Universa Philosophia

An exponible proposition is one which needs exposition; this can happen in many ways, for in many ways someone can speak obscurely. By the Summulists it is taken for an obscure enunciation on account of some adverb, by reason of which it needs resolution (as they say) into clearer propositions equivalent to it, and which have the same sense: that obscure proposition is called exponible, because it is one that needs exposition. But those through which it is expounded are called exponents, because through them the obscure one is clarified. Toletus treats of exponibles, book 3; Fonseca likewise book 3; but Soto diffusely in his little work on exponibles.

The species of these is the exclusive proposition, which is affected by some sign signifying exclusion, e.g. tantum, solum, dumtaxat, etc. Of these, some are affected by a sign on the part of the predicate, which are called of the extreme or excluded predicate. Namely when some co-predicate is excluded from the predicate of the proposition, e.g. Petrus est Summulista tantum, that is, he is ignorant of the other faculties besides the Summulistic. Of these there are two genera: one excluding number, e.g. Apostoli sunt duodecim tantum, that is, they are in the number twelve, and not in a greater. Which exclusion is called according to plurality. The other genus excludes some thing, as Petrus est tantum musicus. Which is called exclusion according to thing. There is a great difference when the exclusion is placed on the part of the predicate, and when it is placed on the part of the subject. e.g. Apostoli sunt tantum duodecim is a true proposition, but this is false, tantum Apostoli sunt duodecim; for it renders this sense, in solo Collegio Apostolorum est numerus duodenarius, which is false, because also the Senate of Pamplona is in the same number. In these exclusives there is little difficulty.

The second genus of exclusives is that by which the exclusion prefixed to the proposition affects the whole of it, which is called exclusion simply, as tantum homo currit. These are four. The first is entirely affirmative, by which both the sign of exclusion and the copula of the verb are affirmed, as tantum homo currit. The second, opposed to the first, is that by which the sign is denied, with one negation prefixed, as non tantum homo currit. The third, by which the copula is denied and the sign affirmed, as tantum homo non currit. The fourth, opposed to this, is with both denied, as non tantum homo non currit. The Summulists resolve these propositions thus: the first through a hypothetical copulative proposition, whose first part is a particular affirmative concerning the same subject, with the sign also removed; the second is a universal negative with the opposite of the subject, e.g. this, tantum homo currit, is expounded thus: aliquis homo currit, et nihil praeter illum currit. The second they resolve through a hypothetical disjunctive, e.g. this, non tantum homo currit, is resolved thus: nullus homo currit, vel aliquod non homo currit. The third they resolve through a hypothetical copulative, as the first, e.g. this, tantum homo non currit, is resolved thus: homo non currit, et omne aliud currit. The fourth they resolve through a hypothetical disjunctive in this way: non tantum homo non currit, that is, omnis homo currit, vel aliquod non homo currit. Thus commonly the Summulists.

Among these propositions they assign every kind of opposition. To these attend: that by the vowel i is signified a particular affirmative enunciation, by the vowel a a universal affirmative, by o a particular negative, by e a universal negative: from which are formed four words, iste, regit, proram, clavo. In the word iste is placed the first proposition, tantum homo currit; in regit is placed the second, non tantum homo currit; in proram is placed the third, tantum homo non currit; in clavo is placed the fourth, non tantum homo currit. In this quadrangle you will discern the opposition.

Iste and Proram are called universals, perhaps because their exponents are hypothetical copulatives, which require for their truth a collection of the object, just as a universal proposition does. For this copulative, Petrus currit, et Ioannes non loquitur, requires for its truth that Peter run and that John not speak; if either fails, the proposition is not true. Clavo and Regit are called particulars, perhaps because their exponents are disjunctives; but where there is a disjunction, there is a particular proposition requiring one part of the object for its truth, as for the truth of this, Petrus currit, vel Ioannes loquitur, it suffices if Peter runs while John is silent.