Abstract
A celebrated argument at once springs to mind when the syllogism comes under discussion. The Scholastics called it Barbara, and it runs as follows:
All men are mortal,
Socrates is a man,
therefore: Socrates is mortal.
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Notes
These names, or at least their close relatives, are first found in the Summulae Logicales of Petrus Hispanus (Pope John XXI, ob. 1277). Cf. I.M. Bochenski, Formale Logik (hereafter cited as: FL), pp. 244 sqq., English translation (hereafter: HFL), pp. 210 sqq.
E.g. H. Maier, Die Syllogistik des Aristoteles (1896–1900; hereafter cited as: SdA) II, 1, p. 74; F. Überweg, System der Logik,(5th ed. 1882; hereafter: SdL5), p. 331. Characteristically, C. Prantl passes over this distinction in silence in his Geschichte der Logik im Abendlande (I 1855, II 1861; hereafter: Prantl).
J. Lukasiewicz, Aristotle’s Syllogistic from the standpoint of modern formal logic (1951; 2nd ed. 1957; hereafter: AS), pp. 1 sqq. (The page-numbers of all my citations from this book apply to the first and second editions alike.)
A.N. Whitehead and B. Russell, Principia Mathematica I (1910; hereafter: PM), p. 28: “Syllogisms are traditionally expressed with ’therefore’ as if they asserted both premisses and conclusion. This is, of course, merely a slipshod way of speaking, since what is really asserted is only the connection of premisses with conclusion.”
On this cf. my paper ’Aristotle and syllogisms from false premisses’, Mind 68 (1959), 186–192 (See Appendix, below p. 196).
W.D. Ross, Aristotle’s Prior and Posterior Analytics (1949; hereafter: APPA), p. 289.
Bochenski (FL, p. 81; HFL, p. 70) supposes the reason why Aristotle restricted terms to members of the ’middle class’ to be the logical fact that “the technique of the syllogism requires that each outer term occur at least once as predicate”. But this is not a logical fact: in figures I and II S occurs only as subject.
Aristotle says (A 28, 44a7 sq.) that this is an argument in Celarent (I), and that, with the aid of an element common to the set of predicates of P and the set of contraries of S,we could also construct a syllogism in Camestres (II) (PaMandSeM - -SeP). Thus he tacitly - and legitimately - converts PeM to MeP; he makes the same conversion to transform Fesapo (IV) (PeMandMaS-.SoP) into Felapton (III). Clearly the notion of a contrary predicate-set would suffice: there is no need to introduce the further notion of a contrary subject-set (oiç aú2Ò xì év8txstat rzapeivat). Here the strikingly modern tendency to make do with a minimum of concepts and logical laws is apparent: it can be traced throughout the Analytics and appears at its clearest in the reduction of the second and third figures to the first.
H. Steinthal, Die Sprachwissenschaft bei den Griechen and Römern I (2nd. ed., 1891), p. 222.
For the interpretation of APr. A 41, cf. Bochetíski, FL, pp. 49, 92, 96; HFL, pp. 42, 80, 83.
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Patzig, G. (1968). What is an Aristotelian Syllogism?. In: Aristotle’s Theory of the Syllogism. Synthese Library, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0787-9_1
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