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肯定前件.
在逻辑中,肯定前件(拉丁语:Modus ponens)是有效的、简单的论证形式(常缩写为MP):
- 如果P,则Q;且P為真,故Q為真。
肯定前件規則可以用相繼式符號寫為:
![{\displaystyle P\to Q,P\vdash Q}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2f6b1bf712367f9c2db9774415f397953dda2fc8)
或用規則形式寫為:
![{\displaystyle \qquad {\frac {P\rightarrow Q,P}{Q))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/66e890cefa64f04338f5bc975994632086c2083f)
在元逻辑中肯定前件是切规则。切消定理声称切是在某些逻辑演算(相继式演算)中有效的(可容纳规则)。
这个论证形式有两个前提。第一个前提是"if-then"或逻辑条件断言,表示为P蕴涵Q。第二个前提是这个条件断言的前件P是真的。从这两个前提可以在逻辑上得出后件Q一定也是真的。
下面是符合这种肯定前件的论证的例子:
- 如果今天是星期二的话,那小明就要去上班。
- 今天是星期二。
- 所以小明要去上班。
这个论证是有效的的事实不能确保在论证中的任何陈述是真的;肯定前件的有效性告诉我们结论必然是真的,如果所有前提是真的。记住在其中一个或多个前提不是真的的有效论证是不可靠的论证,而如果所有前提都是真的,则这个论证是可靠的。在多数逻辑系统中,肯定前件是有效的。但是它的应用实例可以是可靠的也可以是不可靠的。
- 如果一个论证是肯定前件的并且前提都是真的,则它是可靠的。
- 前提都是真的。
- 所以,它是可靠的论证。
使用肯定前件的命题论证被称为是演绎的。
肯定前件也叫做"分拆律"。
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