33 : On the Disjunctive Proposition
33: On the Disjunctive Proposition A disjunctive proposition is one composed of two or more categoricals joined by the conjunction 'or' or by some equivalent. For example, this is a disjunctive proposition: 'You are a man or a donkey'. Likewise, this is a disjunctive proposition:
"You are a man or Socrates is debating'.
Now for the truth of a disjunctive proposition it is required that some part be true. And this should be understood to apply when the propositions are present-tense and not future-tense or equivalent to future-tense propositions. This is what the Philosopher would say.' However, the fact of the matter is that for the truth of a disjunctive proposition it is required that one of the parts be true. For, in fact, a future-tense proposition is either true or false, though not in a deterministic way.
But in order for a disjunctive proposition to be necessary it is not required that one of its parts be necessary. For example, in order for 'Socrates is sitting or not sitting' to be necessary, it is not required that either part be necessary. Rather, for a disjunctive proposition to be necessary it is required either that one part be necessary or that the parts contradict each other—or that they be equivalent to contradictories or that they be interchangeable with contradictories. Hence, this is necessary: 'Socrates is running or God exists'. For the second part is necessary. On the other hand, 'God creates or does not create' is necessary because the parts contradict each other.
Now for a disjunctive proposition to be possible it is sufficient that one of its parts be possible. But for a disjunctive proposition to be impossible it is required that both parts be impossible.
It should also be noted that the contradictory opposite of a disjunctive proposition is a conjunctive proposition composed of the contradictories of the parts of that disjunctive proposition.
Thus, the same thing that is necessary and sufficient for the truth of the opposite of a disjunctive proposition is necessary and sufficient for the truth of a conjunctive proposition.
It should also be noted that it is valid to argue from one part