31 8 THE SCIENCE OF LOGIC 



regarded as &quot; inferior,&quot; in quality and quantity, to the affirmative 

 and the universal, respectively. 1 



In scholastic treatises on logic, the following eight rules of 

 syllogism are uniformly enumerated, 2 the first four applying to 

 the terms, the second four to the propositions : 



1 . Terminus esto triplex, major, mediusque, minorque. 



2. Latins hos quam praemissae conclusio non vult. 



3. Nequaquam medium capiat conclusio opportet. 



4. Aut semel aut iterum medius generaliter esto. 



5. Utraque si praemissa neget nihil inde sequetur. 



6. Ambae affirmantes nequeunt generare negantem. 



7. Pejorem sequitur semper conclusio partem. 



8. Nil sequitur geminis ex particularibus unquam. 



It will be noted that, on the one hand, these eight rules do 

 not include among them what we have called the second rule of 

 structure : that the syllogism contains three and only three pro 

 positions ; that the part of the sixth or last rule which states that 

 a negative premiss necessitates a negative conclusion, is here in 

 volved in the rule 7, Pejorem, etc. ; while, on the other hand, the 

 two canons given above (156) as corollaries are here stated as 

 rules (7 and 8), together with the rather superfluous rule (3) that 

 the middle term should not appear in the conclusion. 



WELTON, Logic^ i., pp. 282 sqq. JOSEPH, Logic, chap. xii. KEYNES, 

 Formal Logic - , part iii., chap. i. JOYCE, Logic, xi. and xii. 



1 In regard to the material aspect of syllogistic reasoning, this same phrase may 

 be taken to mean that the conclusion cannot be more probable, or certain, than the 

 less probable, or less certain, of the premisses. 



2 Cy. HICKEY, Summula Philosophicae Scholasticae (Dublin, Browne and Nolan, 

 editio altera, 1908), vol. i., pp. 90,91. REINSTADLER, Elementa Philosophicae Scho 

 lasticae (Herder, ed. altera, 1907), vol. i., p. 83. ZIGLIARA, Summa Philosophica 

 (edit, tertia, 1880), vol. i., p. 113. &quot; According to Prantl (Geschichte der Logik im 

 Abendlande II, S. 275, Leipzig, 1861) these rules were first formulated by Psellus [the 

 younger] in the eleventh century. He expressed them in five formulae, which were 

 afterwards increased by the explicit statement of their implications to the number of 

 eight.&quot; MERCIER, Logique, p. 207, n. The work ascribed to Psellus, in which 

 they occur, is now believed to have been a Greek version, by Georgius Scholarius 

 (Gennadius, isth century), of the Summulae Logicales of Petrus Hispanus (1226- 

 1277). C/. DE WULF, History of Medieval Philosophy, p. 356; JOSEPH, op. cit., p. 

 244, n. 



