truly universal paradigm. Although his philosophical ideas inaugurated a new philosophical current known as "lullism", today we can consider it a universal paradigm. Because of his ambition in this regard, we must consider Lully a unique figure in history.

Ars Magna vs. MENTAL
There are numerous analogies between the Ars Magna and MENTAL:

• Both are based on simple and universal principles. Both agree that one must base oneself on the universal in order to understand the particular.
  
  
• Both are universal systems or paradigms, but in MENTAL the theological aspect is discarded, although it must be considered that the universal semantic primitives are primary archetypes that border on the Absolute, so there is a certain connection with the transcendent.
  
  
• Both have a combinatorial method to generate new knowledge and new discoveries, a combinatorial method that can be considered a universal semantic grammar since it is based on universal principles.
  
  The language of the Ars is a simple, linear combinatorial language. The language of MENTAL is more elaborate, as a consequence of more precise semantic primitives.
  
  
• In the Ars the essence of every entity (including thought) is the act, which plays the role of unifying element. In MENTAL, the act is the process of evaluation of expressions, which connect subject and object, internal world and external world.
  
  
• In MENTAL all primitives are of the same level and combinatorics is not restricted, as all primitives combine with each other in both directions, including with themselves (self-combinatorics). In the Ars Magna, there are two types of principles (the absolute and the relative ones), and combinatorics is restricted.
  
  
• MENTAL is a descriptive and operative language, with defined semantics. The Ars is symbolic, speculative and dialectical.
  
  
• In both systems there are combinations that make no sense, but constitute a source of creativity and imagination.
  
  
• Lully intended to solve or clarify all kinds of problems from great principles. MENTAL pursues the same thing: to clarify or solve problems, although not all kinds of problems, but those of a formal nature, those of the formal sciences. Problems are clarified or solved from the deep level of primary archetypes.
  
  
• In the absolute principles, the relative ones and in the chambers of Figure 2 of the Ars we can recognize several primitives and derivatives of MENTAL:
  
  

  Ars Magna	MENTAL
  	Primitives	Derivatives	Other / Comments
  Sensitive			The datum, the particular
  Inteligible			The expressible
  Substance			The primitives themselves
  Accident			Expressions
  Cause	Condition
  Quantity	Sum
  Time	Associated with sequence		Abstract time
  Conjunction	Grouping		Serial and parallel grouping
  Measurement		Length, Depth
  End			First and last element (sequence)
  Perfection			Completeness of the primitives
  Termination		Stop
  Deprivation			Elimination
  Difference		Distinct	A type of condition
  Concordance	Equivalence
  Opposition			Opposition (meta-primitive)
  Beginning	Start of execution
  Medium			In progress
  Final	End of execution
  Majority		Majority	Is a type of condition
  Equality		Equal	id.
  Minority		Minor	id.

  
  
• In MENTAL there are no a priori rules. The principles (primitives) are self-sufficient. The rules are implicit in the combinatorial capacity of the primitives. However, in the rules of Ars we can also identify aspects or characteristics of MENTAL.
  
  

  Ars rule	Appearance	MENTAL feature
  B	Existence	Existence is a key aspect of language. It is a metaexpression
  C	Definición	Definition of expressions (particular or general)
  D	Composition	Contents or components of an expression
  E	Purpose	Functional definition
  F	Quantity	Quantity
  G	Quality	Quality, attribute or predicate
  H	Time	Abstract time in a sequence
  I	Position	Position in a sequence
  K-1	Mode	Relationships between expressions
  K-2	Instrument	The construction detail of expressions

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Addenda
The diffusion of Ars Magna

The Ars Magna spread throughout Europe during the 14th to 17th centuries. Schools and disciples grew very rapidly, mainly because of the support of the Franciscans. In Spain the Lullists became as numerous as the Thomists. Lully himself taught his method at the University of Paris, an honor for a person with no academic degree.

This universalist system attracted the attention of philosophers, writers and scientists such as Francis Bacon, John Dee, Athanasius Kircher, Pascal, Newton, Leibniz, Nicholas of Cusa, Giordano Bruno, Giovanni Pico della Mirandola, Marsilio Ficino and Hegel.

• Nicholas of Cusa collected a large number of manuscripts on Lully's Ars in his library, studied and commented on them, and saw in them a path of dialogue between cultures.
  
