Authors/Ockham/Summa Logicae/Book III-1/Chapter 20

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Latin English
Cap. 20. de uniformi generatione syllogismorum ex propositionibus de necessario in prima figura Chapter 20: of the uniform generation of syllogisms from de necessario propositions in the first figure.
Tractatum est prius de uniformi generatione syllogismorum de inesse, et specialiter quando nulla adverbialis determinatio ponitur in praemissa, ideo nunc restaret dicere de syllogismis recipientibus aliquam talem adverbialem determinationem; sed quia eaedem regulae observandae sunt circa tales adverbiales determinationes et alias eis aequivalentes et circa determinationes modales in propositionibus acceptis in sensu divisionis vel eis aequivalentibus, ideo non oportet de eis separatim tractare. We dealt before with the uniform generation of assertoric syllogisms, and specifically when no adverbial determination is given in the premisses. Thus it would remain to speak of syllogisms receiving some such adverbial determination. But because the same rules are to be observed about such adverbial determinations, and others equivalent to them, and about modal determinations in propositions taken in the sense of division, or equivalent to them, thus we do not have to deal with them separately.
Sed dicendum est post praedicta de uniformi generatione syllogismorum modalium. Et primo dicendum est de uniformi ex illis de necessario[1]. But it should be said after what was said about the uniform generation of modal syllogisms. And first we should speak about the uniform [generation] of syllogisms de necessario.
Et est primo sciendum quod, sicut dictum est frequenter[2], quando dictum propositionis ponitur cum modo, illa propositio est distinguenda penes compositionem et divisionem vel secundum amphiboliam. In sensu compositionis denotatur quod ille modus praedicetur de illa propositione tota; in sensu divisionis denotatur quod praedicatum praedicetur de subiecto mediante verbo determinato per talem > modum vel mediante verbo tali modali. And it should first be known that, just as was said frequently before , when the dictum of the proposition is given with a mode, that proposition is to be distinguished between composition, division, or amphiboly. In the sense of composition it is denoted that that mode is predicated of the whole proposition. In the sense of division it is denoted that the predicate is predicated of the subject by a mediating verb determined by such a mode, or by a mediating verb with such a modality.
Sicut per istam ‘album esse nigrum est possibile’ in sensu compositionis denotatur quod iste modus ‘possibile’ verificatur de ista tota propositione ‘album est nigrum’; in sensu divisionis denotatur quod hoc praedicatum ‘nigrum’ verificatur de hoc subiecto ‘album’ mediante hoc verbo ‘est’, determinate uno adverbio vel aliqua alia determinatione aequivalente, correspondente tali modo, vel mediante verbo correspondente, adiecto hoc infinitivo ‘esse’, sic ‘album potest esse nigrum’. For example, by ‘it is possible that a white thing is black’, it is denoted in the sense of composition that the mode ‘possible’ is verified of the whole proposition ‘a white thing is black’. In the sense of division it is denoted that the predicate ‘black’ is verified of the subject ‘white’, with the verb ‘is’ mediating, determinately with one adverb or with some other equivalent determination, corresponding to such a mode, or by a corresponding mediating verb, adjoined to the infinitive ‘to be’. Thus: ‘A white thing can be black’.
Et manifestum est quod isti sensus multum differunt, quia unus est verus et alius falsus. Et sicut est de praedicta propositione, ita, proportionaliter, dicendum est de aliis.Quamvis ista distinctio communis possit sustineri, nec velim eam improbare, tamen potest aliter distingui, et forte magis artificialiter, eo quod dictum propositionis potest sumi materialiter, et tunc non supponit pro se sed pro propositione cuius est dictum. Et iste sensus est idem cum illo qui ponitur sensus compositionis. Vel potest sumi significative, et tunc est idem sensus cum sensu divisionis. Sed quia sive distinguatur uno modo sive alio, non est variatio quantum ad veritatem et falsitatem propositionum nec quantum ad modum arguendi, ideo volo uti communi distinctione in processu. And it is manifest that these senses are greatly different, because one is true and the other false. And it is so in the proposition above. Thus, proportionately, it must be said of the others. Although that common distinction could be sustained, nor do I wish to disprove it, yet it can be distinguished otherwise, and perhaps more artificially, in that the dictum of the proposition can be taken materially, and then it does not supposit for itself, but for the proposition of which it is the dictum. And that sense is the same as that which the sense of composition is given. Or it can be taken significatively, and then it is the same sense as the sense of division. But because – whether it is distinguished in one way or the other – there is no variation in the truth or falsity of propositions, neither in the mode of arguing. Therefore I wish to use the common distinction in proceeding.
