The Proto-exposition of Aristotelian Categorical Logic

Chapter
Part of the Studies in Universal Logic book series (SUL)

Abstract

The aim of this paper is to state that the oldest Western treatises on categorical logic, the one attributed to Apuleius of Madaurus (I–II AD) and the other written by Boethius (VI AD), follow a common plan rather than a common written source. I call this common plan the proto-exposition of categorical logic as much as it can be reconstructed in its formality. Its limits exceed those of Aristotle’s written works on logic, and both Apuleius and Boethius suggest that Aristotle’s first disciples, Theophrastus and Eudemus, play an important role in its arrangement. After remarking its main characteristics, I describe its limits, by including indefinite terms in syllogistic premises, in connection with three general rules or Axioms making decidable every categorical syllogism. Accordingly, I analyze some study cases in order to distinguish strict conclusions from non-strict ones, which represents a new discernment on existential-import discussion. Then, I remark the importance of the concept of quantitative symmetry by showing how the three general rules can assess the validity of classical hypothetical syllogistic. Thus, the paper presents an extension of Aristotelian logic by taking its proto-exposition as starting point.

Keywords

Aristotelian logic Ancient commentators Syllogistic Existential import Indefinite terms 

Mathematical Subject Classification

Primary 03-02 Secondary 03B5 

Notes

Acknowledgements

This article was made possible thanks to Fondecyt N°1141135. I am grateful to Prof. Dr. Jean-Yves Beziau for his invitation to the 4th World Congress on the Square of Opposition, May 5-9, 2014, Vatican City, where a first version of this paper was given. I am also thankful to the editor and the referees for their useful comments.

