Book 7
1.73
Opposite in character to the foregoing is a proposition which declares what is less the fact, as e.g. It is less or not so much night as day. Further, among propositions there are some which in respect of truth and falsehood stand opposed to one another, of which the one is the negative of the other, as e.g. the propositions It is day and It is not day. A hypothetical proposition is therefore true, if the contradictory of its conclusion is incompatible with its premiss, e.g. If it is day, it is light. This is true. For the statement It is not light, contradicting the conclusion, is incompatible with the premiss It is day. On the other hand, a hypothetical proposition is false, if the contradictory of its conclusion does not conflict with the premiss, e.g. If it is day, Dion is walking. For the statement Dion is not walking does not conflict with the premiss It is day.
