假設我們假設“All S is P”是真的。
這是否允許我們得出“No Non-S is Non-P”的真值，其中non-X是X的互補類。
- If "All S is P" is true, it is also true that S refers to a collection of objects that is smaller than or equal to the collection of objects referred to by P.
- If S<=P, then No Non-P can be S.
- All Non-P must therefore be Non-S.
- By subalternation, since All Non-P is Non-S, there must be some Non-P that is Non-S.
- If there is some Non-P that is Non-S, then there is some Non-S that is Non-P.
- If there is some Non-S is Non-P, then the statement "No Non-S is Non-P" must necessarily be false, because it is contradictory with the former statement, which has been arrived at via valid inferences from true premises and must therefore be true.
然而，當我在維恩圖上繪制“All S is P”時，有一種情況是P指的是ALL對象的集合，這意味著Non-P不存在，因此所有Non-S必須是P這承認了一個罕見的情況，即該陳述成立，因此該陳述的真值不確定。