Authors/Ockham/Summa Logicae/Book III-2/Chapter 17

Latin	English
[CAP. 17. DE DUPLICI DEMONSTRATIONE: A PRIORI ET A POSTERIORI]	[On two types of demonstration: a priori and a posteriori]
Postquam tractatum est breviter de terminis et propositionibus ad demonstrationem pertinentibus, restat dicere de demonstratione.	After we have dealt briefly with terms and propositions pertaining to demonstration, it remains to talk about demonstration.
Est autem primo sciendum quod cum dictum sit in principio quod demonstratio est syllogismus faciens scire, accipiendo `scire' pro notitia evidenti et certa, ubi necessarium sequitur ex propositionibus necessariis, ƿ et talis syllogismus sit multiplex, necesse est quod multiplex sit demonstratio.	And you should know first that when it was said at the beginning that ‘demonstration is a syllogism bringing about science’, in taking ‘to have science’ for evident and certain knowledge, where the necessary follows from necessary propositions, and such a syllogism has manifold types, it is necessary that demonstration has manifold types.
Propter quod oportet scire quod quaedam est demonstratio cuius praemissae sunt simpliciter priores conclusione, et illa vocatur demonstratio a priori sive propter quid.	On account of this we must scientifically know that one sort of demonstration whose premisses are absolutely prior to the conclusion, and this is called demonstration a priori or propter quid.
Quaedam est demonstratio cuius praemissae non sunt simpliciter priores conclusione, sunt tamen notiores sic syllogizanti, per quas devenit sic syllogizans in notitiam conclusionis, et talis demonstratio vocatur demonstratio quia sive a posteriori.	Another sort is demonstration whose premisses are not absolutely prior to the conclusion, and which are nevertheless better known to the one syllogising in this way, through which the syllogiser thus arrives to knowledge of the conclusino. And such demonstration is called demonstration quia or a posteriori.
Verbi gratia si aliquis nesciens lunam nunc eclipsari, sciens tamen cursus et motus planetarum, consideret istas praemissas `quando luna est in tali situ etc., tunc luna eclipsatur; luna est nunc in tali situ', et ex istis propositionibus deveniat in notitiam istius conclusionis `luna nunc eclipsatur', talis habet demonstrationem a priori et propter quid, quia praemissae exprimunt causam propter quam sic est a parte rei sicut significatur esse per conclusionem.	For example. If someone, not knowing that the moon is now eclipsed, but knowing the course and movement of the planets, considers the premisses ‘when the moon is in such a place etc., then the moon is eclipsed, [and] the moon is now in such a place’, and from these propositions arrives at the knowledge of the conclusion ‘the moon is now eclipsed’, such a person has demonstration a priori and propter quid, because the premisses expound the cause why it is in reality just as it is signified by the conclusion.
Si autem alius, e converso, videns lunam eclipsari et nesciens terram interponi, sic arguat `quando luna eclipsatur terra interponitur inter lunam et solem; luna nunc eclipsatur; ergo nunc terra interponitur', talis facit demonstrationem a posteriori; et scit quod terra interponitur, tamen nescit quare interponitur, et ita scit quia ita est, sed nescit propter quid ita est; quia tamen per propositiones sibi notas adquirit cognitionem sibi ignoti necessarii, ideo habet demonstrationem.	But if, on the other hand, another [person], seeing the moon is eclipsed and not knowing the earth is interposed, argues as follows: ‘when the moon is eclipsed, the earth is interposed between the moon and the sun, [and] the moon is now eclipsed, therefore the earth is now interposed’, such a person performs a demonstration a posteriori; and he has scientific knowledge that the earth is interposed, but does not know why it is interposed, and so he knows that [quia] it is, but does not know on account of what [propter quid] it is so. For nevertheless through propositions known in themselves he acquires cognition for himself of unknown necessary [truth], and therefore he has demonstration.
Est tamen advertendum quod praedicti syllogismi tantum adducti sunt gratia exempli, non quod ita sit, sed ut sentiant qui addiscunt. Ex praedictis sequitur quod possibile est duos formare eundem syllogismum et tamen unus demonstrabit et alius non demonstrabit; sicut unus ex praemissis adquirit notitiam conclusionis et alius ex eisdem praemissis non adquirit notitiam conclusionis; propter quod idem sylloƿgismus est uni demonstratio et alteri non est demonstratio, sicut praemissae in uno faciunt notitiam conclusionis et non in alio.	It should nevertheless be noted that the previously mentioned syllogisms are only cited for sake of example, not because it is so, but so that those who learn may perceive [sentiant]. From what was mentioned it follows that is possible for two to form the same syllogism and yet one will demonstrate, and the other will not demonstrate, just as one acquires knowledge of the conclusion from the premisses, and the other does not acquire knowledge of the conclusion from the same premisses. On account of this the same syllogism is a demonstration to one, and is not a demonstration to the other, according as the premisses create knowledge of the conclusion in one, and not in the other.
Et ideo `scire' non ponitur in definitione demonstrationis tantum sicut importans causam finalem demonstrationis, sed in definitione demonstrationis ponitur tamquam pars definitionis, exprimens illud quod significatur per demonstrationem in obliquo.	And therefore ‘to have scientific knowledge’ is not given in the definition of demonstration merely as meaning the final cause of demonstration, but it is given in the definition of demonstration, as if part of the definition, expounding what is signified through demonstration obliquely.
Unde hoc nomen `demonstratio' significat non tantum syllogismum talem, sed etiam significat in obliquo ipsam scientiam conclusionis natam causari a notitia principiorum. Et quia ita est, ista definitio `syllogismus faciens scire' potest esse medium notificandi ceteras definitiones de demonstratione, quae quidem definitiones significant aliquid quod nec in recto nec in obliquo significat hoc nomen `demonstratio'.	Therefore the name ‘demonstration’ signifies not only such a syllogism, but also it signifies obliquely that scientific knowledge of the conclusion suited to be caused by the knowledge of the principles. And because it is to, the definition ‘syllogism causing scientific knowing’ can be a medium of knowing the rest of the definitions of demonstrations. These definitions signify something that neither directly nor obliquely is signified by the name ‘demonstration’.
Sicut si haec oratio `potens scindere dura' sit definitio exprimens quid nominis serrae, ista oratio potest esse medium notificandi quod serra debet esse acuta et ferrea, et sic de aliis. Et sic loquuntur multi quando dicunt quod definitio sumpta a causa finali est medium demonstrandi definitionem sumptam a causa materiali sive a partibus de definito.	Just as the expression ‘able to cut hard things’ is a definition expressing the nominal definition of a saw, that expression can be the medium of giving knowledge that a saw ought to be sharp and made of iron, and so on. And so speak many when they say that a definition taken from the final cause is a medium of demonstrating a definition taken from a material cause, or from the parts of the thing defined.
Et hoc non est verum, nisi quando definitio sumpta a causa finali est definitio exprimens quid nominis. Tunc tamen talis processus non erit proprie demonstratio, sed erit notificatio quaedam.	And this is not true, except when a definition taken from the final cause is a definition expounding that nominal essence of the name. Then, nevertheless, such a procedure will not be properly demonstration, but will be a sort of knowledge-giving.