SOPhiA 2021
Salzburgiense Concilium Omnibus Philosophis Analyticis
Programme - Talk
The preface paradox and higher-order belief
(Epistemology, )
he preface paradox illustrates that the normative Lockean thesis, the conjunction principle, and the consistency principle can_t be consistent with each other. Can we solve the preface paradox without denying any of the three assumptions? In this paper, I show that we can, and suggest that this line of solution requires a new view about the nature of belief. I argue that the crux of the preface paradox is the assumption that all our beliefs belong to a single type. Because of this assumption, inconsistent beliefs are always considered as irrationality. Instead of thinking all beliefs of a person as the members of a huge, single set, we could perhaps allow that there is a stratified hierarchy of belief-types. On this view, beliefs belong to different types or levels rather than a set. If one_s overall doxastic state is understood as a stratified hierarchy of belief-types, then one can be justified in holding first-order belief 'p' and higher-order belief 'not-p' at the same time without inconsistency. If belief is so understood, we may be able to overcome the problem of the preface once and for all.
In a type-theoretic framework, there are at least two types of beliefs. Following the convention of type theory, we may say that first-order beliefs belong to type-0 level, and second-order beliefs belong to type-1 level. In the preface case, one has a first-order belief that (iii) each claim is true, and has a second-order belief that (iv) some claim is false. According to the normative Lockean thesis, one is justified in holding both types of beliefs. Apply the conjunction principle as usual. Now one is justified in holding both one's first-order belief (iii) and second-order belief (iv) at the same time. But there is no inconsistency at all. For we don_t presuppose that one's beliefs (iii) and (iv) form a single inconsistent set. Instead, we understand her overall doxastic state as a stratified hierarchy belief-types. One can rationally believe that (iii) in type-0 level, and that (iv) in type-1 level. If the type-theoretic conception of belief is plausible, one can rationally doubt everything one believes. It sounds paradoxical in a set-theoretic conception of belief, but it makes good sense in the type-theoretic one. If we allow that there are two types of beliefs in one's overall doxastic state, then we won_t run into the preface paradox.
Chair: Kimon Sourlas-Kotzamanis
Time: 10:40-11:10, 10 September 2021 (Friday)
Location: HS E.002
Remark: (Online Talk)
Pak-Him Lai
(Texas AM University, )
