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Abbreviations
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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.
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References
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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.
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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).
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