建构第一人称信念逻辑的一致性难题(英文)

The Difficulties of Constructing a Consistent First-person Doxastic Logic

研究信念逻辑的有趣之处在于:可以在没有清楚的存在与等同条件下,建立一套元目的形式理论。现有的合理且可能为真的形式系统皆因为著名的"知识拥有者的悖论(Knower's Paradox)"而导致不一致。这篇论文将建构一套第一人称信念的形式系统。用来建构系统的信念将来自内在观点,因此信念的拥有者将不在讨论的范围中。此外,本篇论文将论证信念的背景将扮演语意、知识论及语用的角色。本篇论文建构的系统将是标准初阶逻辑的有限延展,并将使用到引述。本系统所使用的公理及规则相对较弱,且因为太弱而不足够,因此导致了系统的不一致。本论文欲藉此论证:可被定义的信念集合将不可能被找到。在现有的信念理论及所有的第一人称信念理论中,有限且可被定义的信念集合皆为不一致的原因在于并未涵盖我们真实拥有的信念。

The study of doxastic theories is interesting because thereby a formal theory of enities without clear existence and identity conditions can be established. Plausible formal systems which have been proposed, however, turn out to be inconsistent due to a variant of the famous Knower＇s Paradox. In this paper, a formal system for modeling first-person belief is constructed. Belief from an inner perspective is taken, so no belief agent is considered, and it is argued that belief backgrounds are to be added that play semantic, epistemic and pragmatic r61es. The constructed system is a conservative extension of standard first-order logic, which uses quotation. Its axioms and rules are comparatively weak, indeed too weak to be adequate, yet it is shown that they result again in an inconsistency. Hence that no definable set of beliefs is found. Exploring remedies to lift the inconsistency reveals that in the present doxastic theory, and possibly in any other first-person doxastic theory, each set of beliefs that is finite and definable is incomplete in the sense that it does not cover beliefs we actually have.