5: On Universal Propositionsin which the Sign Distributes over Two Things Only
Propositions in which the Sign Distributes over Two Things the plural, it can have either a collective or a distributive sense. If it is taken distributively, then it is asserted that the predicate truly belongs to all those things of which the subject is truly predicated.
For example, by means of 'All the apostles of God are twelve' it is asserted that the predicate 'twelve' is truly said of each thing of which the subject 'apostles' is truly predicated. And so, since
Peter and Paul are apostles, it follows that Peter and Paul are twelve. But if 'all' is understood collectively, then it is not asserted that the predicate agrees with each thing of which the subject is truly predicated. Rather, it is asserted that the predicate belongs to all the things—taken at once—of which the subject is truly predicated. Hence, it is asserted that these apostles, referring to all the apostles, are twelve.
5: On Universal Propositions in which the Sign Distributes over Two Things Only Concerning signs which distribute not over any number of things but over two things only, e.g. 'both' and 'neither', it should be noted that for the truth of such a proposition it is required that the predicate truly belong to each of the things referred to— if the proposition is affirmative—or that it be 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 this one is not running and that one is not running.
And it should be noted that a universal proposition in which 'both' occurs differs from a universal proposition in which 'every' occurs in the following way: 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' or4vith the sign 'both'.