31: On the Conditional Proposition
31: On the Conditional Proposition _ Next we will look at these propositions specifically. However, since a conditional proposition is equivalent to a consequence— so that a conditional proposition is true when the antecedent entails the consequent and not otherwise—this discussion will be deferred until the tract on consequences.'
Nevertheless, it should be noted that a hypothetical proposition is called conditional when it is composed of two categoricals joined by the conjunction 'if? or some equivalent. For this reason it should be said that this is a conditional proposition: 'Socrates does not teach unless he is an instructor'. For it is equivalent to: 'If Socrates is not an instructor, Socrates does not teach'.
And it is always the case that when two propositions are joined by some conjunction and the whole is equivalent to a conditional proposition, then the proposition in question will be called hypothetical and conditional.
It should also be noted that neither the truth of the antecedent nor the truth of the consequent is required for the truth of a conditional proposition. In fact, sometimes a conditional proposition is necessary even though each of its parts is impossible, as in 'If Socrates is a donkey, Socrates is able to bray'.
32: On the Conjunctive Proposition A conjunctive proposition is one which is composed of two or more categoricals joined by the conjunction 'and' or by some particle equivalent to such a conjunction. For example, this'is a conjunctive proposition: 'Socrates is running and Plato is debating'.
Similarly, this proposition is conjunctive: 'Socrates is neither white On the Conjunctive Proposition nor black'; and so is this: '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'.
Now for the truth of a conjunctive proposition it is required that both parts be true. Therefore, if any part of a conjunctive proposition is false, then the conjunctive proposition itself is false. Similarly, in order for a conjunctive proposition to be necessary it is required that each of its parts be necessary. And for it to be possible it is required that both parts be possible.
However, in order for it to be impossible it is not required that both parts be impossible. For this is impossible: 'Socrates is sitting and not sitting'. And yet each part is possible. Rather, for a conjunctive 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, since 'Socrates is a donkey' is impossible.
And 'Socrates is sitting and not sitting' is impossible, since the two parts are not compossible.
It should also be-noted that the contradictory opposite of a conjunctive proposition is a disjunctive proposition composed of the contradictories of the parts of the conjunctive. Thus, the same thing that is necessary and sufficient for the truth of the opposite of a conjunctive proposition is necessary and sufficient for the truth of a disjunctive proposition. Hence, the following are not contradictories: 'Socrates is white and Plato is black' and 'Socrates is not white and Plato is not black'. Rather, the contradictory of the first conjunctive is this: 'Socrates is not white or Plato is not black'.
Now it is necessary to note that there is always a valid consequence from a conjunctive proposition to either of its parts.
For example, this follows: 'Socrates is not running and Plato is debating, therefore Plato is debating'. But the converse commits a fallacy of consequent. Still, it should be noted that sometimes, in virtue of the material element, there can be a valid consequence from one part of a conjunctive proposition to that conjunctive.
For example, if one part of a conjunctive proposition entails the ather part, then there is a valid consequence from that part to the whole conjunctive proposition.