Authors/Ockham/Summa Logicae/Book III-1/Chapter 6

Latin	English
[Cap. 6 De sufficientia modorum primae figurae]	[Chapter 6. On the sufficiency of the modes of the first figure]
Sciendum est etiam circa syllogismos regulatos per dici de omni vel de nullo quod, cum quatuor sint modi, quorum primus est ex duabus universalibus affirmativis inferentibus universalem affirmativam per dici de omni, secundus est ex maiori universali negativa et minori universali affirmativa inferentibus universalem negativam per dici de nullo, tertius est ex maiori universali affirmativa et minori particulari affirmativa inferentibus particularem affirmativam, quartus est ex maiori universali negativa et minori particulari affirmativa inferentibus particularem negativam, istae conclusiones praenominatae sunt primo sequentes ex praemissis, mediate tamen et secundario sequuntur aliae conclusiones.	It should be known also that, concerning syllogisms governed by dici de omni, since the modes are four, of which the first is from two universal affirmatives implying a universal affirmative by dici de omni, the second is from a universal negative major and a universal affirmative minor implying a universal negative by dici de omni, the third is from a universal affirmative major and a particular affirmative minor implying a particular affirmative, the fourth from a universal negative major and a particular affirmative minor implying a particular negative, these aforesaid conclusions primarily follow from the premisses, but indirectly and secondarily there follow other conclusions.
Nam in primo modo, praeter universalem conclusionem sequentem, sequitur conclusio particularis et etiam conversa primae conclusionis universalis. Et ita tres conclusiones sequuntur in primo modo; et ultima conclusio potest sequi in illo modo qui dicitur Baralipton.	For in the first mode, beyond the universal conclusion which follows, there follows a particular conclusion, and also the converse of the first universal conclusion.  And so three conclusions follow in the first mode, and the final conclusion can follow in the mode which is called 'Baralipton'.
Ex praemissis autem dispositis in secundo modo sequuntur quatuor conclusiones: prima, universalis negativa, in qua negatur maior extremitas de minori; secunda, conversa illius universalis, et tunc habetur ille modus qui dicitur Celantes; tertia est particularis subalterna primae universalis; quarta est particularis negativa de terminis transpositis, quae est subalterna secundae conclusionis universalis.	Now from the premisses arranged in the second mode there follow four conclusions: first, the universal negative, in which the major extremity is denied from the minor; the second, the conversion of that universal, and then it is that mode which is called Celantes; the third is the particular subordinate of the first universal; The fourth is the particular negative of transposed terms, which is subordinate to the second universal conclusion.
Ex praemissis dispositis in tertio modo sequuntur duae conclusiones, scilicet particularis directa et secundario conversa illius; et tunc habetur ille modus qui dicitur Dabitis.	From the premisses arranged in the third way, two conclusions follow, namely, the direct particular and the secondary inversion thereof; and then there is that mode which is called Dabitis [from the mnemonic. See discussion].
Ex praemissis dispositis in quarto modo non sequitur nisi una conclusio, et hoc quia conclusio particularis negativa non convertitur. Sed illa eadem conclusio particularis negativa sequitur ex universali affirmativa de terminis transpositis ipsius minoris et universali negativa conversa maioris, ipsis propositionibus transpositis, concludentibus conclusionem indirectam; et similiter ex conversa minoris et conversa maioris, transpositis praemissis et indirecte concludentibus. Et tunc habentur illi duo modi Fapesmo et Frisesomorum.	From the premisses arranged in the fourth way, only one conclusion follows, and this because the particular conclusion is not reversed. But that same particular negative conclusion follows from the universal affirmative from the transposed terms of the minor, and the universal negative inverted from the major, by the transposed propositions themselves, concluding an indirect conclusion; and in like manner from the minor converse and the major converse, transposing the premisses and concluding indirectly. And thence are the two modes Fapesmo and Frisesomorum. [from the mnemonic]
Omnia autem praedicta probantur per istas duas regulas quae semper verae sunt 'quidquid sequitur ad consequens, sequitur ad antecedens'; 'quidquid sequitur ad consequens cum addita propositione, sequitur ad antecedens cum eadem propositione'.	Now all that has been said is proved by these two rules which are always true: 'whatever follows from a consequence, follows from an antecedent'; 'whatever follows from the consequent with an added proposition, follows from the antecedent with the same proposition'.
Tales autem modi non possunt accipi penes alios tres modos per transpositionem propositionum. Nam modi affirmativi non possunt reduci per conversionem in modos affirmativos, propter hoc quod nec universalis affirmativa nec universalis negativa potest converti in universalem affirmativam. Et eadem ratio est quare penes modum universalem non potest sumi talis modus concludens indirecte per transpositionem propositionum de terminis transpositis.	But such modes cannot be taken close to the other three modes by the transposition of propositions. For positive modes cannot be reduced by conversion into positive modes, for the reason that neither the affirmative of a universal nor the negative of a universal can be converted into the universal positive. And this is the same reason why such a method concluding indirectly by transposition of propositions about transposed terms cannot be taken as a universal mode.