Authors/Ockham/Summa Logicae/Book II/Chapter 5

Latin	English
[2.05 DE PROPOSITIONIBUS UNIVERSALIBUS IN QUIBUS SIGNUM DISTRIBUIT PRO DUOBUS TANTUM]	[Chapter 5. On universal propositions in which the sign distributes for two things only]
De signis distributivis non pro quibuscumque sed pro duobus tantum, cuiusmodi sunt 'uterque' et 'neuter', sciendum est quod ad veritatem talis requiritur quod praedicatum vere competat utrique illorum demonstratorum, si sit affirmativa, vel negetur ab utroque, si sit negativa. Sicut ad veritatem istius 'uterque istorum currit' sufficit quod iste currat et ille currat, et ad veritatem istius 'neuter istorum currit' requiritur quod nec iste nec ille currat.	On signs which distribute not for any number of things but for two things only, such as 'both' and 'neither', it should be known that for the truth of such a proposition it is required that the predicate truly belong to each of the things demonstrated, if the proposition is affirmative, or that it is denied of each, if the proposition is negative. For example, for the truth of 'both of them are running' it is sufficient that this one is running and that one is running, and for the truth of 'neither of them is running' it is required that neither this one is running nor that one is running.
Et est sciendum quod in hoc differt universalis in qua ponitur hoc signum 'uterque' ab universali in qua ponitur hoc signum 'omnis' quod numquam potest talis universalis esse vera in qua praedicatur praedicatum universaliter sumptum, sive praedicatum sumatur cum hoc signo 'omnis' sive cum hoc signo 'uterque' Unde ista nullo modo potest esse vera 'uterque istorum est omnis homo' vel 'uterque istorum est uterque istorum', quibuscumque demonstratis. Haec tamen potest esse vera 'omnis homo est omnis homo' et similiter ista 'omne album est omne album' et 'omne animal est omne animal', quia si esset tantum unus homo vel tantum unum animal vel tantum unum album, esset vera.	And it should be known that a universal proposition in which 'both' occurs differs from a universal proposition in which 'every' occurs, in that a proposition in which 'both' occurs can never be true when the predicate is taken universally, whether the predicate is taken with the sign 'every' or with the sign 'both'. Hence the propositions "both of them are every man" and "both of them are both of them" can in no way be true, no matter which things are demonstrated. Yet "every man is every man" and similarly "every white thing is every white thing", and "every animal is every animal" can be true. For if there were only one man or only one animal or only one white thing, then the proposition in question would be true.
Et causa istius diversitatis est quia hoc signum 'omnis' potest convenienter addi termino habenti unum suppositum, sed 'uterque' semper requirit duo supposita, scilicet duo demonstrata. Et ita si praedicatum non haberet nisi unum suppositum in ista 'uterque istorum est omnis homo', manifeste esset propositio falsa; quia in subiecto oportet quod duo demonstrentur: et non duo homines, igitur vel unus homo et unus non-homo, vel duo non-homines; et quodcumque detur, est propositio manifeste falsa. Et ita patet de omnibus aliis.	And the reason for this diversity is that the sign 'every' can properly be added to a term which has one suppositum, while 'both' always requires two supposita, namely, the two things demonstrated. And so if the predicate in "Both of them are every man" had only one suppositum, the proposition would manifestly be false, for in the subject two things have to be referred to, and not two men, therefore one man and one non-man, or two non-men. And whichever is given, the proposition is manifestly false. And so it is clear for all the other cases.