Universa Philosophia

Although these things are to be understood thus, nevertheless on account of the diverse quantities of propositions they are said to be opposed in diverse ways, on account of which they are repugnant in quality in diverse ways. Yet I judge that every opposition of this kind is in reality contradictory, and that it is on that account that they are repugnant; so that contraries are at once true, subcontraries at once false, but contradictories neither at once true nor at once false.

Accordingly I say that every opposition of propositions in quality is most formally on account of two singular propositions mutually contradicting, which would be contained in the opposed propositions. For example, the opposition of contraries in truth is on account of two contradictory singular propositions which would follow from the truth of each contrary; the same holds for the falsity of subcontraries; but because neither in the truth of subcontraries nor in the falsity of contraries are two contradicting singulars contained, therefore contraries can be false and subcontraries true. Therefore the adequate and sole reason for the opposition of propositions is contradictory opposition, which is clear in contraries.

For two contrary propositions can be false, because under them are contained many singular propositions, two of which can be false, whose falsity makes the universal proposition false, e.g. omnis homo currit contains under itself these two, Petrus currit, Antonius currit, of which, when Peter is running, if Antonius non currit, this is false, Antonius currit, and consequently this omnis homo currit. But this universal proposition, nullus homo currit, contains under itself these, Petrus non currit, Antonius non currit, of which the first is false, because Petrus currit, and consequently nullus homo currit is false. Hence it is clear that universal propositions are not opposed in falsity, because either can be false, because their falsity is taken from objects which do not have contradictory opposition among themselves, because Petrum currere, et Antonium non currere have no opposition, for both can be at once; but they are opposed in truth, because the truth of each would depend on contradictorily opposed objects. For if omnis homo currit is true, therefore Petrus currit. Likewise if nullus homo currit is true, therefore Petrus non currit will also be true, because, the universal being true, all its singulars are true. Behold where two contradictory predicates are affirmed of Peter, namely currere, et non currere. And the same will happen to each individual, therefore the opposition of contraries is insofar as they are affirmation and negation of the same concerning the same singular object, which can be explained by two perfectly contradictory singular propositions, as Petrus currit, Petrus non currit. Therefore the adequate reason for the opposition of contraries is contradiction, which would be contained in the truth of each. But because in a universal proposition many things are predicated of many, which can be found in one and not in another without any contradiction on the part of the object, therefore they are not called contradictories, although their falsity depends on a contradiction of the object.

The same is clear in subcontraries, which can be at once true, for they are propositions enjoying disjunctive descent, because they are confused and indeterminate, for whose truth it suffices that what is pronounced by them be found in one single individual, e.g. aliquis homo currit is a true proposition when Peter alone is running, although the others are not running; for its falsity it is required that no one at all be running. Likewise this proposition, aliquis homo non currit, is true when Antony is not running, although Petrus currat; but for it to be false it is required that all men be running. Behold why they can be true, because their truth is established in individuals altogether really distinct, of which, when the one is running, the other can be not running, and accordingly two contradictory predicates are not affirmed of any individual.