References

  1. 1.
    E. Alvarez, M. Correia, Syllogistic with indefinite terms. Hist. Philos. Log. 33, 297–306 (2012)CrossRefGoogle Scholar
  2. 2.
    E. Alvarez, M. Correia, Conversion and opposition: traditional and theoretical formulations, in New Dimensions of the Square of Opposition, ed. by J.-Y. Béziau, K. Gan-Krzywoszynska (Philosophia Verlag, Muenchen, 2014), pp. 87–106Google Scholar
  3. 3.
    Alexander: Alexandri Aphrodisiensis, Aristotelis Topicorum Libros Octo Commentaria, in Commentaria in Aristotelem Graeca, vol. ii, 2, ed. by M. Wallies (Berlin, 1891)Google Scholar
  4. 4.
    Alexander: Alexandri Aphrodisiensis in Aristotelis Analyticorum Priorum Librum I Commentarium, in Commentaria in Aristotelem Graeca, vol. ii.1, ed. by M. Wallies (Berlin, 1883)Google Scholar
  5. 5.
    Ammonius: Ammonii In Aristotelis De Interpretatione Commentarius, in Commentaria in Aristotelem Graeca, vol. iv, 4.6, ed. by A. Busse (Berlin, 1895)Google Scholar
  6. 6.
    Apuleius: Apuleius Platonici Madaurensis opera quae supersunt, vol. III: De philosophia libri, ed. by C. Moreschini (Stuttgart, 1991), pp. 189–215Google Scholar
  7. 7.
    Aristotle: Aristotelis Categoriae et Liber de Interpretatione, ed. by L. Minio-Paluello (Oxford, 1949)Google Scholar
  8. 8.
    Aristotle: Aristotle’s Prior and Posterior Analytics. A revised text with introduction and commentary by W.D. Ross (Oxford, 1949)Google Scholar
  9. 9.
    O. Bird, Syllogistic and its extensions (Prentice-Hall, Englewood Cliffs, NJ, 1964)Google Scholar
  10. 10.
    I.M. Bochenski: La Logique de Théophraste (Collectanea Friburgensia) (Fribourg en Suisse, Librairie de l’ Université, 1947)Google Scholar
  11. 11.
    I.M. Bochenski, On the categorical Syllogism, in Dominican Studies, vol. I, 1 (1948), pp. 35–37—Reprinted in Logico Philosophical Studies, ed. by A. Menne (Dordrecht, 1962)Google Scholar
  12. 12.
    Boethius: Anicii Manlii Severini Boetii Commentarii in Librum Aristotelis PERI ERMHNEIAS. Prima et secunda editio, ed. by C. Meiser (Leipzig, 1877–1880)Google Scholar
  13. 13.
    Boethius: Severino Boezio De hypotheticis syllogismis. Testo, traduzione e commento. Obertello L.A.M. (Brescia, 1969)Google Scholar
  14. 14.
    Boethius: Boethius’s De Topicis Differentiis. Translation with notes and Essays by E. Stump (Ithaca, NY, 1978)Google Scholar
  15. 15.
    Boethius: Anicii Manlii Seuerini Boethii De syllogismo categorico. A critical edition with introduction, translation, notes and indexes by C. Thomsen Thörnqvist. Studia Graeca et Latina Gothoburgensia LXVIII (University of Gothenburg, 2008)Google Scholar
  16. 16.
    Boethius: Anicii Manlii Severini Boethii Introductio ad syllogismos categoricos. A critical edition with introduction, commentary and indexes by C. Thomsen Thörnqvist. Studia Graeca et Latina Gothoburgensia LXIX (University of Gothenburg, 2008)Google Scholar
  17. 17.
    J. Corcoran, A bibliography: John Corcoran’s publications on Aristotle 1972-2015. Aporía Int. J. Philos Invest. 10, 73–118 (2015)Google Scholar
  18. 18.
    M. Correia, ¿Es lo mismo ser no-justo que ser injusto? Aristóteles y sus comentaristas, Méthexis. Int. J. Anc. Philos. 19, 41–56 (2006)Google Scholar
  19. 19.
    M. Correia, Los tratados silogísticos de Boecio y su interdependencia temática, Teología y Vida. L, 4, 729–745 (2009)Google Scholar
  20. 20.
    M. Correia: Boethius on the Square of Opposition, in: Around and Beyond the Square of Opposition, ed. by J.-Y. Béziau, D. Jacquette (Studies in Universal Logic, Basel, 2012), pp. 41–52Google Scholar
  21. 21.
    M. Correia, Categorical syllogistic in G.W. Leibniz’s De arte combinatoria, in Leibniz’ Rezeption der aristotelischen Logik und Metaphysik, ed. by J.A. Nicolás, N. Öffenberger (Hildesheim, Zürich, New York, 2016), pp. 79–92Google Scholar
  22. 22.
    Galen: Galen’s Institutio Logica, English translation, Introduction, and Commentary by J.S. Kieffer (Baltimore, 1964)Google Scholar
  23. 23.
    J. Isaac: O.P., Le Peri hermeneias en Occident de Boèce à Saint Thomas. Histoire littéraire d'un traité d'Aristote (Paris, 1953)Google Scholar
  24. 24.
    T.-S. Lee, Die grieschische Tradition der aristotelischen Syllogistik in der Späntantike, eine Untersuchung über die Kommentare zu den Analytica Priora von Alexander Aphrodisiensis, Ammonius und Philoponus, in Hypomnemata, vol. 79 (Göttingen, 1984)Google Scholar
  25. 25.
    G.W. Leibniz, Dissertatio de arte combinatoria (1666), in Die philosophischen Schriften von Gottfried Wilhelm Leibniz, vol. iv, ed. by C.J. Gerhardt (Hildesheim, 1960), pp. 27–102Google Scholar
  26. 26.
    Philoponus: Ioannis Philoponi in Aristotelis Analytica Priora, in Commentaria in Aristotelem Graeca, vol. xiii, 1.2, ed. by M. Wallies (Berlin, 1905)Google Scholar
  27. 27.
    A.N. Prior, The logic of the negative terms in Boethius, Franciscan Stud. 13. I, 1–16 (1953)Google Scholar
  28. 28.
    J.C. Smith: The culmination of the science of logic, with synopses of all possible valid forms of categorical reasoning in syllogisms of both three and four terms (Brooklyn, NY, 1888)Google Scholar
  29. 29.
    R. Sorabji, Aristotle Transformed. The Ancient Commentators and their Influence, ed. by R. Sorabji (London, 1991)Google Scholar
  30. 30.
    M.W. Sullivan, Apuleian Logic. The Nature, Sources and Influence of Apuleius’s Peri Hermeneias (Studies in Logic and the Foundations of Mathematics, Amsterdam, 1967)Google Scholar
  31. 31.
    Theophrastus: Theophrastus of Eresus. Sources for His Life, Writings, Thought and Influence (2 vols). Edited and Translated by William W. Fortenbaugh, Pamela M. Huby, Robert W. Sharples (Greek and Latin) and Dimitri Gutas (Arabic) (Leiden, Boston, 1993)Google Scholar
  32. 32.
    I. Thomas, O.P.: CS(n): An Extension of CS, in Dominican Studies, vol. 2 (1949), pp. 145–160. Reprinted in Logico Philosophical Studies, ed. by A. Menne (Dordrecht, 1962)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Facultad de FilosofíaPontificia Universidad Católica de Chile, Campus San JoaquínMaculChile

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