Topoi

, Volume 23, Issue 1, pp 113–137 | Cite as

From Aristotle's Syllogistic to Stoic Conditionals: Holzwege or Detectable Paths?

  • Mauro Nasti De Vincentis

Abstract

This paper is chiefly aimed at individuating some deep, but as yet almost unnoticed, similarities between Aristotle's syllogistic and the Stoic doctrine of conditionals, notably between Aristotle's metasyllogistic equimodality condition (as stated at APr. I 24, 41b27–31) and truth-conditions for third type (Chrysippean) conditionals (as they can be inferred from, say, S.E. P. II 111 and 189). In fact, as is shown in §1, Aristotle's condition amounts to introducing in his (propositional) metasyllogistic a non-truthfunctional implicational arrow '⇒', the truth-conditions of which turn out to be logically equivalent to truth-conditions of third type conditionals, according to which only the impossible (and not the possible) follows from the impossible. Moreover, Aristotle is given precisely this non-Scotian conditional logic in two so far overlooked passages of (Latin and Hebraic translations of) Themistius' Paraphrasis of De Caelo (CAG V 4, 71.8–13 and 47.8–10 Landauer). Some further consequences of Aristotle's equimodality condition on his logic, and notably on his syllogistic (no matter whether modal or not), are pointed out and discussed at length. A (possibly Chrysippean) extension of Aristotle's condition is also discussed, along with a full characterization of truth-conditions of fourth type conditionals.

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References

  1. Aglianò, P. et al.: 1996, Logic and Algebra, New York: Dekker.Google Scholar
  2. Angell, R. B.: 1986, 'Truth-Functional Conditionals and Modern vs. Traditional Syllogistic', Mind 95, 210–223.CrossRefGoogle Scholar
  3. Angell, R. B.: 2002, A-Logic, Lanham, New York, Oxford: University Press of America.Google Scholar
  4. Barnes, J.: 1980, 'Proof Destroyed', in Schofield et al., 1980, pp. 161–181.Google Scholar
  5. Barnes, J.: 1981, 'Proof and the Syllogism', in Berti 1981, pp. 17–59.Google Scholar
  6. Barnes, J.: 1999, 'Aristotle and Stoic Logic', in Ierodiakonou 1999, pp. 23–53.Google Scholar
  7. Berti, E. (ed.): 1981, Aristotle on Science: The 'Posterior Analytics', Proceedings of the Eighth Symposium Aristotelicum, Padua: Antenore.Google Scholar
  8. Bobzien, S.: 1996, 'Stoic Syllogistic', Oxford Studies in Ancient Philosophy 14, 133–192.Google Scholar
  9. Frede, M.: 1974, Die stoische Logik, Göttingen: Vandenhoeck & Ruprecht.Google Scholar
  10. Ierodiakonou, K. (ed.): 1999, Topics in Stoic Philosophy, Oxford: Clarendon Press.Google Scholar
  11. Nasti De Vincentis, M.: 2002, Logiche della connessività: Fra logica moderna e storia della logica antica, Bern-Stuttgart-Wien: Verlag Paul Haupt.Google Scholar
  12. Nelson, E.: 1932, 'The Square of Opposition', The Monist 42, 269–278.Google Scholar
  13. Pizzi, C.: 1996, 'Weak vs. Strong Boethius' Thesis: A Problem in the Analysis of Consequential Implication', in Aglianò et al. 1996, pp. 647–654.Google Scholar
  14. Quine, W. V. O.: 1970, Philosophy of Logic, Englewood Cliffs, N.J.: Prentice-Hall.Google Scholar
  15. Quine, W. V. O.: 1992, Pursuit of Truth, Cambridge, Mass.: Harvard University Press.Google Scholar
  16. Schofield, M. et al. (eds.): 1980, Doubt and Dogmatism: Studies in Hellenistic Epistemology, Oxford: Clarendon Press.Google Scholar
  17. Van Rijen, J.: 1986, Aristotle's Logic of Necessity, Alblasserdam: Offsetdrukkerij Kanters B.V.Google Scholar
  18. Zonta, M.: 1994, 'Hebraica veritas: Temistio, Parafrasi del De Coelo, Tradizione e critica del testo', Athenaeum 82, 403–428.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Mauro Nasti De Vincentis
    • 1
  1. 1.Department of Communication SciencesUniversity of SalernoFisciano (Salerno)Italy

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