Ir al menú de navegación principal Ir al contenido principal Ir al pie de página del sitio


Núm. 54

The problem of arity in Stoic logic: The case of the disjunction

diciembre 4, 2015


Both ancient sources and contemporary authors seem to agree, in general, that the Stoic disjunction was exclusive. The problem is that some ancient sources inform that the Stoics also considered disjunctions with more than two disjuncts and stated that such disjunctions were true if only one of their disjuncts was true as well. This appears to be a logical mistake, since an exclusive disjunction with three disjuncts can be true if its three disjuncts are true too. However, in this paper, I analyze this problem based on the mental models theory, and try to show that, under criteria different from those of standard logic, it is possible to claim that, in an exclusive disjunction with more than two disjuncts, only one disjunct can be true.


  1. Bobzien, S.: “Stoic syllogistic” in Taylor, C. C. W.: Oxford Studies in Ancient Philosophy. Oxford: Clarendon Press, 1996, pp. 133-192.
  2. Bocheński, I. M.: Ancient Formal Logic. Amsterdam: North-Holland, 1963.
  3. Cicero: Topica.
  4. Diogenes Laërtius: Vitae Philosophorum.
  5. Galen: Institutio Logica.
  6. Gellius: Noctes Atticae.
  7. Johnson-Laird, P. N.: How We Reason. Oxford: Oxford University Press, 2006.
  8. Johnson-Laird, P. N.: “Against logical form” in Psychologica Belgica 5(3/4), 2010, pp. 193-221.
  9. Johnson-Laird, P. N.: “Inference with mental models” in Holyoak, K. J. & Morrison, R. G.: The Oxford Handbook of Thinking and Reasoning. New York: Oxford University Press, 2012, pp. 134-145.
  10. Khemlani, S. & Johnson-Laird, P. N.: “Disjunctive illusory inferences and how to eliminate them” in Memory & Cognition 37(5), 2009, pp. 615-623.
  11. Khemlani, S., Orenes, I., & Johnson-Laird, P. N.: “Negation: A theory of its meaning, representation, and use” in Journal of Cognitive Psychology 24(5), 2012, pp. 541-559.
  12. Khemlani, S., Orenes, I., & Johnson-Laird, P. N.: “The negation of conjunctions, conditionals, and disjunctions” in Acta Psychologica 151, 2014, pp. 1-7.
  13. Kneale, W. & Kneale, M.: The Development of Logic. Oxford: Clarendon, 1962.
  14. López-Astorga, M.: “Chrysippus’ indemonstrables and mental logic” in Croatian Journal of Philosophy, 15(43), 2015, pp. 1-15.
  15. Lukasiewicz, J.: “On the history of the logic of propositions” in McCall, S.: Polish Logic: 1920-1939. New York: Oxford University Press, 1967, pp. 67-68.
  16. Mates, B.: Stoic Logic. Berkeley and Los Angeles: University of California Press, 1953.
  17. Mueller, I.: “An introduction to Stoic logic” in Rist, J. M.: The Stoics. Berkeley: University of California Press, 1978, pp. 1-26.
  18. Oakhill, J. & Garnham, A. (Eds.): Mental Models in Cognitive Science. Essays in Honour of Phil Johnson-Laird. Hove: Psychology Press, 1996.
  19. Orenes, I. & Johnson-Laird, P. N.: “Logic, models, and paradoxical inferences” in Mind & Language 27(4), 2012, pp. 357-377.
  20. O’Toole, R. R. & Jennings, R. E.: “The Megarian and the Stoics” in Gabbay, M. D. & Woods, J.: Handbook of the History of Logic, Volume I. Greek, Indian and Arabic Logic. Amsterdam: Elsevier, 2004, pp. 397-522.
  21. Sextus Empiricus: Pyrrhoniae Hypotyposes.


Los datos de descargas todavía no están disponibles.