建立在"笛卡尔公理"上的一个怀疑逻辑系统

怀疑逻辑是关于人们合理怀疑的逻辑。如果说知道逻辑、信念逻辑都是"正"的逻辑的话,那么怀疑逻辑则是"负"的逻辑。将怀疑算子D加于命题之上就构成怀疑命题。笛卡尔的"我思,故我在"可以作为怀疑逻辑的特征公理:某人怀疑p,蕴涵着他对怀疑p是不可怀疑的———我们可以将之命名为"笛卡尔公理"。从该公理可以推论得到定理:某人不怀疑p,蕴涵着他对不怀疑p是不可怀疑的。该定理与笛卡尔公理一起作为当下思维存在的自明性公理。我们可以建立一个以"笛卡尔公理"作为一个特征公理的怀疑逻辑系统(PD)。笛卡尔公理与知道逻辑中的智慧公理(苏格拉底公理)在逻辑上是同构的,它们均对应于模态逻辑中的E公理。怀疑逻辑作为一种认知逻辑,有广泛的用途,它可以运用到政策反驳、科学批判、法律推理等领域。

A Doubting Logic System Containing Descartes Axiom

Doubting logic is a logic that studies how people doubt something rationally. Logic such as knowledge logic, belief logic, and so on, can be regarded as a "positive" logic, and doubting logic as a "negative" one. Doubting logic is a kind of epistemic logic. By loading doubting operator D on a proposition, we obtain a doubting proposition. The famous Descartes' sentence "cogito ergo sum" can be employed as an axiom of doubting logic system, named "Descartes axiom". The axiom means that if someone doubts a proposition p, he shouldn't doubt the activity of his doubting p. A theorem can be derived from Descartes axiom that if someone doesn't doubt p, such a doubting activity cannot be doubted. The theorem and "Descartes axiom" show that existing of present thinking of a person is self-evident. Descartes axiom and wisdom axiom in knowledge logic are isomorphic, both of which are corresponding to axiom E in modal logic. A Doubting logic PD contained Descartes axiom has been established, which has been widely used.