Unde circa primam figuram est sciendum quod quando praemissae de necessario sunt acceptae in sensu compositionis, vel accipiuntur aliquae aequivalentes talibus propositionibus in sensu compositionis, semper est bonus syllogismus, inferens conclusionem consimilem quantum ad sensum compositionis vel aequivalentem. Unde iste syllogismus est bonus ‘omnem hominem esse animal est necessarium; Sortem esse hominem est necessarium; igitur Sortem esse animal est necessarium’. Similiter iste syllogismus est bonus ‘haec est necessaria: omnis homo est animal; haec est necessaria: Sortes est homo; igitur haec est necessaria: Sortes est animal’. Et tenet talis discursus per istam regulam ‘praemissae > in syllogismo regulato per dici de omni vel de nullo sunt necessariae igitur conclusio est necessaria’. Therefore, concerning the first figure it must be known that when premisses de necessario are taken in the sense of composition, or some equivalent to such propositions are taken in the sense of composition, it is always a good syllogism, implying a similar conclusion in the sense of composition or equivalent. Therefore the syllogism ‘it is necessary that every man is an animal, it is necessary that Socrates is a man, therefore it is necessary that Socrates is an animal’, is a good one. Similarly the syllogism ‘“every man is an animal” is necessary, “Socrates is a man” is necessary, “Socrates is an animal” is necessary’ is good. And such discourse holds under the rule ‘the premisses in a syllogism regulated by dici de omni or de nullo are necessary, therefore the conclusion is necessary’.
Utrum autem debeat dici quod talis syllogismus ‘omnem hominem esse animal est necessarium; Sortem esse hominem est necessarium; igitur Sortem esse animal est necessarium’ sit syllogismus ex universalibus vel non, non est magna cura, quia haec est magis difficultas vocalis quam realis. Vocando enim syllogismum ex universalibus omnem syllogismum habentem propositionem universalem, quae ideo dicatur universalis propositio quia subiectum propositionis materialis sumitur cum signo universali, sic manifestum est quod praedictus syllogismus est ex universalibus; et sic vocat Philosophus propositionem universalem et syllogismum ex universalibus in libro Priorum[3]. Now whether it ought to be said that such a syllogism as ‘it is necessary that every man is an animal, it is necessary that Socrates is a man, therefore it is necessary that Socrates is an animal’ is a universal syllogism or not, is no great concern, because this is more a verbal difficulty than a real one. For by calling every syllogism having a universal proposition (which is called a universal proposition because the subject of a material proposition is taken under the universal sign ) a 'syllogism from universals', it is thus manifest that the previous syllogism is 'from universals', and thus the Philosopher talks about a 'universal proposition' and a 'syllogism from universals' in the Prior Analytics
Sic igitur circa tales syllogismos non est difficultas quando propositiones sunt acceptae in sensu compositionis vel eis aequivalentes, quin sequatur conclusio tam directa quam indirecta, sicut in illis de inesse. Sed quando omnes propositiones sumuntur in sensu divisionis vel etiam eis aequivalentes, tunc semper sequitur conclusio directa, sed non semper sequitur conclusio indirecta. Primum patet, quia omnis syllogismus talis regulatur per dici de omni vel de nullo. Nam per propositionem talem universalem denotatur quod de quocumque dicitur subiectum quod de eodem dicitur praedicatum. Sicut per istam ‘omnis homo de necessitate est animal’ denotatur quod de quocumque dicitur hoc subiectum ‘homo’ quod de eodem dicitur de necessitate hoc praedicatum ‘animal’. So, therefore, concerning such syllogisms there is not a difficulty when the propositions, or those equivalent to them, are taken in the sense of composition, but rather the conclusion follows both directly and indirectly, just as with assertoric propositions. But when all the propositions, or those equivalent to them, are taken in the sense of division, then the conclusion always follows directly, but not always indirectly. The first is clear, because every such syllogism is governed by dici de omni. For by such a universal proposition, it is denoted that of whatever the subject is predicated, the predicated is predicated of the same. For example, by 'every man of necessity is an animal', it is denoted that of whatever the subject 'man' is predicated, is predicated of necessity the predicate 'animal'.
