Authors/Ockham/Summa Logicae/Book III-1/Chapter 16
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| ƿ Cap. 16. De syllogismis expositoriis in tertia figura | Chapter 16. On expository syllogisms in the third figure. |
| Praeter praedictos syllogismos fiunt syllogismi expositorii, de quibus est nunc dicendum[1]. | In addition to the aforementioned syllogisms, there are expository syllogisms, which we must now discuss[2]. |
| Unde sciendum est quod syllogismus expositorius est qui est ex duabus praemissis singularibus, dispositis in tertia figura, quae tamen possunt inferre conclusionem tam singularem quam particularem seu indefinitam sed non universalem, sicut nec duae universales in tertia figura possunt inferre universalem. | Hence it should be known that an expository syllogism is one that consists of two singular premises, arranged in the third figure, which nevertheless can infer a conclusion that is both singular and particular, or indefinite but not universal, just as two universals in a third figure cannot infer a universal. |
| Sed intelligendum est quod ad propositionem singularem, quae debet esse in syllogismo expositorio, requiritur quod subiectum supponat pro aliquo quod non est plures res quaecumque, nec est idem realiter cum aliquo quod est plures res, sive relativae sive absolutae, et praecise pro uno tali. Si autem subiectum, sive sit pronomen demonstrativum sive nomen proprium sive pronomen demonstrativum sumptum cum aliquo termino addito, supponat pro aliquo quod quamvis sit unicum et simplex et unum numero et singularissimum et tamen est plures res, non tenet consequentia per rationem syllogismi expositorii. Cuius ratio est, quia sicut quando terminus subiectus est communis non valet consequentia arguendo ex particularibus, propter hoc quod terminus supponit pro diversis et ita una propositio potest verificari pro uno et alia pro alio, ita quando illud quod demonstratur est plures res, poterit una propositio verificari pro una illarum rerum et alia pro alia, et per consequens non contingit inferre praedicatum primae propositionis de praedicato secundae. Unde sicut non sequitur ‘homo est Sortes; homo est Plato; ergo Plato est Sortes’, ita si haec humanitas una numero esset Sortes et Plato, et simul cum hoc Sortes et Plato essent plures homines, non sequeretur ‘haec humanitas est Sortes; haec humanitas est Plato; igitur Plato est Sortes'. Et hoc quia haec propositio ‘haec humanitas est Plato’ verificaretur quia Plato est Plato, et haec propositio 'haec humaƿnitas est Sortes’ verificaretur quia Sortes est Sortes, et propter hoc haec humanitas est tam Sortes quam Plato. | But it must be understood that for a singular proposition, which must be in an expository syllogism, it is required that the subject supposit for something that is not several things whatsoever, nor is it really the same as something that is several things, whether relative or absolute, and precisely for one such thing. But if the subject, whether it be a demonstrative pronoun or a proper name or a demonstrative pronoun taken with some added term, supposits for something that although it is unique and simple and one in number and most singular and yet is several things, the consequence does not hold by the reason of an expository syllogism. The reason for this is that just as when the subject term is common, the consequence is not valid when arguing from particulars, because the term supposits for different things and thus one proposition can be verified for one and another for another, so when what is demonstrated is several things, one proposition can be verified for one of those things and another for another, and consequently it is not possible to infer the predicate of the first proposition from the predicate of the second. Hence just as it does not follow that ‘a man is Socrates; a man is Plato; therefore Plato is Socrates’, so if this humanity were one in number, Socrates and Plato, and at the same time that Socrates and Plato were several men, it would not follow ‘this humanity is Socrates; this humanity is Plato; therefore Plato is Socrates’. And this because this proposition ‘this humanity is Plato’ would be verified because Plato is Plato, and this proposition ‘this humanity is Socrates’ would be verified because Socrates is Socrates, and for this reason this humanity is as much Socrates as Plato. |
