Authors/Ockham/Summa Logicae/Book III-2/Chapter 4

Latin	English
CAP. 4. DE DIVISIONE PROPOSITIONUM REQUISITARUM AD DEMONSTRATIONEM.	Of the division of propositions required for demonstration.
Dicturus autem de propositionibus requisitis ad demonstrationem, primo praemittam aliquas divisiones earum. Est autem primo sciendum quod propositionum requisitarum ad demonstrationem quaedam sunt partes demonstrationis, sicut duae praemissae et una conclusio, et quaedam non sunt partes demonstrationis.	Now I will talk about propositions required for demonstration. First I will set out some of their divisions. And first you should know that of the propositions required for demonstration, some are parts of the demonstration (i.e. two premises and one conclusion) and some are not parts of the demonstration.
Et vocantur dignitates et maximae vel suppositiones, quae sub propria forma non ingrediuntur demonstraƿtionem, virtute tamen illarum propositionum aliquo modo sciuntur praemissae demonstrationis.	And those are called axioms [dignitates], and maxims [maximae] or suppositions [suppositiones]; which are not included in a demonstration under [their] proper form, and yet in virtue of these propositions the premises of a demonstration are known in some way.
Verbi gratia ista est una propositio prima, per experientiam praecise nota ‘omnis calor est calefactivus’, quae non potest esse pars demonstrationis, saltem potissimae et universalis, virtute tamen istius tenent tales demonstrationes ‘omne calidum est calefactivum; omnis ignis est calidus; igitur omnis ignis est calefactivus; ‘omne calidum est calefactivum; omnis aer est calidus; igitur omnis aer est calefactivus’.	For example: "every heat can heat" is a primary proposition, known precisely through experience, which cannot be part of a demonstration (at least of the highest sort and universal). Yet it is in virtue of this that demonstrations hold such as: "Every hot thing can heat, every fire is a hot thing; therefore every fire can heat"; "Every hot thing can heat, every [case] of air is a hot thing; therefore every [case] of air can heat."
Istae igitur sunt distinctae propositiones ‘omnis calor est calefactivus’ et ‘omne calidum est calefactivum’, et prima prior est et secunda posterior. Et tamen secunda non potest proprie demonstrari per primam et secunda intrat demonstrationem non prima, et tamen virtute primae tenent multae demonstrationes quas non potest ingredi.	Therefore, these are distinct propositions: "Every heat can heat," and "Every hot thing can heat," and the first [is] prior and the second posterior. And yet the second cannot properly be demonstrated through the first, and the second enters into demonstration, but not the first. And yet, in virtue of the first many demonstrations hold which it cannot be included into.
Et sicut est de ista, ita est de multis aliis. Propositio autem requisita ad demonstrationem, non tamquam pars, subdividitur, quia quaedam est talis quod necesse est quemlibet docendum habere eam, cuiusmodi sunt tales ‘quidlibet est vel non est’, ‘de quolibet affirmatio vel negatio’ et huiusmodi. Quaedam sunt tales quas non est necesse quemlibet docendum habere, sed necesse est aliquos artifices speciales eas habere, sicut est de istis ‘aliquid est mobile’, ‘si ab aequalibus aequalia demas’ etc.	And just as it is for this [case], so for many others. Now a proposition required for demonstration but not as a part of the demonstration is subdivided, for one sort is such that it is necessary that whoever is to be taught, holds it, and of this sort are "each thing is or is not," “of any [subject] the affirmation or negation [is truly predicated]” and the like. Some are such that it is not necessary for whoever is to be taught to hold them, but it is necessary for some specialist workers to have them. For instance, "something can move" and "if equals be taken from equals, the remainders’ etc.
Propositio autem quae est pars demonstrationis subdividitur, quia quaedam est praemissa tantum, quae scilicet est indemonstrabilis; quaedam est conclusio tantum, quae scilicet est demonstrabilis, sed non potest esse principium demonstrandi aliam propositionem; quaedam est praeƿmissa et conclusio, quia potest demonstrari per praemissas alias et potest esse principium demonstrandi aliam conclusionem.	But a proposition which is part of a demonstration is subdivided, for one sort is a premiss only, namely an indemonstrable proposition; and another is conclusion only, namely a demonstrable proposition which cannot be a principle of demonstrating another proposition. And another sort is both premiss and conclusion, because it can be demonstrated through other premises and also be a principle for demonstrating another conclusion.
Alia divisio potest poni, quia propositionum requisitarum ad demonstrationem quaedam sunt principia, quaedam conclusiones. Principia dicuntur illae propositiones quae non sunt conclusiones et tamen requiruntur ad demonstrationem, sive sint partes demonstrationis sive non sint partes eius.	Another division can be given, for of propositions required for demonstration some are principles and others conclusions. ‘Principles’ is the name of those propositions which are not conclusions and yet are required for demonstration (whether they are parts of the demonstration or not parts of it).
Et vocantur principia prima, quae subdividi possunt: quia quaedam principia prima sunt per se nota, quibus scilicet intellectus statim assentit ipsis terminis apprehensis, ita quod si sciatur quid significant termini, statim sciuntur.	And these are also called first principles. They can be [further] subdivided, for some first principles are known per se, namely, those to which the intellect immediately assents upon apprehending their terms, so that if it is known what the terms signify, they are immediately known.
Quaedam autem principia prima non sunt per se nota sed tantum per experientiam, quia possunt dubitari, sed tamen per experientiam fiunt nota, sicut est de ista propositione ‘omnis calor est calefactivus’, et de multis talibus, quae non possunt fieri notae nisi per experientiam, de quibus specialiter loquitur Aristoteles in I Metaphysicae et in II Posteriorum, in fine.	But some are first principles that are known not per se, but only through experience, for they can be doubted, but nonetheless come to be known through experience. So it is with "Every heat can heat," and many other such [propositions] that cannot be known except through experience, of which Aristotle specifically discusses in Metaphysics I and in Posterior Analytics II at the end.