论形式系统的多样性

形式系统在类型上包括公理系统和自然推理系统,在构成要件上包括的形式语言和演绎装置.构造者的哲学背景、构造形式系统的理论对象和目的不同,所采用的形式语言和演绎装置就可能不同,因而,构造出来的形式系统就多种多样,在不同的系统内证明同一个定理也表现为不同的公式系列.形式系统的形式语言和演绎装置为我们界定了形式证明的工具、出发点和依据,同时语义也包含了构造者构造形式系统的理论对象和目的,离开具体的形式系统去谈论或者证明一个定理,将会导致逻辑的失范.

Discussion on the Diversity of the Formal System

The formal system on type includes the axiomatic system and the system of natural inferencea,nd on structure includes the formal language and the deductive device.As the builders of the formal system,different people have different philosophy background,theoretical object and purpose,and they might use different formal languages and deductive device,so we have various kinds of formal system,and in different system the arguments of the same theorem have different formula series.The formal language and the dudective device not only define for us the tool,the starting point and the basis of the formal argument,but also imply semantically the theoretical object and purpose of the builder,it will lead to illogic to put aside the specific formal syetem to talk about or argue a theorem.