| Ex isto patet quare iste syllogismus non est expositorius ‘haec essentia est Pater; haec essentia est Filius; igitur Filius est Pater’, quia scilicet haec essentia est plures personae distinctae. Similiter iste syllogismus non est expositorius ‘hic Pater est essentia; hic Pater non est Filius; igitur Filius non est essentia’; et hoc quia Pater est realiter divina essentia, quae est tres personae distinctae realiter. | From this it is clear why this syllogism is not expository ‘this essence is the Father; this essence is the Son; therefore the Son is the Father’, because namely this essence is several distinct persons. Similarly this syllogism is not expository ‘this Father is an essence; this Father is not the Son; therefore the Son is not an essence’; and this because the Father is really the divine essence, which is really three distinct persons. |
| Est tamen sciendum quod aliquando talis modus arguendi tenet de illis terminis, quamvis non per virtutem syllogismi expositorii sed per aliam rationem, de qua tactum est prius[3]. | However, it should be known that sometimes such a way of arguing holds about those terms, although not by virtue of the expository syllogism but by another reason, which was touched upon before[4]. |
| Est igitur dicendum quod syllogismus expositorius est quando arguitur ex duabus singularibus in tertia figura, quarum singularium subiectum supponit pro aliquo uno numero quod non est plures res, nec est idem realiter cum aliquo quod est plures res. Et quia in creaturis nulla una res numero est plures res realiter quaecumque, ideo generaliter quando arguitur ex propositionibus singularibus praedicto modo, fit syllogismus expositorius, hoc addito quod minor sit affirmativa. Quia si minor sit negativa, non valet syllogismus; sicut non sequitur ‘Sortes est animal; Sortes non est Plato; igitur Plato non est animal’; et propter eandem rationem propter quam dictum est quod minor in tertia figura non potest esse negativa. Sed si minor sit affirmativa, sive maior sit affirmativa sive negativa, semper est bonus syllogismus. Unde omnes tales syllogismi sunt boni ‘Sortes non est aggregatum per accidens; Sortes est homo albus; igitur homo albus non est aggregatum per accidens’, si termini supponant semper personaliter et significative. Similiter sequitur ‘Sortes non distinguitur a Sorte; Sortes est Sortes albus; igitur Sortes albus non distinguitur a Sorte’; ‘Coriscus cognoscitur a te; Coriscus est veniens; igitur veniens cognoscitur a te’; ‘Sortes est alter a veniente; Sortes est veniens; igitur veniens est alter a veniente’; ‘hoc est Sortes; - demonstrando quoddam singulare, ita tamen quod sit unum ƿ et non plura -; hoc est asinus; igitur aliquis asinus est Sortes’. Et universaliter in talibus non potest assignari fallacia accidentis, sicut aliqui[5] assignant, non plus quam hic ‘Sortes est homo; Sortes est animal; igitur animal est homo’. Et ideo multum errant qui in talibus assignant fallaciam accidentis et destruunt omnem modum arguendi et omnem disputationem. | It must therefore be said that an expository syllogism is when it is argued from two singulars in the third figure, the subject of which singulars supposits for something one in number that is not many things, nor is it really the same as something that is many things. And because in creatures no one thing in number is really many things whatsoever, therefore generally when it is argued from singular propositions in the aforesaid way, it becomes an expository syllogism, with the addition that the minor is affirmative. Because if the minor is negative, the syllogism is not valid; just as it does not follow that ‘Socrates is an animal; Socrates is not Plato; therefore Plato is not an animal’; and for the same reason for which it was said that the minor in the third figure cannot be negative. But if the minor is affirmative, whether the major is affirmative or negative, it is always a good syllogism. Hence all such syllogisms are good ‘Socrates is not an aggregate by accident; Socrates is a white man; therefore a white man is not an aggregate by accident’, if the terms always supposit personally and significatively. Similarly follows ‘Socrates is not distinguished from Socrates; Socrates is white