=== LATIN Ut autem sint falsae, opus est, ut de uno individuo affirmentur duo praedicata contradictoria, nempe de eodem Petro currere, et non currere: nam falsitas huius propositionis, aliquis homo currit, requirit, ut nullus homo currat, et consequenter, ut Petrus non currat. nam si Petrus curreret, esset vera. Item falsitas huius propositionis aliquis homo non currit, requirit, ut omnis homo currat, et consequenter, ut Petrus currat. ergo iam requiritur ad falsitatem utriusque, ut Petrus currat, et non currat, idemque contingit ceteris individuis. ergo oppositio harum propositionum sumitur ex oppositione contradictoria duarum propositionum singularium mutuo contradicentium, quae necessario continerentur in utriusque falsitate: sicut oppositio contrariarum oritur ex duabus singularibus contradictoriis, quae continerentur in veritate utriusque contrariae. Qua vero parte non opponuntur, est, quia in illa carentia oppositionis non continentur duae propositiones singulares mutuo contradicentes. Subcontrariae autem non vocantur contradictoriae, quia versantur circa varia individua, quibus convenire possunt dissimilia praedicata, ob quae hae possunt esse simul verae. === ENGLISH But for them to be false, it is necessary that two contradictory predicates be affirmed of one individual, namely de eodem Petro currere, et non currere: for the falsity of this proposition, aliquis homo currit, requires that no man be running, and consequently that Petrus non currat. For if Peter were running, it would be true. Likewise the falsity of this proposition aliquis homo non currit requires that every man be running, and consequently that Petrus currat. Therefore now for the falsity of each it is required that Petrus currat, et non currat, and the same happens with the other individuals. Therefore the opposition of these propositions is taken from the contradictory opposition of two singular propositions mutually contradicting, which would necessarily be contained in the falsity of each; just as the opposition of contraries arises from two contradictory singulars which would be contained in the truth of each contrary. But in the respect in which they are not opposed, it is because in that absence of opposition two singular propositions mutually contradicting are not contained. But subcontraries are not called contradictories because they are concerned with various individuals, to which dissimilar predicates can belong, on account of which these can be at once true.

=== LATIN Idemque patet in oppositione contradictoria duarum propositionum, quarum altera sit universalis, altera confusa. Nam si universalis esset vera, et particularis falsa, sequeretur de eodem individuo simul proferri duas propositiones singulares mutuo contradicentes, nam si, omnis homo currit, est vera, et aliquis non currit, est vera: ergo de eodem Petro vere affirmari poterit, Petrus currit, Petrus non currit, quia ab universali vera descenditur ad singularem veram, Petrus currit: demus autem ad veritatem particularis negativae illud individuum non currens esse Petrum, in quo vera est illa propositio (idem namque est in quovis alio, quia universalis propositio omnia complectitur) iam Petrus curret, et non curret simul, similiter si utraque sit falsa. demus enim universalem falsam, quia Petrus non currit, si particularis est falsa, sequitur Petrum currere, quia omnis homo necessario currit, ad huius falsitatem aliquis homo non currit, ut dixi, §.27. et 28. ergo Petrus simul curreret, et non curreret. omnis ergo oppositio propositionum re ipsa est contradictoria: explicatur autem triplici illa distinctione, ut ostendantur diversae rationes, quibus haec oppositio cernitur in propositionibus diversarum quantitatum. === ENGLISH The same is clear in the contradictory opposition of two propositions, of which one is universal and the other confused. For if the universal were true and the particular false, it would follow that two singular propositions mutually contradicting are asserted at once of the same individual; for if omnis homo currit is true and aliquis non currit is true: therefore of the same Peter it could be truly affirmed Petrus currit, Petrus non currit, because from a true universal one descends to a true singular, Petrus currit; but let us grant for the truth of the particular negative that the individual not running is Peter, in whom that proposition is true (for it is the same in any other, because the universal proposition embraces all), now Petrus curret, et non curret simul, similarly if both are false. For let us grant the universal false because Petrus non currit; if the particular is false, it follows that Peter runs, because every man necessarily runs, for the falsity of this aliquis homo non currit, as I said, §27 and 28. Therefore Petrus simul curreret, et non curreret. Therefore every opposition of propositions is in reality contradictory; but it is explained by that threefold distinction, so that the diverse reasons may be shown by which this opposition is discerned in propositions of diverse quantities.

