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
Aglianò, P. et al.: 1996, Logic and Algebra, New York: Dekker.
Angell, R. B.: 1986, 'Truth-Functional Conditionals and Modern vs. Traditional Syllogistic', Mind 95, 210–223.
Angell, R. B.: 2002, A-Logic, Lanham, New York, Oxford: University Press of America.
Barnes, J.: 1980, 'Proof Destroyed', in Schofield et al., 1980, pp. 161–181.
Barnes, J.: 1981, 'Proof and the Syllogism', in Berti 1981, pp. 17–59.
Barnes, J.: 1999, 'Aristotle and Stoic Logic', in Ierodiakonou 1999, pp. 23–53.
Berti, E. (ed.): 1981, Aristotle on Science: The 'Posterior Analytics', Proceedings of the Eighth Symposium Aristotelicum, Padua: Antenore.
Bobzien, S.: 1996, 'Stoic Syllogistic', Oxford Studies in Ancient Philosophy 14, 133–192.
Frede, M.: 1974, Die stoische Logik, Göttingen: Vandenhoeck & Ruprecht.
Ierodiakonou, K. (ed.): 1999, Topics in Stoic Philosophy, Oxford: Clarendon Press.
Nasti De Vincentis, M.: 2002, Logiche della connessività: Fra logica moderna e storia della logica antica, Bern-Stuttgart-Wien: Verlag Paul Haupt.
Nelson, E.: 1932, 'The Square of Opposition', The Monist 42, 269–278.
Pizzi, C.: 1996, 'Weak vs. Strong Boethius' Thesis: A Problem in the Analysis of Consequential Implication', in Aglianò et al. 1996, pp. 647–654.
Quine, W. V. O.: 1970, Philosophy of Logic, Englewood Cliffs, N.J.: Prentice-Hall.
Quine, W. V. O.: 1992, Pursuit of Truth, Cambridge, Mass.: Harvard University Press.
Schofield, M. et al. (eds.): 1980, Doubt and Dogmatism: Studies in Hellenistic Epistemology, Oxford: Clarendon Press.
Van Rijen, J.: 1986, Aristotle's Logic of Necessity, Alblasserdam: Offsetdrukkerij Kanters B.V.
Zonta, M.: 1994, 'Hebraica veritas: Temistio, Parafrasi del De Coelo, Tradizione e critica del testo', Athenaeum 82, 403–428.
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De Vincentis, M.N. From Aristotle's Syllogistic to Stoic Conditionals: Holzwege or Detectable Paths?. Topoi 23, 113–137 (2004). https://doi.org/10.1023/B:TOPO.0000021386.76719.2f
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DOI: https://doi.org/10.1023/B:TOPO.0000021386.76719.2f