NOTES

Abbreviations

MOG = Raymundi LuIli Opera omnia, Ivo Salzinger editor, 8 vols., Mainz, 1721-1742 (reprintFrankfurt, 1965)

ROL = Raimundi Lulli Opera Latina, F. Stegmüller et al., editors, 21 vols. published so far, Palma de Mallorca/Turnhout, Belgium, 1959.

References

1. Beth, E. W. (1962) Formal Methods; An introduction to symbolic logic and to the study of effective operations in arithmetic and logic, D. Reidel, Dordrecht.

2. Bonner, A. (1994) "Ramon Llull: relació, acció, combinatòria i lògica moderna", Studia Lulliana 34, pp. 51-74.

3. Colomer, E. (1979a) "Ramon Llull, ¿precursor de la informática?", Boletín CITEMA 81, pp. 7-44.

4. Colomer, E. (1979b) "De Ramon Llull a la moderna informática", Estudios Lulianos 23, pp. 113-135.

5. Deo, N., (1974) Graph Theory, with Applications to Engineering and Computer Science, Prentice-Hall, Englewood Cliffs, N.J.

6. Fleckenstein, J. O. (1967) "Leibniz's algorithmic interpretation of Lullus' art", Organon (1nstitut d'Histoire de la science et de la technique aupres de l'Académie Polonaise des Sciences) 4,171-180.

7. Foulds, L.R. (1992) Graph Theory Applications, Springer-Verlag, New York/Berlin.

8. Gardner, M. (1982) "The Ars Magna of Ramon Lull", Logic Machines and Diagrams, University of Chicago Press, Chicago.

9. Gentzen, G. (1969) The Collected Papers of Gerhard Gentzen, North-Holland, Amsterdam.

10. Künzel W. and Cornelius, H. (1991) Die Ars Generalis Ultima des Raymundus Lullus. Studien zu einem geheimen Ursprung der Computertheorie, Berlin.

11. Llull, R. (1978) Ars notatoria, J. Gayà' editor, CITEMA, Madrid.

12. Llull, R. (1985) Selected Works of Ramon Llull (1232-1316), A. Bonner, editor, 2 vols. Princeton University Press, Princeton, N.J.

13. Llull, R. (1993) Doctor Illuminatus. A Ramon Llull Reader, A. Bonner and E. Bonner, editors, Princeton University Press, Princeton, N.J.

14. McLean, I. and London, J. (1990) "The Borda and Condorcet Principles: Three Medieval Applications", Social Choice and Welfare 7, 99-108.

15. McLean, 1. i London, J. (1992) "Ramon Llull and the Theory of Voting", Studia Lulliana 32, 21-37.

16. Maróstica, A. H. (1992) "Ars combinatoria and Time: Llull, Leibniz and Peirce", Studia Lulliana 32, 105-134.

17. Nerode, A. and Shore, R. A. (1993) Logic for Applications, Springer Verlag, New York/Berlin.

18. Orio, B. (1994) "Leibniz y la tradición neoplatónica. Estado actual de la cuestión», Revista de Filosofía 7 , p. 493-517.

19. Smullyan, R. M. (1968) First Order Logic, Springer-Verlag, Berlin.

Notes

[1] The tactic was psychologically important. Instead of forcing his adversaries to justify their own faith, he gave them the opportunity to "falsify", as Popper would say, Christianity.

[2] And not dying martyred, as pious legends would have it. He is buried in Palma, in the Church of San Francisco.

[3] This first version of the Art (of which we'll get a glimpse at the end of this paper) was logically quite different from the second, and included two iuteresting attempts to establish a new notation, one in the Ars notatoria (see Llull, 1978), and the other in the Introductoria Artis demonstrativae printed in MOG III.

[4] The best edition is that of ROL XIV.

[5] The Latin text is in ROL XII, and an English translation in Llull (1985) and (1993).

[6] The reader mustn't be disturbed by the lack of the letter J, which didn't exist as a separate letter in Llull's time. The Middle Ages used I/J as well as U/V interchangeably; they weren't differentiated till the Renaissance.

[7] It received the letter T because in the previous version of the Art the alphabet used not just nine but all the letters of the alphabet, and the position of this figure followed that of a Figure S. Even though the intervening letters aud figures disappeared from his system, Llull, perhaps not to confuse users of the earlier system adapting to his "update", continued referring to as Figure T.

[8] Quoted in Orio (1994).