Ars demonstrativa

This work was the second version of the Art, and revised and completed the Ars compendiosa inveniendi veritatem (1274). It belongs to the second stage of the first of the Art’s phases and was composed in Montpellier in 1283. The work comes accompanied by Figures and an Alphabet; the former are graphic symbols which make the structural components of the Art visible and facilitate the operation of the combinatorial mechanisms and the calculations.

‘Primary’ Figures

The Ars demonstrativa contains 12 ‘primary’ figures, which Llull designates by letters. Except for the Elemental Figure, they are all circular and carry words inscribed around their circumference. The diametrical lines indicate the binary combinations of the concepts in question.

Figure A represents God and sixteen of his attributes or dignities (goodness, greatness, eternity, power, wisdom, will, virtue, truth, glory, perfection, justice, generosity, simplicity, nobility, mercy, lordship).

Figure V exists in two colours: blue V represents the virtues (faith, hope, charity, justice, prudence, fortitude, temperance) and red V the vices (greed, lust, avarice, pride, sloth, envy, anger)

Figure X contains eight pairs of opposing concepts: predestination-free will, being-privation, perfection-deficiency, merit-blame, supposition-demonstration, immediately-mediately, reality-reason, potency-object.

Figures Y and Z each represent a single concept: truth and falsity.

Figure S focuses on the rational soul and is made up from four interlocking squares drawn inside a circle, each square representing a different combination of the acts of man’s higher faculties,: the understanding and its corresponding act (knowing or not knowing); memory and its corresponding act (remembering or forgetting); the will and its corresponding act (loving or hating).

Figure T consists of five interlinked triangles, each of a different colour, drawn inside a circle; it represents five triads of concepts: difference-concordance-contrariety (green); beginning-middle-end (red); majority-equality-minority (yellow); affirmation-doubt-negation (black); God-creature-operation (blue).

The Figure of Theology, the Figure of Law and the Figure of Philosophy represent the principles of the respective sciences.

The Demonstrative Figure provides a semi-mechanical method for combining the concepts from certain figures with those from other figures.

The Elemental Figure is formed by four rectangles which represent the binary combinations of the four elements starting from each element (fire, red; air, blue; water, green; earth, black). To make this figure work one must keep in mind the structure of concentric circles circumscribing the simplified Aristotelian cosmos, the elemental spheres, the elemental square, and the corresponding circularity and relationships of concordance and contrariety.

‘Secondary’ Figures

Alongside the twelve ‘Primary’ Figures, the Ars demonstrativa includes ten ‘Secondary’ Figures.

The ‘Secondary’ Figures have a triangular form and are tables of all the possible binary combinations of the concept from the ‘Primary’ figures.


As regards the Alphabet, the letters A S T V Y and Z represent the figures described above, while the others, namely those between B and R, serve to designate the concepts contained within Figure S, the figure pertaining to the rational soul, as can be seen in the Alphabet of the Ars demonstrativa compiled by A. Bonner.

Parts of the work

The Ars demonstrativa has four parts or distinctions, of which the final part is a list of questions relating to the preceding parts, accompanied by their corresponding solutions in symbolic notation.

  • The first distinction gives a detailed description of the figures.
  • The second distinction expounds the ‘conditions’ of the Art, in other words, the mechanisms which enable the reader to obtain information on the basis of the principles from Figures A V X, with a view to discovering the truth or falsity (Figures Y Z), by using Figures T and S, which establish relationships, from within or externally, between the principles. Learning to handle these tools signifies the discovery of the potential for the meaning hidden in the binary combinations.
  • The third distinction offers sixteen modes, or rather, sixteen applications for the mechanisms of the Art, which are: remembering, understanding, loving, believing, contemplating, finding (=discovering), ordering (=directing), preaching, expounding (=interpreting), resolving, judging, showing (=demonstrating), disputing, advising, accustoming (=acquiring good habits), curing (=healing).
See: Anthony Bonner, Selected Works of Ramon Llull (Princeton: Princeton University Press, 1985), Vol. I, pp. 305-568.; Catalan version: Obres Selectes de Ramon Llull (Palma de Mallorca: Moll, 1989), Vol. I, pp. 275-521.