Et ita est, proportionaliter, de universali negativa. Igitur accipiendo sub minorem affirmativam, in qua subiectum dicatur de aliquo cum modo necessitatis, arguitur per dici de omni vel de nullo. Unde bene sequitur ‘omnis homo de necessitate est animal; Sortes de necessitate est homo; igitur Sortes de necessitate est animal’. Sed conclusio indirecta, scilicet conversa conclusionis sine omni variatione praeter transpositionem terminorum, non sequitur; et hoc quia non semper illa de > necessario in sensu divisionis, nec aequivalens ei, est convertibilis in talem, sicut ostensum est prius[4]. And so it is, proportionally, with the universal negative. Therefore, in subsuming the minor premiss, in which the subject is predicated of something with the mode of necessity, it is argued by the dici de omni. Hence "Every man of necessity is an animal, Socrates of necessity is an animal, therefore Socrates of necessity is an animal" follows well. But the indirect conclusion, namely the converse of the conclusion without any variation apart from the transposition of the terms, does not follow. And this is because that de necessario proposition in the sense of division, nor one equivalent to it, is not always convertible into such a proposition, as was shown before.
Et ideo quamvis sequatur ‘quaelibet persona divina de necessitate est Deus; creans de necessitate est persona divina; igitur creans de necessitate est Deus’, tamen ista conclusio ‘Deus de necessitate est creans’ non sequitur, quia praemissae sunt verae et conclusio falsa. Sed sequitur ista conclusio indirecta, conversa prioris conclusionis, ‘aliquid, quod de necessitate est Deus, est creans’. And therefore, although "every divine person by necessity is God, a creator by necessity is a divine person, therefore creator by necessity is God" follows, nevertheless the conclusion "God of necessity creates" does not follow, because the premisses are true and the conclusion false. And yet the indirect conclusion "something, that of necessity is God" follows, which is the converse of the earlier conclusion
Ex isto sequitur quod illi quinque modi primae figurae, concludentes indirecte[5], non concludunt in uniformi de necessario conclusionem de necessario, praemissis sumptis in illo sensu. From this it follows that those five modes of the first figure, concluding indirectly, do not reach the conclusion de necessario in a syllogism that is uniformly de necessario.
Si autem praemissae sumantur in sensu divisionis vel aequivalentes eis et conclusio in sensu compositionis vel aequivalens ei, non valet discursus. Sicut non sequitur ‘quaelibet persona divina de necessitate est Deus; creans de necessitate est persona divina; igitur haec est necessaria: creans est Deus’, quia praemissae sunt verae et conclusio falsa. But if the premisses, are those equivalent to them, are taken in the sense of division, and the conclusion, or one equivalent to it, is taken in the sense of composition, the discourse is not valid. For example "any divine person of necessity is God, a creator by necessity is a divine person, therefore 'a creator is God' is necessary" does not follow, because the premisses are true and the conclusion false.
