Authors/Ockham/Summa Logicae/Book II/Chapter 32

Latin	English
[2.32 DE PROPOSITIONE COPULATIVA ET QUID REQUIRITUR AD VERITATEM EIUS]	32: On the Copulative Proposition and what is Required for its Truth
Copulativa est illa quae componitur ex pluribus categoricis coniunctis mediante hac coniunctione 'et' vel mediante aliqua parte aequivalente tali coniunctioni. Sicut ista est copulativa 'Sortes currit et Plato disputat'. Similiter ista est copulativa 'Sortes nec est albus nec niger'; similiter ista 'Sortes est tam albus quam calidus'; quia prima aequivalet isti 'Sortes non est albus et Sortes non est niger', et secunda isti 'Sortes est albus et Sortes est calidus'.	A copulative proposition is one which is composed of several categoricals conjoined by the intermediary conjunction 'and' or by some intermediary part equivalent to such a conjunction. For example, 'Socrates is running and Plato is disputing' is a copulative proposition. Likewise 'Socrates is neither white nor black' is copulative, likewise 'Socrates is both white and hot', for the first is equivalent to 'Socrates is not white and Socrates is not black', while the second is equivalent to 'Socrates is white and Socrates is hot'.
Ad veritatem autem copulativae requiritur quod utraque pars sit vera, et ideo si quaecumque pars copulativae sit falsa, ipsa copulativa est falsa. Et similiter ad necessitatem copulativae requiritur quod quaelibet pars sit necessaria. Et ad hoc quod sit possibilis requiritur quod utraque pars sit possibilis. Sed ad hoc quod sit impossibilis non requiritur quod utraque pars sit impossibilis, nam haec est impossibilis 'Sortes sedet et non sedet', et tamen utraque pars est possibilis; sed ad hoc quod copulativa sit impossibilis requiritur quod altera pars sit impossibilis vel quod una sit incompossibilis alteri, sicut haec est impossibilis 'Sortes est albus et Sortes est asinus', quia haec est impossibilis 'Sortes est asinus', et haec est impossibilis 'Sortes sedet et non sedet', quia duae partes sunt incompossibiles.	Now for the truth of a copulative it is required that both parts are true, and therefore if any part of a copulative proposition is false, that copulative proposition is false. And likewise, for the necessity of a copulative proposition it is required that each of its parts are necessary. And for it to be possible it is required that both parts are possible. But for it to be impossible it is not required that both parts be impossible, for 'Socrates is sitting and not sitting' is impossible, and yet each part is possible. Rather, for a copulative proposition to be impossible it is required either that one part be impossible or that one part be incompossible with the other. For example, 'Socrates is white and Socrates is a donkey' is impossible, because 'Socrates is a donkey' is impossible, and 'Socrates is sitting and not sitting' is impossible, because the two parts are incompossible.
Sciendum est etiam quod opposita contradictorie copulativae est una disiunctiva composita ex contradictoriis partium copulativae'. Et ideo idem requiritur et sufficit ad veritatem oppositae copulativae quod sufficit et requiritur ad veritatem disiunctivae. Unde istae non contradicunt 'Sortes est albus et Plato est niger', 'Sortes non est albus et Plato non est niger', sed illi copulativae contradicit ista 'Sortes non est albus vel Plato non est niger'.	It should also be known that the contradictory opposite of a copulative is a disjunctive proposition composed of the contradictories of the parts of the copulative. And so the same thing is required and is sufficient for the truth of the opposite of a copulative proposition as what is required and is sufficient for the truth of a disjunctive proposition. Hence 'Socrates is white and Plato is black' and 'Socrates is not white and Plato is not black' are not contradictories, but the contradictory of the first copulative is this: 'Socrates is not white or Plato is not black'.
Oportet autem scire quod semper a copulativa ad utramque partem est consequentia bona, sicut sequitur 'Sortes non currit et Plato disputat, ergo Plato disputat'; sed e converso est fallacia consequentis. Tamen sciendum est quod quandoque ab altera parte copulativae ad copulativam potest esse consequentia bona gratia materiae, puta si una pars copulativae inferat aliam, tunc ab illa parte ad totam copulativam est consequentia bona.	But you have to know that there is always a good consequence from a copulative proposition to either of its parts. For example, 'Socrates is not running and Plato is disputing, therefore Plato is disputing' follows, but the converse is the fallacy of consequent. Yet it should be known that sometimes from one part of a copulative proposition to that copulative there can be a good consequence in virtue of the material. For example, if one part of a copulative proposition entails the other part, then there is a valid consequence from that part to the whole copulative proposition.