AO and EI premisses each distribute two terms, one of which must be the middle term by Rule 3: so that there is only one term left which may be distributed in the conclusion. But the conclusion must be negative by Rule 4. Therefore its predicate must be distributed. Hence its subject cannot be so. Therefore the conclusion must be particular. § 597. Rules 6 and 9 are often lumped together in a single expression--'The conclusion must follow the weaker part,' negative being considered weaker than affirmative, and particular than universal. § 598. The most important rules of syllogism are summed up in the following mnemonic lines, which appear to have been perfected, though not invented, by a mediæval logician known as Petrus Hispanus, who was afterwards raised to the Papal Chair under the title of Pope John XXI, and who died in 1277-- Distribuas medium, nec quartus terminus adsit; Utraque nec praemissa negans, nec particularis; Sectetur partem conclusio deteriorem, Et non distribuat, nisi cum praemissa, negetve. CHAPTER XII. _Of the Determination of the Legitimate Moods of Syllogism._ § 599. It will be remembered that there were found to be 64 possible moods, each of which might occur in any of the four figures, giving us altogether 256 possible varieties of syllogism. The task now before us is to determine how many of these combinations of mood and figure are legitimate. § 600. By the application of the preceding rules we are enabled to reduce the 64 possible moods to 11 valid ones. This may be done by a longer or a shorter method. The longer method, which is perhaps easier of comprehension, is to write down the 64 possible moods, and then strike out such as violate any of the rules of syllogism. AAA -AEA- -AIA- -AOA- -AAE- AEE -AIE- -AOE- AAI -AEI- AII -AOI- -AAO- AEO -AIO- AOO -EAA- -EEA- -EIA- -EOA- EAE -EEE- -EIE- -EOE- -EAI- -EEI- -EII- -EOI- EAO -EEO- EIO -EOO- [Illustration] § 601. The batches which are crossed are those in which the premisses can yield no conclusion at all, owing to their violating Rule 6 or 9; in the rest the premises are legitimate, but a wrong conclusion is drawn from each of them as are translineated. § 602. IEO stands alone, as violating Rule 4. This may require a little explanation. Since the conclusion is negative, the major term, which is its predicate, must be distributed. But the major premiss, being 1, does not distribute either subject or predicate. Hence IEO must always involve an illicit process of the major. § 603. The II moods which have been left valid, after being tested by the syllogistic rules, are as follows-- AAA. AAI. AEE. AEO. AII. AOO. EAE. EAO. EIO. IAI. OAO.