Authors/Ockham/Summa Logicae/Book III-2/Chapter 12

Latin	English
CAP. 12. QUAE PROPOSITIO POTEST ESSE CONCLUSIO DEMONSTRATIONIS ET QUAE NON?.	Chapter 12. Which proposition can be the conclusion of a demonstration and which cannot?
Ex praedictis patere potest quod non quaelibet propositio in qua praedicatur passio de suo subiecto primo potest esse conclusio demonstrationis. Haec enim est talis ‘omnis calor est calefactivus’, si nihil sit calefactivum nisi calor; et tamen, ex quo non potest evidenter cognosci nisi per experientiam, manifestum est quod demonstrari non potest.	From what has been said it is clear that not every proposition in which an effect is predicated of its first subject can be the conclusion of a demonstration. For this is such that 'all heat is heating', if there is nothing heating but heat; and yet, from what cannot be evidently known except by experience, it is evident that it cannot be demonstrated.
Et si dicatur quod haec potest demonstrari sic ‘omne productivum caloris est calefactivum; omnis calor est productivus caloris; igitur omnis calor est calefactivus’, ubi per definitionem passionis concluditur passio de subiecto: Dicendum quod haec non est demonstratio sed petitio principii. Unde universaliter quando pro medio accipitur definitio exprimens quid nominis tantum, in tali illatione est petitio principii. Cuius ratio est, quia apud omnem demonstrantem ante conclusionem debet praecognosci quid nominis tam subiecti quam passionis.	And if it is said that this can be demonstrated thus, 'everything productive of heat is warming; all heat is productive of heat; therefore all heat is warming', where by the definition of an effect, the effect is concluded from the subject: It must be said that this is not a demonstration but a petition to a principle. Hence, universally, when a definition is taken as a means, expressing what is only a name, in such an inference there is a petition to a principle. The reason for this is that with every demonstrative, before the conclusion, it must be known in advance what the name of both the subject and the effect is.
Propter quod ante illationem conclusionis aequaliter erit nota passio de subiecto et definitio exprimens quid nominis illius passionis, et ita minor erit aeque ignota et aeque nota cum conclusione.	Because of this, before the inference of the conclusion, the passion of the subject and the definition expressing the name of that passion will be equally known, and so the lesser will be equally unknown and equally known with the conclusion.
Propter quod in tali illatione erit petitio principii et non demonstratio.	Because of this, in such an inference there will be a petition to a principle and not a demonstration.
Est igitur sciendum quod aliqua propositio in qua praedicatur passio ƿde suo subiecto primo est demonstrabilis et aliqua non. Ad cuius evidentiam est notandum quod aliqua passio importat in recto praecise illud idem quod importat subiectum et aliquam formam realiter inhaerentem sibi in obliquo; aliqua autem passio praecise importat in recto illud quod importatur per subiectum et in obliquo aliquam rem non inhaerentem nec essentialem sibi; aliqua autem passio importat in recto illud quod importat subiectum et in obliquo importat partes illius rei et aliquam rem sibi non inhaerentem; aliqua autem passio importat in recto illud quod importat subiectum et negative vel in obliquo importat partes subiecti.	It must be known, therefore, that some propositions in which an effect is predicated of its first subject are demonstrable and some are not. For the evidence of which it must be noted that a certain effect conveys in a direct way precisely the same thing that the subject conveys and some form really inherent in it in the oblique; Now some effect precisely conveys directly what is implied by the subject, and in the oblique some thing neither inherent nor essential to it; But some effect directly conveys that which the subject conveys, and indirectly conveys the parts of that thing and some thing not inherent in it. and some effect directly conveys that which the subject conveys, and negatively or obliquely conveys the parts of the subject.
