从弗雷格理论看逻辑常项

Logical Constants from the Point of Fregean View

自塔尔斯基提出逻辑常项(逻辑概念)的变换不变性标准以来,人们相继提出了同构、同态与潜同构等不变性标准。这种考察方式从形式语义学的角度,给出代数刻画,虽然精确但都与人们既有的逻辑概念有明显差异。通过分析弗雷格的论述,可以合理地推断出逻辑常项的本质在于描述真,进而得到弗雷格标准。据此标准有两类逻辑常项,一类以真为描述对象,即真值函项。另一类是以谓述本身为描述对象,且能归约为基本逻辑关系。后者也即量词,刻画了“是真”。弗雷格标准深化了我们对逻辑以及逻辑与哲学关系的认识。运用此标准分析集合论的属于关系、模态、规范等概念会获得与流行看法很不相同的认识。

Since Tarski proposed to take keeping invariant under all transformation as the standard of logical notions,people have put forward successively alternatives such as keeping invariant under isomorphism,homomorphism and potential isomorphism.This way of investigation is to give algebraic characterization from the perspective of formal semantics,which is accurate but cannot fully reflect the logical conception having existed in our mind.By analyzing Frege’s argument,we can reasonably infer that the essence of logical constants is to describe Truth and then obtain Fregean standard.There are two types of logical constants in terms of Fregean standard.One is truth functions,which take Truth as the description object.The other is to take the predication as the description object,and can be reduced to the fundamental logical relation.The second is just the quantifiers,which characterize“Wahrsein”.Fregean’s standard deepens our understanding of logic and the relationship between logic and philosophy.we obtain a very different understanding of the membership,mode and norm from the popular view when applying the standard to analyze them.