Authors/Ockham/Summa Logicae/Book III-2/Chapter 5

Latin	English
CAP. 5. DE PROPRIETATIBUS PROPOSITIONUM AD DEMONSTRATIONEM REQUISITARUM; ET QUOMODO EST EX INCORRUPTIBILIBUS.	Chapter 5. On the properties of propositions required for demonstration, and how this is from indestructible things.
Istis praemissis videndum est de proprietatibus propositionum ad demonstrationem requisitarum.	After these preliminaries, we must look at the properties of propositions required for demonstration.
Illarum autem proprietatum quaedam sunt communes omnibus propositionibus requisitis ad demonstrationem, quaedam sunt propriae conclusionibus, quaedam sunt propriae praemissis, quaedam sunt propriae principiis non ingredientibus demonstrationem.	And of those properties, certain ones are common to all propositions required for demonstration, others are proper to conclusions, others are proper to premisses, and others are proper to principles not involved in demonstration.
Una proprietas communis omni propositioni requisitae ad deƿmonstrationem est necessitas.	One property common to every proposition required for demonstration is necessity.
Nulla enim propositio requisita ad demonstrationem est contingens vel impossibilis, sed quaelibet est necessaria. Quod enim conclusio sit necessaria, patet ex definitione demonstrationis, quia demonstratio est syllogismus faciens scire propositionem necessariam, igitur conclusio est necessaria. Sed necessarium, quamvis possit inferri ex contingentibus vel impossibilibus, non tamen potest sciri per contingentia vel impossibilia, igitur necessario praemissae, propter quas scitur conclusio, sunt necessariae.	For no proposition required for demonstration is contingent or impossible, but every one is necessary. For that the conclusion is necessary, is clear from the definition of demonstration, for demonstration is a syllogism producing knowledge of necessary propositions. Therefore the conclusion is necessary. But the necessary, although it could be inferred from contingent or impossible [propositions], still cannot be known from contingent or impossible [propositions], therefore necessarily the premisses, on account of which the conclusion is known, are necessary.
Sed propositiones rectificantes demonstrationem sunt priores et notiores praemissis, igitur illae sunt necessariae, et ita patet quod omnes propositiones requisitae ad demonstrationem sunt necessariae, et sicut sunt necessariae ita sunt perpetuae et incorruptibiles.	But propositions ensuring the correctness of demonstration are prior and better known than the premisses. Therefore they are necessary, and so it is clear that all propositions required for demonstration are necessary, and just as they are necessary, so they are perpetual and incorruptible.
Quod non est sic intelligendum quod propositiones illae sunt quaedam entia perpetua et incorruptibilia.	This should not be understood as [meaning] that these propositions are sorts of perpetual and incorruptible beings.
Hoc enim falsum est. Solus enim Deus est perpetuus et incorruptibilis, nec aliquid aliud a Deo potest esse simpliciter perpetuum et incorruptibile quin per aliquam potentiam posset fieri non-ens.	For this is false. For only God is perpetual and incorruptible. Nor can anything other than God be absolutely perpetual and incorruptible, but that it could by some power be made into a non-being.
Propter quod sciendum quod ‘necessarium’, ‘perpetuum’ et ‘incorruptibile’ dupliciter accipiuntur. Uno modo dicitur aliquid necessarium, perpetuum et incorruptibile quia per nullam potentiam potest incipere vel desinere esse; et sic solus Deus est perpetuus, necessarius et incorruptibilis.	On account of this it should be known that ‘necessary’, ‘perpetual’ and ‘incorruptible’ are taken in two senses. In one sense something is called ‘necessary’, ‘perpetual’ and ‘incorruptible’ because through no power can it begin or cease to be. And thus God alone is perpetual, necessary and incorruptible.
Aliter dicitur necessarium, perpetuum et incorruptibile propositio quae non potest esse falsa; quae scilicet est ita vera quod, si formetur, non est falsa sed vera tantum. Et isto modo demonstratio est necessariorum, perpetuorum et incorruptibilium, hoc est propositionum quae non possunt esse falsae sed tantum verae.	Otherwise a proposition is called necessary, perpetual and incorruptible when it cannot be false; namely true in the sense that if it is formed, it is not false but true only. And in this way demonstration is of necessary, perpetual and incorruptible propositions, i.e. of propositions which cannot be false, but only true.