  
• Bruno was impressed by the possibilities of the Ars, which he considered divinely inspired, and tried to improve it, devoting several works to the subject.
  
  
• Kircher was a lullist. He published in 1669 a volume of almost 500 pages entitled "Ars Magna sciendi sive combinatoria", where he makes several reforms to LLull's method, to perfect it.
  
  
• It is known that he influenced Descartes in his "Mathesis Universalis", the search for a universal science that would found all the other particular sciences.
  
  
• But his greatest influence was on Leibniz. In his youth he studied the Ars and produced a short essay entitled "Dissertatio de Arte Combinatoria" (1666), in which he pointed out the limitations of the Lullian method. In this essay he reduced thought to arithmetic, assigning numbers to simple notions and products to compound notions.
  
  He wrote his doctoral thesis on Lullian combinatorics and influenced or was inspired by it in his idea of the "Lingua Characteristica Universalis" (universal conceptual or philosophical language) in three respects: 1) in the attempt to base thought on a few simple principles (the alphabet of thought) and their combinatorics; 2) in the mechanization of deductive processes; 3) in the use of symbols in language. This universal language would have the potential of a rational calculus (Calculus Ratiocinator) that would allow to decide mathematically the validity of reasoning.

The 16th century, in particular, was when there was most interest in Lully's system. It was in this context that his process of beatification took place. His canonization was halted by the doubts of the Catholic Church regarding the orthodoxy of some of his ideas, especially his idea of blurring the boundary between the natural and the supernatural, that is, his rationalist mysticism. In fact, two popes formally condemned Lullianism: Gregory IX and Paul IV. Pope Pius IX acknowledged the cult that he was being honored as blessed in Majorca and in the Franciscan order. During the pontificate of John Paul II the title of blessed was ratified. His canonization process is currently underway.


The zairja

Lully's idea for his Ars seems to have come to him in the form of a mystical vision he had after a period of fasting and contemplation. But another less divine origin has also been suggested. It seems that Lully, in one of his many trips, met a kind of "thinking machine" built by a group of Arab astrologers, to which they gave the name of zairja. This instrument was the product of the idea that it was possible to mechanize thought in order to generate ideas mechanically. It was based on the 28 letters of the Arabic alphabet and represented the 28 kinds of ideas, concepts or categories of things contemplated by Arabian philosophy. By combining the numerical values associated with these categories, new thoughts and new ways of looking at things were created. Enthused by this idea, Lully was inspired by it to construct a Christian version of the zairja, but with a more ambitious objective, by including the religious or theological.


Lullian-inspired artifacts

In Jonathan Swift's "Gulliver's Travels," a teacher shows the hero of the story a mechanical device that generates random sequences of words. When three or four words in a row made sense, they were written down in a notebook. The professor said the machine enabled the most ignorant person to write books effortlessly on philosophy, poetry, law, mathematics and theology. Swift, although he knew Lully's Ars, does not mention his name. This passage is considered a parody of his method.

Another Lullyian-inspired system is the "Think Tank". It consists of a plastic sphere filled with 13,000 small flat rectangular pieces, each with a word written on it, and a small window from which you can see some of the pieces with their corresponding words. By rotating the sphere, the window shows new visible pieces, corresponding to a set of randomly related words. The idea is to generate new mental associations that help to create new channels of thought and break the habits of "vertical" thinking for others of "lateral" thinking and thus favor creativity. The Think Tank was invented by the Yugoslavian Savo Bojicic, which includes a manual on lateral thinking.

The technique of "lateral thinking" was invented by Edward de Bono. He describes it in his work "New Think: The Use of Lateral Thinking in the generation of new ideas" (1967). It refers to a technique of solving problems indirectly, seeking different, unorthodox points of view, which logical, linear thinking normally ignores or rejects. The result is the development of intuition and creativity.


Bibliography

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• Cruz Hernández, Miguel. El pensamiento literario de Ramon Lully. Editorial Castalia, 1975.
  
  
• Fidora, Alexander y Rubio, Josep E. Rubio (eds.). Raimundus Lullus. An Introduction to his Life, Works and Thought, Turnhout: Brepols (Corpus Christianorum. Continuatio Mediaevalis 214, Supplementum Lullianum II), 2008.
  
  
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