Exemplum primi: ‘colorabile’ respectu subiecti sui primi. Nam ‘colorabile’ nihil importat nisi illud quod importatur per subiectum et colorem in obliquo; quod patet per definitionem exprimentem quid nominis ipsius, quae est ‘aliquid potens habere colorem’. Exemplum secundi: ‘creativum’. Nam ‘creativum’ nihil importat nisi Deum in recto et creaturam in obliquo; quod patet ex definitione exprimente quid nominis ipsius, quae est ista ‘aliquid potens creare aliquid’. Exemplum tertii: ‘habens tres angulos aequales duobus rectis’. Nam ista passio in recto significat triangulum et in obliquo partes eius et alios angulos qui non sunt partes eius. Exemplum quarti: ‘corruptibile’ respectu substantiae. Nam ‘corruptibile’ in recto et affirmative significat illam substantiam quae est corruptibilis, negative autem et in obliquo partes eius; quod patet ex definitione exprimente quid nominis eius, quae est ‘aliquid cuius partes possunt non esse’ vel ‘cuius una pars potest ab alia separari’.	An example of the first: 'colorable' with respect to its first subject. For 'colorable' implies nothing but that which is implicitly implied by subject and color; which is clear from the definition that expresses the meaning of the name itself, which is 'something capable of having color'. Example of the second: 'creative'. For 'creative' implies nothing but God in the straight and the creature in the oblique; which is clear from the definition expressing what the name itself is, which is that 'something capable of creating something'. A third example: 'having three angles equal to two straight lines'. For this effect on the straight side signifies the triangle, and on the oblique side its parts, and other angles which are not parts of it. Example of the fourth: 'corruptible' with respect to substance. For 'corruptible' directly and affirmatively signifies that substance which is corruptible, but negatively and obliquely its parts; which is clear from the definition expressing the meaning of its name, which is 'something whose parts may not exist' or 'one part of which can be separated from another'.
De prima passione dico universaliter quod nulla talis passio potest demonstrari de subiecto suo primo, quia talis passio, si primo ignoretur de ƿ suo subiecto primo, non potest sciri de eo nisi per experientiam tantum.	Of the first effect, I say universally that no such effect can be shown about its first subject, because such an effect, if it is first unknown about its first subject, cannot be known about it except by experience alone.
Patet inductive. Idem dico de passione secunda, propter eandem rationem.	It is clear inductively. I say the same about the second effect, for the same reason.
Sed passio tertio modo dicta et quarto potest demonstrari de subiecto suo primo, quia potest ignorari de suo subiecto, quamvis sciatur quid significatur per subiectum et quid etiam significatur per passionem.	But the effect, said in the third way, and the fourth, can be shown from its first subject, because it can be ignorant of its subject, although it is known what is signified by the subject and what is also signified by the effect.
Postea autem cognito quae et qualis naturae sunt suae partes, sine ulteriori experientia de passione potest eadem passio sciri de subiecto, et hoc per definitionem exprimentem illas partes quae in obliquo vel negative importantur per passionem.	But after knowing what and what kind of parts are of its nature, without further experience of the effect, the same effect can be known of the subject, and this by definition expressing those parts which are indirectly or negatively carried by the effect.
Et tales sunt demonstrationes mathematicae, propter quod in eis parva vel nulla requiritur experientia, et demonstratur in eis semper vel frequenter per definitionem subiecti tamquam per medium.	And such are mathematical demonstrations, because in them little or no experience is required, and in them it is always or frequently demonstrated by the definition of the subject as if by means.
Et quia in paucis scientiis habemus demonstrationem proprie a priori nisi in mathematicis in quibus communiter passio demonstratur de subiecto suo primo per definitionem subiecti tamquam per medium, ideo frequenter dicit Aristoteles indistincte quod passio est demonstrabilis de subiecto et quod definitio est medium; non quod omnis passio sit demonstrabilis de subiecto suo primo, sed quia omnis passio est demonstrabilis de aliquo subiecto, et in mathematicis semper vel frequenter passio est demonstrabilis de subiecto suo primo.	And since in few sciences we have demonstration properly a priori, except in mathematics, in which a result is commonly demonstrated from its subject first through the definition of the subject as through a medium, therefore Aristotle frequently says indistinctly that a result is demonstrable from a subject and that a definition is a medium; not that every result is demonstrable from its first subject, but because every result is demonstrable from some subject, and in mathematics always or frequently result is demonstrable from its first subject.
Nec intendit Aristoteles quod in omni demonstratione medium sit definitio, sed intendit quod in omni demonstratione in qua demonstratur passio de subiecto suo primo medium est definitio, in aliis non oportet.	Nor does Aristotle intend that in every demonstration there is a definition, but he intends that in every demonstration in which the effect of its subject is first demonstrated the definition is the middle, but in others it is not necessary.