Et si dicatur quod minor propositio est falsa, ista scilicet ‘creans de necessitate est persona divina’, nam possibile est quod creans non sit Deus, dicendum est quod haec est simpliciter vera ‘creans de necessitate est persona divina’, quamvis sit contingens et possit esse falsa. Nam per istam propositionem ‘creans de necessitate est persona divina’ non plus denotatur nisi quod aliquis est creans et ipse de necessitate est Deus, ut ista ‘creans de necessitate est Deus’ aequivaleat isti copulativae ‘aliquis est creans et ipse de necessitate est Deus’, sicut ista ‘album potest esse nigrum’ aequivalet isti copulativae ‘aliquid est album et illud potest esse nigrum’. And if it is said that the minor proposition is false, namely "a creator by necessity is a divine person", for it is possible that a creator is not God, it should be said that "a creator by necessity is a divine person" is absolutely true, although it is contingent, and could be false. For by the proposition "a creator by necessity is a divine person", no more is denoted than that something is a creator and by necessity is God, so that "a creator by necessity is God" is equivalent to the conjunction "something is a creator and of necessity is God", just as "a white thing can be black" is equivalent to the conjunction "something is white, and that thing can be black"
Sed manifestum est quod ista copulativa potest esse vera ‘aliquis est creans et ipse de necessitate est Deus’, quia Pater est creans et ipse de necessitate est Deus; igitur ista est modo vera ‘creans de necessitate est Deus’. Sicut tamen copulativa potest esse falsa, eo quod prima pars potest esse falsa, ita ista ‘creans de necessitate est > Deus’ potest esse falsa, tamen modo de facto est vera. Nec est inconveniens propositionem veram de necessario esse contingentem, quamvis propositio necessaria non sit contingens. But it is manifest that the conjunction "something is a creator and that of necessity is God" can be true, because the Father is a creator and he by necessity is God, therefore "a creator of necessity is God" is now true.  Yet just as the conjunction can be false, in that the first part can be false, so "a creator of necessity is God" can be false, yet now, as a matter of fact, it is true.  Nor is it an absurdity that a true de necessarioproposition  can be contingent, although a necessary proposition is not contingent.
Si autem maior sumatur in sensu compositionis vel aequivalens et minor in sensu divisionis, sequitur conclusio in sensu divisionis et non in sensu compositionis. Primum patet, quia bene sequitur ‘haec est necessaria: quaelibet persona divina est Deus; creans de necessitate est persona divina; igitur creans de necessitate est Deus’, sed non sequitur ista ‘igitur haec est necessaria: creans est Deus’. But if the major, or one equivalent to it is taken in the sense of composition, and the minor in the sense of division, the conclusion follows in the sense of division and not in the sense of composition.  The first is clear, because "this is necessary: any divine person is God, a creator of necessity is a divine person, therefore a creator of necessity is God" follows well.  But "therefore this is necessary: a creator is God" does not follow.
Si autem maior sumatur in sensu divisionis vel aequivalens et minor in sensu compositionis, sequitur conclusio in sensu divisionis et in sensu compositionis. Et ratio est ista: quia impossibile est aliquid per se inferius vel per accidens inferius necessario praedicari de aliquo, ita quod propositio sit necessaria nisi etiam propositio sit necessaria in qua superius ad illud inferius praedicatur de eodem. But if the major, or one equivalent to it is taken in the sense of division and the minor in the sense of composition, the conclusion follows in the sense of division and in the sense of composition.  And the reason is that it is impossible for anything that is per se or per accidens inferior to be predicated necessarily of anything, so that the proposition is necessary unless also the proposition is necessary in which a superior to that inferior is predicated of the same thing.

Notes

  1. Cf. Aristotle, Anal. Priora I, c.8 (29b 29-30a 14).
  2. Supra II 9 et 24.
  3. Cf Aristot., Anal. Priora I, c.24 (41b 7-32)
  4. Supra, Parte II, c.24, lin. 29-79
  5. Cf. Boethius, De syllogismo categorico II (PL 64, 815s)
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