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Syllogism


Allan Bäck


Pages 540 - 544



Before Aristotle ‘syllogism’ had the general sense of ‘reckoning up’ or ‘inference’ (Herodotus, Histories 2.148; Plato, Republic 516B). But Aristotle narrowed the usage. The precise nature of what counts as a syllogism for Aristotle is obscure. It does not include all the arguments that would be reckoned valid today in a system of predicate logic, e.g. those having no or only one premise (μоνоλήμματα). On the other hand, Aristotle, outside of his syllogistic proper, does not restrict ‘syllogism’ to arguments having only two premises in the canonical forms (A, E, I, O) standardised in later textbooks (Prior Analytics 24 b 19-20; Topics 100 a 25-7; Sophistical Refutations 164 b 27-165 a 2; Rhetoric 1356 b 16-8; Smith 1989, xvi). He does make that restriction once he discusses his categorical syllogistic with its three figures (Prior Analytics, 25 b 32-5; 41 b 36-8; 42 a 30-3; 44 b 6-8). Alexander, 8, 19-24; 20, 24-6, is right to insist that Aristotle develops his syllogistic to construct the logical theory for his demonstrative science. So perhaps he focuses on syllogisms having those forms of use to him.




1Department of Philosophy, Kutztown University



1 Albertus, Magnus, (1890), Opera Ad Logicam Pertinentia, in Opera Omnia, ed. A. Borgnet, Vol. I, Paris: Vivès (Venice 1632 and Lyons 1651 were consulted).

2 Alexander, of Aphrodisias, (1883), Alexandri Aphrodisiensis in Aristotelis analyticorum priorum librum I commentarium, ed. M. Wallies, in Commentaria in Aristotelem graeca Vol. 2.1, Berlin: Georg Reimer.

3 Alexander, of Aphrodisias, (1991), On Aristotle’s Prior Analytics I: 1-7, trans. & comm. by Barnes, J.; Bobzien, S.; Flannery, K.; Ierodiakonou, K., London: Duckworth.

4 Alexander, of Aphrodisias, (1999), On Aristotle’s Prior Analytics I.8-13, trans. & comm. by Mueller, I.; Gould, J., Ithaca: Cornell University Press.

5 Avicenna Al-Qīyās (Syllogism), ed. Zayid, S.; Madkour, I., Cairo: al-Matba“a I-Amiriyya, 1964. (Volume I, Part 4 of al-Shifa’)

6 Boethius, M. S. De Hypotheticis Syllogismis, in Opera Omnia, ed. J.-P. Migne, Patrologia Latina, Vol. 64, Paris, 1891.

7 Dambska, F., (1978), “Brentano et la pensée philosophique en Pologne: Casimir Twardowski et son école”, Grazer philosophischen Studien 5: 117-129.

8 Herodotus Historiae.

9 Henry, D. P., (1958), Medieval Logic and Metaphysics, London: Hutchinson. Kahn, C., 1976, “Why Existence Does not Emerge as a Distinct Concept in Greek Philosophy”, Archiv für Geschichte der Philosophie, Vol. 58.4; repr. in Morewedge, P. (ed.), 1982, Philosophies of Existence, New York: Fordham University Press.

10 Lax, G., (1509), Tractatus syllogismorum, Paris.

11 Leśniewski, S., (1983), “On the foundations of mathematics”, Topoi 2: 7-52 (English translation of 1928, “O podstawach matematyki”, Przeglad filozoficzny 34: 142-170).

12 Leśniewski, S., (1992), “On the Foundations of Mathematics”, in Surma, S. J.; Srzednicki, J. T.; Barnett, D. I.; Rickey, V. F. (eds.), Collected Works, Kluwer: Dordrecht (English translation of 1928, “O podstawach matematyki”, Przeglad filozoficzny 34: 142-170).

13 Łukasiewicz, J., (1957), Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic, second edition, Oxford: Clarendon Press.

14 Malink, M., (2013), Aristotle’s Modal Syllogistic, Cambridge Mass.: Harvard University Press.

15 Mates, B., (1961), Stoic Logic, Berkeley: University of California Press.

16 Mendell, H., (1998), “Aristotelian Demonstration”, Oxford Studies in Ancient Philosophy 16: 161-225.

17 Mignucci, M., (1961), Gli analitici primi, traduzione, introduzione e commento di Mario Mignucci, Naples: Luigi Loffredo.

18 Mignucci, M., (1991), “Expository Proofs in Aristotle’s Syllogistic”, Oxford Studies in Ancient Philosophy 9: 9-28.

19 Ockham, William, (1974), Summa Logicae, in Opera Philosophica et Theologica, Vol. I, St. Bonaventure, NY.

20 Patzig, G., (1969), Aristotle’s Theory of the Syllogism, Dordrecht: Reidel (J. Barnes’s English translation of Die Aristotelische Syllogistik, 1959).

21 Plato Republic.

22 Poli, R.; Libardi, M., (1999), “Logic, Theory of Science, and Metaphysics according to Stanisław Leśniewski”, Grazer Philosophische Studien 57: 183-219.

23 Rescher, N., (1974), “A New Approach to Aristotle’s Apodeictic Syllogisms”, in Studies in Modality, Oxford: Oxford University Press.

24 Simons, P., (1994), “Discovering Lesniewski”, History and Philosophy of Logic 15: 227-235.

25 Smith, R., (1982), “What Is Aristotelian Ecthesis?”, History and Philosophy of Logic 3: 113-127.

26 Smith, R., (1983), “Completeness of an Ecthetic Syllogistic”, Notre Dame Journal of Formal Logic 24: 224-232.

27 Smith, R.[trans. & comm.], 1989, Aristotle’s Prior Analytics, Indianapolis: Hackett.

28 Smith, R., (1983), “An Ecthetic Syllogistic”, Notre Dame Journal of Formal Logic 24: 224-232.

29 Thom, P., (1981), The Syllogism, Munich: Philosophia Verlag.

30 Thom, P., (1991), “The Two Barbaras”, History and Philosophy of Logic 12: 135-150.

31 Thom, P., (1976), “Ecthesis”, Logique et Analyse 74-6: 299-310.

32 Thom, P., (1993), “Apodeictic Ecthesis”, Notre Dame Journal of Formal Logic 34: 183-208.

33 Thom, P., (1996), The Logic of Essentialism, Dordrecht: Kluwer.

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