Universa Philosophia

Hence it is clear that purpurea and illiace are opposed contrarily, because it cannot be denied that they are opposed in affirmation, and otherwise they are universals, therefore they are contraries; the major is proved, because this first proposition of purpurea, Petrum non currere non est possibile, has this sense, Petrus non potest existere, quin currat. Likewise this first proposition of illiace, Petrum currere non est possibile, yields this sense, Petrus, quamvis existat, non potest currere; but that Peter cannot exist without running, and that Peter cannot exist except by running, are openly opposed, because Peter existing and necessarily running cannot lack running; therefore those propositions are opposed.

It is confirmed: it is repugnant that both be true, therefore they are opposed. I proved the consequence above, showing that every repugnance of propositions in truth or falsity is by reason of two singulars reciprocally contradicting one another. The antecedent is clear, because if it is true that Peter can exist at some time without running, then it will not be true that Peter existing necessarily runs; for if he necessarily runs, he cannot exist except running; but if he cannot exist except running, then he cannot exist without running. Therefore if the first proposition in purpurea, affirming that Peter cannot exist without running, is true, the first in illiace is necessarily false, because it affirms that Peter existing cannot run; for if he necessarily runs, how is it impossible that he run? As if God necessarily is God, how can he not be God? Therefore those propositions are opposed in truth.

At length they can be false at the same time, which is the property of contraries, for this Petrum non currere non est possibile is openly false, because Peter can exist without running. Likewise this Petrum currere non est possibile is equally false, because Peter existing can run, since both running and its absence are accidents separable from Peter. And so because in the falsity of both there are not contained two singular propositions mutually contradicting, therefore they can be false; but because in the truth of both they are contained, therefore they cannot be true at the same time, which is the property of contrary propositions, as I said concerning absolute ones.

Purpurea and amabimus are subalterns, because amabimus is particular, while purpurea is universal, under which mode amabimus is contained; for this first proposition of amabimus, Petrum currere est possibile, is contained under this first of purpurea, Petrum non currere non est possibile, for it is necessary that Peter run; but if Peter necessarily runs, then currere potest, which is the first proposition of amabimus; that it is contained under purpurea is clear: because the consequence from purpurea to amabimus is valid affirmatively, yet it is not valid from amabimus to purpurea. For everything that necessarily runs (which purpurea affirms) can run (which amabimus affirms), but not everything that can run necessarily runs, as is clear. In this respect these modes preserve the proportion of these absolute propositions, omnis homo currit, aliquis homo currit; and so to be able to run is verified in one time taken vaguely, as aliquis homo currit in some individual; but to run necessarily must be verified at every time distributively, as omnis homo currit in all individuals. But truth depending on every time contains in itself the truth depending on one, indeed it depends on it as the truth of this, omnis homo currit, depends on the truth of this, aliquis homo currit. But the truth of this, Petrus potest currere, does not depend on the truth of this, Petrus necessario currit, just as neither does the truth of this, aliquis homo currit, depend on the truth of this, omnis homo currit.

The same judgment is to be made concerning edentuli, which mode is subalternated to illiace, because this first proposition of illiace, Petrum currere non est possibile, contains this first of edentuli, and depends on it, Petrum non currere est possibile; for if it is not possible that he run, then it is possible that he not run; as if it is not possible that I be a stone, then it is possible that I not be a stone. Weigh these propositions, which when mutually compared preserve the same proportion as purpurea and amabimus among themselves.

Hence I further deduce that amabimus and edentuli are subcontrary propositions, because they are subalterns to two contraries. Likewise because they are particulars, or confused, and can be true at the same time, yet not false at the same time. For this first of amabimus, Petrum currere est possibile, is indeed true; similarly also this first of edentuli, Petrum non currere est possibile, because in their truth there are not contained two singulars mutually contradicting, since, as running is an accident separable from Peter, he can have it and not have it. That they cannot be false is proved, because if this of amabimus, Petrum currere est possibile, were false, then it would be possible that Peter not run, as is clear from the terms; therefore this proposition of edentuli, Petrum non currere est possibile, could not be false, because Peter could truly not run. But if it could be false, there would be contained in the falsity of both two contradictory singulars, because Petrum currere est possibile requires for its falsity that running be impossible, and this, Petrum non currere est possibile, requires for its falsity that Peter's running be necessary, and that Peter always run; but that Peter cannot run and that he necessarily runs are contradictories, because he would run and not run at the same time. Therefore amabimus and edentuli cannot be false at the same time, and can be true at the same time, which is proper to subcontraries.

