# 在形式邏輯中，具有矛盾結論的論證如何才能有效？

• 如果草是綠色，那就下雨了。
• 如果水是濕的，那就不是 下雨。
• 因此：下雨而不下雨。

## 最佳答案

An argument is valid if and only if the truth of its premises entails the truth of its conclusion and each step, sub-argument, or logical operation in the argument is valid. – Wikipedia

P → Q.
P.
∴ Q.

If it's raining, I eat the cat.
It's raining.
∴ I eat the cat.

1. 論證有效。
2.
3. 所有前提都是正確的。
4.   </醇>

1: By concrete argument I mean an argument with concrete premises, i.e. without variables. So some 'P' can only be part of a concrete argument if we know what is meant by 'P'. I will use abstract argument for an argument with variables.
2: The symbol ∴ means 'therefore' and is used to indicate the conclusion.
3: Whether or not the first premise is true is out of the scope of this answer.