Authors/Ockham/Summa Logicae/Book III-1/Chapter 15

Latin	English
Cap. 15. De syllogismis ex obliquis in tertia figura	Chapter 15. On syllogisms from oblique (cases) in the third figure.
Quantum ad syllogismos ex obliquis in tertia figura est sciendum quod in primo modo possunt fieri octo combinationes: quia aut utraque praemissarum est de obliquo aut altera. Si utraque, aut obliquitas est a parte subiecti in utraque aut a parte praedicati in utraque, aut a parte subiecti in maiore et a parte praedicati in minore, aut a parte praedicati in maiore et a parte subiecti in minore. Si primo modo, syllogismus non valet: non enim sequitur ‘cuiuslibet hominis est asinus; cuiuslibet hominis est leo; igitur leo est asinus vel leo est asini’. Si secundo modo, non valet, quia non sequitur ‘omnis asinus est Sortis; omnis asinus est Platonis; igitur Plato est Sortes vel Sortis’. Tamen si conclusio resolvatur sic ‘aliquid, quod est Platonis est Sortis’, est consequentia bona. Si tertio modo, non sequitur, sicut non sequitur formaliter ‘omnem hominem videt asinus; omnis homo videt bovem; igitur bovem videt asinus vel est asinus'. Si altera praemissarum sit de obliquo, aut maior aut minor. Si maior, aut habet praedicatum obliquum, et tunc bene tenet; sicut sequitur ‘omnis asinus est hominis; omnis asinus est animal; igitur aliquod animal est hominis’; aut habet subiectum obliquum, et ƿ valet; sicut bene sequitur ‘cuiuslibet hominis est asinus; omnis homo est animal; igitur alicuius animalis est asinus’. Si autem. minor sit de obliquo, aut de praedicato obliquo, et valet; sicut bene sequitur ‘omnis asinus est animal; omnis asinus est hominis; igitur hominis est animal’. Aut est de subiecto obliquo, et sequitur conclusio de praedicato obliquo; sicut bene sequitur ‘omnis homo est animal; aliquem hominem videt asinus; igitur aliquis asinus videt animal’.	As for syllogisms from obliques in the third figure, it should be noted that in the first mode eight combinations can be made: because either both of the premises are from the oblique or (one or) the other. If both, either the obliqueness is on the part of the subject in both or on the part of the predicate in both, or on the part of the subject in the major and on the part of the predicate in the minor, or on the part of the predicate in the major and on the part of the subject in the minor. If in the first way, the syllogism is not valid: for it does not follow ‘a donkey is some man's; a lion is some man's; therefore a lion is a donkey or a lion is a donkey's’. If in the second mode, it is not valid, because it does not follow ‘every donkey is Socrates’; every donkey is Plato’s; therefore Plato is Socrates or Socrates’. However, if the conclusion is resolved thus ‘something that is Plato’s is Socrates’, the consequence is good. If in the third way, it does not follow, just as it does not follow formally ‘a donkey sees every man; every man sees an ox; therefore an ox sees a donkey or is a donkey’. If one of the premises is oblique, either it is major or minor. If it is major, either it has an oblique predicate, and then it holds well; as follows ‘every donkey is a man’s; every donkey is an animal; therefore some animal is a man's’; or it has an oblique subject, and holds; as it follows well ‘a donkey is some man's; every man is an animal; therefore a donkey belongs to some animal’. But if the minor is of an oblique, or of an oblique predicate, and is valid; it follows well ‘every donkey is an animal; every donkey belongs to a man; an animal belongs to a man’. Or it is of an oblique subject, and the conclusion follows from the oblique predicate; as it follows well ‘every man is an animal; a donkey sees some man; therefore a donkey sees an animal’.
Praedictae combinationes possunt fieri circa secundum modum. Primo modo sequitur conclusio in recto, sic ‘nullius hominis est asinus; cuiuslibet hominis est leo; igitur aliquis leo non est asinus’. Secundo etiam modo sequitur conclusio in recto ‘nullus asinus est Sortis; omnis asinus est Platonis; igitur Plato non est Sortes'. Sed tertio modo non valet; non enim sequitur ‘nullum hominem videt asinus; omnis homo videt rudibile; igitur rudibile non videt asinum vel non est asinus’. Si quarto modo, non sequitur; sicut non sequitur ‘nullus homo videt asinum; omnem hominem videt rudibile; igitur aliquod rudibile non videt asinum vel non est asinus’. Quinto modo tenet, nam sequitur ‘nullus asinus est hominis; omnis asinus est animal; igitur aliquod animal non est hominis’. Sexto modo tenet, sicut patet. Septimo modo non tenet; non enim valet ‘nullus asinus est bos; omnis asinus est hominis; igitur alicuius hominis non est bos’. Octavo modo non valet; non enim sequitur 'nullus homo est asinus; aliquem hominem videt bos; igitur aliquis bos non videt asinum.	The above combinations can be made about the second mode. In the first mode, the conclusion follows in the direct (nominative case), thus ‘a donkey is no man's; a lion is some man's; therefore any lion is not a donkey’. In the second way, the conclusion also follows in the nominative 'no donkey is Socrates’; every donkey is Plato’s; therefore Plato is not Socrates'. But in the third way, it is not valid; for it does not follow ‘no man is seen by a donkey; every man sees a rude thing; therefore any rude thing does not see a donkey or is not a donkey’. If in the fourth way, it does not follow; just as it does not follow ‘no man sees a donkey; a rude thing sees every man; therefore any rude thing does not see a donkey or is not a donkey’. In the fifth way, it holds, for it follows ‘no donkey is a man's; every donkey is an animal; therefore some animal is not a man's’. In the sixth way, it holds, as is clear. In the seventh way, it does not hold; for it does not follow ‘no donkey is an ox; every donkey is a man's; therefore an ox is not any man's’. In the eighth way, it does not hold; for it does not follow ‘no man is a donkey; an ox sees a man; Therefore, an ox does not see a donkey.
Per praedictum modum potest leviter sciri quando syllogismus ex obliquis valet in aliis modis tertiae figurae et quando non.	By the aforementioned method it can be easily known when a syllogism from obliques is valid in other modes of the third figure and when it is not.
Ultimo, pro tota ista parte de syllogismis et pro sequentibus est sciendum quod numquam refert ponere indefinitam pro particulari vel e converso quando termini supponunt personaliter et significative, quia si termini tam particularis quam indefinitae supponant personaliter, generaliter - sine instantia - particularis et indefinita convertuntur.	Finally, for this entire part on syllogisms and for what follows, it should be known that it never matters to put the indefinite for the particular or vice versa when the terms supposit personally and significantly, because if the terms both particular and indefinite supposit personally, generally - without instance - the particular and indefinite are converted.