At length I deduce that purpurea and edentuli are contradictorily opposed, similarly illiace and amabimus; for one contrary is contradictorily opposed to the subaltern of the other contrary, as omnis homo currit is contradictorily opposed to this aliquis homo non currit, because it is contained under this, nullus homo currit. The reason a priori: because purpurea is a universal negative proposition concerning the mode, while edentuli is a particular affirmative concerning the same mode, therefore they are contradictories. The consequence is clear from the definition of contradictories (the same holds for illiace and amabimus); for purpurea denies the dictum in three propositions, and affirms it in the fourth, and denies the mode in two, and affirms it in the third and fourth. But edentuli in three denies also the dictum, and affirms the mode in two, and denies it in the last two, e.g. Petrum non currere non est possibile is the first of purpurea, to which is contradicted this, Petrum non currere est possibile, which is the first of edentuli; but possibile and non possibile mutually contradict one another, which is clearer in illiace, Petrum currere non est possibile, to which amabimus, Petrum currere est possibile, contradicts; can and cannot are contradictorily opposed, nor can they be true at the same time, or false at the same time, because two contradictories would be found on the side of the thing. But they can be opposed contradictorily, as singulars, if we restrict the terms, as Petrum non currere hic et nunc (ut aiunt) non est possibile, Petrum non currere hic, et nunc est possibile, because one difference of time is signified in the particular.

You ask whether contradiction is found in modals other than in the contradiction of the mode? I answer negatively, because in whatever other way propositions are related, they can either be false at the same time, as contraries, or true at the same time, as subalterns. The reason a priori: because contradiction is in the affirmation and negation of the copula, which in modals is the mode itself; but in this modal proposition: Petrum currere est verum, Petrum non currere est verum, contradiction is found, because the mode itself is denied at least remotely; for to say that it is true that Peter does not run virtually says that it is not true that Peter runs, because in these the mode essentially depends on the dictum; for from the fact that the thing is or is not, the proposition is called true or false. Hence from the affirmation and negation of the dictum follows the affirmation and negation of the mode, and of the truth in the proposition, which is not the case with the other modes.

The dicta can be singular, or universal, or confused, as Petrum currere est possibile, Omnem hominem currere, Aliquem hominem currere. And there can be descent in the dictum, with the same mode retained in singulars, e.g. in amabimus, Omnem hominem currere est possibile has this descent: therefore Petrum currere est possibile, Paulum, etc.; to which is contradicted this in illiace, Hominem currere non est possibile, ergo nec Petrum, etc.; to which is also contradicted this in illiace, Aliquem hominem currere non est possibile. For although the dictum is changed in illiace, nevertheless because this proposition in amabimus, Omnem hominem currere est possibile, includes this, Aliquem hominem currere est possibile, therefore this of illiace, Aliquem hominem currere non est possibile, contradicts this of amabimus, Omnem hominem currere est possibile, because from the truth or falsity of either, there would be given in one individual two contradictory predicates. For it would be possible and not possible for one man to run.

Modals are converted on the part of the dictum, but not on the part of the mode, e.g. Petrum currere est possibile is converted thus: aliquod currens esse Petrum est possibile; but the dicta are converted while observing the rules of conversion of an absolute proposition. Modals are called exclusive which are made through an adverbial mode, as Petrus contingenter disputat; for although the words are different, because disputation is affirmed of Peter, and not the mode, nevertheless in reality both the mode and the disputation are affirmed, as in composite ones, because Petrum currere, est necesse affirms both the running and its necessity; just as this Petrus contingenter disputat asserts both contingency and disputation, yet they are affirmed improperly through the adverb, as this Petrus impossibiliter disputat. Soto treats of these in lecture 2, and Toletus, book 3, chapter 6; nor is there need for their opposition and quantity except to consider how the adverb is equivalent to a verb. Impossibiliter, et necessario are universal modes; possibiliter, et contingenter are particular. And let their equipollence be considered; which, along with other things, because they are more troublesome than useful, I omit. Aristotle forms the proposition in another way, for he calls the first de necesse, the second de possibili, the third de contingenti, the fourth de impossibili; Fonseca imitated him, but the matter is the same; usage, however, stands with Peter of Spain.