Ex quo patet quod quamvis repugnet dictis Aristotelis, tamen secundum veritatem nulla propositio de illis quae important praecise res corruptibiles, mere affirmativa et mere categorica et mere de praesenti, potest esse principium ƿ vel conclusio demonstrationis, quia quaelibet talis est contingens.	From which it is clear that although it is repugnant to what Aristotle says, still in truth no proposition of those things that convey precisely corruptible things, purely affirmative and purely categorical and purely present [tense], can be the principle or conclusion of demonstration, because any such [proposition] is contingent.
Si enim aliqua talis esset necessaria, hoc maxime videretur de tali ‘homo est animal rationale’. Sed haec est contingens, quia sequitur ‘homo est animal rationale, igitur homo est animal’, et ultra ‘igitur homo componitur ex corpore et anima sensitiva’. Sed haec est contingens, quia si nullus homo esset, ipsa esset falsa propter falsam implicationem, quia implicaretur aliquid componi ex corpore et anima, quod tunc foret falsum.	For if any such were necessary, then especially would seem to be in the case such as ‘a man is a rational animal’. But this is contingent, because ‘a man is a rational animal, therefore [some] man is an animal’ follows, and furthermore ‘therefore [some] man is composed from a body and a sensitive soul’. But this is contingent, because if there were no man, that proposition would be false on account of a false implication, because it would be implied that something was composed from a body and soul, which would then be false.
Nec valet dicere quod ista aequivalet isti ‘si homo est, homo est animal rationale’, quia haec est condicionalis et non categorica. Et ita stat primum dictum, quod nulla talis mere categorica et mere de praesenti est necessaria.	Nor is it valid to say that this is equivalent to ‘if a man exists, a man is a rational animal’, for this is conditional and not categorical. And thus holds the first thing we said, that no such purely categorical, and purely present tense proposition is necessary.
Et ideo dico quod nulla talis potest esse principium vel conclusio demonstrationis. Hoc tamen non obstante dicendum est quod multae propositiones compositae ex talibus terminis possunt esse principia vel conclusiones demonstrationis, quia propositiones condicionales et de possibili et aequivalentes eis possunt esse necessariae. Haec enim simpliciter est necessaria ‘si homo est, animal est’; et ista ‘si homo ridet, animal ridet’; et ista ‘omnis homo potest ridere’, si subiectum stet pro his quae possunt esse.	And therefore I say that no such [proposition] can be a principle or conclusion of demonstration. Notwithstanding this, it must be said that many propositions composed from such terms can be principles or conclusions of demonstration, for conditional propositions and those involving the possible and their equivalents can be necessary. For this is necessary simpliciter: "If it is a man, it is an animal," and this, "If a man laughs, an animal laughs," as well as this, "Every man can laugh," if the subject stands for those that can be.
Et eodem modo propositiones aequivalentes eis sunt necessariae. Et ex isto patet quomodo, non obstante quod genera et species et quaecumque universalia distincta a cognitione Dei sunt simpliciter corruptibilia sic quod possunt esse nihil, tamen de eis possunt fieri demonstrationes et scientiae, propter hoc quod, non obstante quod possunt simpliciter destrui, tamen de eis possunt formari propositiones necessariae, quae possunt sciri scientia proprie dicta.	And in the same way propositions equivalent to these are necessary. And from this it is clear in what way, notwithstanding that genera and species and every universal distinct from the cognition of God are destructible simpliciter, so that they can be nothing, demonstrations and sciences can still be produced about them, because, even though they can be destroyed simpliciter, necessary propositions can still be formed about them, which can be known by knowledge properly so-called.
Ex isto etiam patet quomodo de contingentibus potest esse scientia; quia secundum quod veniunt in demonstrationem necessaria sunt, hoc est propositiones formatae de terminis importantibus talia contingentia quae veniunt in demonstrationem sunt necessariae, quae non sunt mere ƿ de praesenti et de inesse, categoricae et affirmativae, sed vel sunt negativae vel hypotheticae vel de possibili vel alio modo, vel aequivalentes eis.	From this it is clear in what way there can be knowledge about contingent things. For according as they enter into demonstration they are necessary, i.e. propositions formed from terms conveying such contingent things that enter into demonstration are necessary, which are not about the present and assertoric, and are categorical and affirmative alone, but are either negative or hypothetical or about the possible or some other mode, or equivalent to these.