=== LATIN Unde liquido constat cur contrariae non possint simul esse verae, et possint esse simul falsae, subcontrariae autem possint esse simul verae, non tamen simul falsae; contradictoriae autem nec simul verae, nec simul falsae, sed altera vera, altera falsa, quia idem affirmari, et negari simul de eodem vere, repugnat, quia sicut Petrus non potest simul currere, et non currere, quia opponuntur immediate, ita non potest utrumque vere aut affirmari, aut negari. Haec autem est ratio a priori, et unicum fundamentum, cui innititur tota doctrina de oppositione propositionis. === ENGLISH Hence it is plainly evident why contraries cannot be at once true and can be at once false, while subcontraries can be at once true, yet not at once false; but contradictories neither at once true nor at once false, but the one true and the other false, because it is repugnant that the same be at once truly affirmed and denied of the same, because just as Peter cannot at once currere, et non currere, because they are immediately opposed, so neither can both be truly either affirmed or denied. But this is the a priori reason and the sole foundation on which the whole doctrine of the opposition of propositions rests.

=== ENGLISH Hence all the adjuncts must be weighed by which the same is affirmed and denied: namely all the terms of opposed propositions must in both supposit in the same way for the same thing, in the same place, time and other circumstances, otherwise there will be no opposition; for example, these are not opposed, Mater diligit filium, Mater non diligit filium, if in the first it supposits for the son John and in the second for Peter. Likewise neither are these, ego fui in templo, ego non fui in templo, if it is understood either of different temples or of different times. Likewise these are not opposed, ego occidi Petrum, ego non occidi Petrum, if in the first it is understood that Peter was killed at Rome and not killed at Madrid; similarly if in one it is understood that he was killed with a knife and in the other with a sword. Likewise these are not opposed, omne animal fuit in arca Noë, aliquod animal non fuit in arca Noë, because in the first proposition the word animal supposits for some vague individual of the species, which is called pro generibus singulorum, that is, for some individual of each species, as for some horse, and lion, etc.; and in the second it supposits discretely for determinate individuals, which is called pro singulis generum, that is, for each man, each lion, etc., that is, every species of animal was in Noah's ark, and Peter was not in Noah's ark, in which no opposition is discerned, because although Peter was not there, Noah was, and in him the species of man.

=== ENGLISH Likewise note that for true opposition according to quality it is necessary that the negation deny the copula of the proposition, as these: Petrus currit, Petrus non currit, where the word non denies the word currit; otherwise there is no opposition, as in this, Petrus currit, non Petrus currit: these propositions are not opposed, because each is affirmative, for the sense of the second is aliquid, quod non est Petrus, currit; just as these, in secana sunt pisces, in secana sunt non pisces, where each is affirmative, because in the net there are fish, and there are stones which are not fish; but for them to be contradictory let them be put thus, in secana sunt pisces, in secana non sunt pisces.

=== ENGLISH Moreover note that there are falsifying propositions, which destroy themselves; for example, someone says, ego sum mutus, qui non loquor, ego iuro me numquam iurare, ego semper mentior; behold these are falsifying. The first, because he says he does not speak, when nevertheless he speaks; the second, because he says he does not swear, and nevertheless he swears. The third, because he says he always lies, when nevertheless by that proposition he destroys what he says, because if he always lies, therefore he also lies then; but if he lies then, therefore he says the truth, because he says what is; but if he does not lie then, therefore he does not always lie. Likewise these are falsifying: Deus dabit mihi librum, Deus non dabit mihi librum, given this case, that someone says to Peter, Deus tibi dabit librum, si prima propositio, quam dixeris, fuerit vera, and then Peter says, Deus mihi non dabit librum, this proposition is falsifying, because it is impossible for the promise to be fulfilled, because if God gives the book, that first proposition was not true; but if God does not give the book, that proposition was true, and it cannot be fulfilled, nor can it be promised thus by God. Therefore if you pay attention to falsifying propositions, and likewise to the circumstances of the subject, predicate and negation, you will never be caught, but you will easily fall into the hands of the enemy if you gape. But what is said, nulla est melior contradictio, quam toti propositioni negationem praeponere: understand it if the negation is not infinitizing; but if it is infinitized, it is not a contradiction.

But in exclusive propositions this rule is false, as will be clear in section 13, where the opposition of exclusives will be treated.