“形式逻辑”，可能99％的人都理解错了，以为是演绎的必然性推理

“雅典学园”微信学习群已经度过了3年多的时光，现在调整原来按照时间顺序的学习进路，插入逻辑的学习。微信公号“哲学门”同步“雅典学园”群的学习内容，精选紧扣学习内容的文章发布。

老蝉按：雅典学园逻辑专题的学习，以赫尔利的逻辑学名著《简明逻辑学导论》为教材。这本书已经在网上买不到了。但赫尔利在这本书的基础上续写的书《逻辑学基础》还可以买到，链接见下。

《逻辑学基础》第三章

【美】Patrick J. Hurley

形式逻辑

选自《西方哲学英汉对照辞典》

有效推理模式（形式）和在命题之间成立的某些蕴涵关系的系统展示，这些模式和关系严格依赖于像“所有”、“有些”、“如果”、“并非”并且”、“或”等结构词的意义。

形式逻辑分为：

1、标准(经典)逻辑、

2、非标准逻辑和

3、归纳逻辑

标准逻辑包括：

传统逻辑(亚里士多德三段论)和

现代经典逻辑，

后者是传统逻辑的扩展，主要由命题演算和谓词演算组成。

非标准逻辑包括：

经典逻辑的扩充系统(有时称“扩充逻辑”)和变异系统(有时称“变异逻辑”)

扩充逻辑包括模态逻辑，时态逻辑，道义逻辑，认知逻辑，优先逻辑，命令逻辑等。

变异逻辑包括多值逻辑、直觉主义逻辑、量子逻辑等。

我们通过弄清楚某些逻辑系统能够相互映人，而能对其形式获得额外的洞见。形式逻辑系统能够以从公理出发进行证明的形式展开，也能够通过自然演绎加以展开，后者给出了从给定假设出发进行推理的规则。形式逻辑与非形式逻辑形成对照,后者处理从语境相关的词语中产生的蕴涵关系。

逻辑系统力求获得相容性和完全性，尽管哥德尔证明，对任何能够表达算术的逻辑系统来说，都存在着不能在该系统内证明的真语句，这使得该系统是不完全的。他还证明，这些系统不能证明它们自身的相容性。这两个结果显示了任何形式系统程序的局限性。

“形式逻辑的题材将是研究那些普遍的逻辑规律，它们是依据结构词语的意义和自然语言的句法而成立的。”---米切尔:《逻辑导论》1964 年，第 121 页。

Formal logic

The systematic presentation of the valid patterns( forms ) of inference and certain implications which holdmong propositions, relying heavily on the meaning of struc-tural words such as“all"，“some”，“if"，"not”“and”and"or". It is divided into standard (or classical) logic,nonstandard logic and inductive logic. Standard logic includestraditional logic (Aristotelian syllogism) and modern classicallogic . which is an expansion of traditional logic and is composed mainly of the propositional calculus and predicate calculus.Non-standard logics include the extensions of classicallogic， sometimes called extended logic , and deviations fromclassica] logic ,sometimes called deviant logic. Extended logic includes logics such as modal logic, tensed logic , deontitlogic,epistemic logic, preference logic and imperative logiceviant logic includes logics such as many valued logic,intuitionist logic and quantum logic. We can gain additional insight into the form of some systems of logic by seeing thatthey can be mapped onto one another. Systems of formal logic can be developed by proof from axioms or through natura!deduction，which gives rules of inference from given assumptions, Formal logic contrasts with informal logic, whichdeals with the relations of implication arising from contextrelated words.

L.ogical systems seek to attain consistency and completeness， although Godel showed that for any consistent logicalsystem capable of expressing arithmnetic there are irue sentences which cannot be proved in the system ,thus renderinpthe sysiem incomplete. He also showed that such systemscannot prove their own consistency. Both results show thelimitations of the procedures of any formal system.

“The subject-matter of formal logi will be the investigation of those general logical laws which hold in virtue ofthe meanings of the structural words and the syntax of natural languages,”--Mitchell，An Inlroduction to Logic，1964 p.121.

“形式逻辑”，可能99％的人都理解错了，以为是演绎的必然性推理 | 雅典学园逻辑专题（5）