Socrates; therefore white Socrates is not distinguished from Socrates’; ‘Coriscus is known by you; Coriscus is coming; therefore someone who is coming is known by you’; ‘Socrates is other than one who is coming; Socrates is coming; therefore someone who is coming is other than someone who is coming’; ‘this is Socrates; - demonstrating a certain singular, yet in such a way that it is one and not more -; this is an ass; therefore some ass is Socrates’. And universally in such things the fallacy of accident cannot be assigned, as some[6] assign, no more than here ‘Socrates is a man; Socrates is an animal; therefore an animal is a man’. And therefore they greatly err who assign the fallacy of accident to such things and destroy every method of argument and every disputation. |
| Notandum est hic quod, quamvis syllogismus expositorius sit in tertia figura tantum, tamen arguendo in secunda figura ex duabus praemissis affirmativis in quibus ponitur terminus singularis, est bonus syllogismus, secundum quod dictum est[7]. Sicut bene sequitur ‘homo est Sortes; animal est Sortes; igitur animal est homo’. Et probatur iste syllogismus per conversionem maioris, sic: ista ‘homo est Sortes’ convertitur in istam ‘Sortes est homo’; nunc autem sequitur in prima figura ‘Sortes est homo; animal est Sortes; igitur animal est homo’, quia dictum est prius[8], quod in prima figura non refert an maior sit universalis an singularis. Sed si altera praemissarum talium in secunda figura sit negativa, discursus non valet, quia non sequitur ‘aliquod animal non est Sortes; homo est Sortes; igitur aliquis homo non est animal’. Nec valet ‘aliquod animal est Sortes; aliquis homo non est Sortes; igitur aliquis homo non est animal’. Nec potest aliquis istorum discursuum probari, sicut probatur primus. Non primus istorum; quia maior, cum sit particularis negativa, non convertitur; nec secundus potest probari, quia minor in prima figura non potest esse negativa. | It should be noted here that, although the expository syllogism is in the third figure only, nevertheless, arguing in the second figure from two affirmative premises in which the singular term is placed, it is a good syllogism, according to what was said[9]. Just as it follows well ‘a man is Socrates; an animal is Socrates; therefore an animal is a man’. And this syllogism is proven by the conversion of the major, thus: this ‘a man is Socrates’ is converted into this ‘Socrates is man’; but now it follows in the first figure ‘Socrates is man; an animal is Socrates; therefore an animal is man’, because it was said before[10] that in the first figure it does not matter whether the major is universal or singular. But if one of such premises in the second figure is negative, the discourse is not valid, because it does not follow ‘some animal is not Socrates; a man is Socrates; therefore some man is not an animal’. Nor is it valid to say, ‘some animal is Socrates; some man is not Socrates; therefore some man is not an animal.’ Nor can any of these discourses be proven, as the first is proven. Not the first of these; because the major, since it is a particular negative, is not converted; nor can the second be proven, because the minor cannot be negative in the first figure. |
| Sic igitur patet quod aliquis discursus in secunda figura valet ex omnibus affirmativis, sed iste discursus non disponitur in aliquo praedictorum modorum. Patet etiam quod aliquis discursus ex omnibus particularibus tenet, sed de talibus non loquitur Philosophus in libro Priorum. ƿ | Thus it is clear that some discourse in the second figure holds from all affirmatives, but this discourse is not disposed in any of the aforementioned ways. It is also clear that some discourse holds from all particulars, but the Philosopher does not speak of such things in the book of Prior Analytics.
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Notes
- ↑ De syllogismo expositorio iam sermo erat supra, Parte II c.27, lin. 65-133.
- ↑ The expository syllogism was already discussed above, in Part II c.27, lines 65-133.
- ↑ Cf. supra c.5, lin. 86-106.
- ↑ Cf. supra c.5, lines 86-106.
- ↑ Ut Magister Abstractionum, de quo supra, c.4, lin. 38
- ↑ As the Master of Abstractions, of whom above, c.4, line. 38
- ↑ Supra, c.13
- ↑ Supra, c.8
- ↑ Supra, c.13
- ↑ Supra, c.8
