Authors/Ockham/Summa Logicae/Book III-2/Chapter 13

Latin	English
CAP. 13. DE PROPRIETATIBUS PRINCIPIORUM INGREDIENTIUM DEMONSTRATIONEM.	Chapter 13. On properties of principles involved in a demonstration
Post praedicta videndum est de proprietatibus principiorum ingredientium demonstrationem, quae non possunt esse conclusiones. Talia ƿ enim principia oportet esse prima, sic scilicet quod per priora demonstrari non possunt.	After what has been said, we must see a demonstration of the properties of the first ingredients, which cannot be conclusions. For such principles must be first, so of course that they cannot be demonstrated by prior ones.
Unde non ideo dicuntur principia esse prima quia nulla sit propositio quocumque modo prior eis. Hoc enim non est verum. Nam, secundum Aristotelem, aliqua est propositio negativa prima, et tamen omni negativa est aliqua affirmativa prior. Per quam tamen affirmativam demonstrari non potest, cum non sit processus in infinitum in demonstrationibus, et propositio negativa sine praemissa negativa demonstrari non potest. Ista enim propositio affirmativa ‘omne calidum est calefactivum’ sive ‘omne habens calorem est calefactivum’ habet aliquam propositionem priorem ea, istam scilicet ‘omnis calor est calefactivus’; quia tamen ista demonstrari non potest, ideo prima dici potest.	Hence it is not for this reason that principles are said to be first, because there is no proposition in any way prior to them. For this is not true. For, according to Aristotle, there is some first negative proposition, and yet to every negative there is some affirmative prior. By which, however, the affirmative cannot be demonstrated, since there is no process ad infinitum in demonstrations, and a negative proposition cannot be demonstrated without a negative premise. For this affirmative proposition 'everything hot is heating' or 'everything having heat is heating' has some previous proposition, that is, 'every heat is heating'; but because the latter cannot be demonstrated, it can therefore be said to be the first.
Item, omni propositione de terminis specialibus priores sunt communes animi conceptiones de terminis communibus; sicut omni tali propositione ‘omne calidum est calefactivum’ prior est ista ‘quidlibet est vel non est’, et tamen per istam propositionem demonstrari non potest.	Likewise, every proposition about special terms is preceded by common conceptions of the mind about common terms; just as every such proposition 'everything hot is heating' is prior to that 'anything is or is not', and yet it cannot be demonstrated by this proposition.
Est igitur aliqua propositio prima, quia est indemonstrabilis, et tamen aliquo modo alia prior illa. Oportet autem scire quod quamvis principia demonstrationis sint prima, sic quod non sunt demonstrabilia, tamen aliqua propositio non necessaria, quae non est principium alicuius demonstrationis, potest esse prima.	There is, therefore, some first proposition, because it is indemonstrable, and yet in some way another is prior to it. Now it is necessary to know that although the principles of demonstration are first, so that they are not demonstrable, yet some proposition which is not necessary, which is not the principle of any demonstration, may be first.
Unde sicut ordo est inter propositiones necessarias, quod aliqua est prima et aliqua est posterior, ita ordo est inter propositiones contingentes, quod aliqua est prima et aliqua est posterior.	Hence, just as there is an order among necessary propositions, that some are first and some are posterior, so there is an order among contingent propositions, that some are first and some are posterior.
Sicut ista ‘Sortes ƿ est’ prior est ista ‘Sortes est homo’, quia sequitur, tamquam a priori, ‘Sortes est; Sortes non est non-homo; igitur Sortes est homo’.	Just as this `Socrates is' is prior to that `Socrates is man', because it follows, as if from the prior, 'Socrates is; Socrates is not a non-man; Therefore Socrates is a man.
Et ita est de aliis.	And so it is with others.