Recently, a paper co-authored by Professor HSIUNG Ming, Executive Director of our Center, and doctoral student YUAN Zhaolong, Kripke’s Intrinsic Truths in Boolean Systems (布尔系统中的克里普克内在真), was published in the 2025, Vol. 18, No. 6 issue of Studies in Logic (《逻辑学研究》, English Edition), a leading Chinese journal in the field. The journal is jointly sponsored by Sun Yat-sen University and The Chinese Society of Logic, and is indexed in CSSCI.

Founded in 2008, Studies in Logic is a bimonthly journal published in both Chinese and English. The main fields that it concentrates on include Symbolic Logic, Informal Logic, Logic and Philosophy, Logic and Cognition, Logic and Language, and Logic and Culture. The journal is administered by Sun Yat-sen University, jointly sponsored by Sun Yat-sen University and The Chinese Society of Logic, and hosted by the Institute of Logic and Cognition, Sun Yat-sen University (a Key Research Base of Humanities and Social Sciences under the Ministry of Education). It is a formally published specialist journal in China’s logic community.

=====Abstract=====

In Kripke’s theory of truth, the largest intrinsic fixed point—like the least fixed point—is of special theoretical interest among all fixed points. However, for intrinsic yet ungrounded sentences (i.e., those belonging to the largest intrinsic fixed points but not to the least fixed point), only sporadic examples have been provided so far, and a universal criterion for deciding such sentences remains unknown. This paper aims to establish a general criterion for determining intrinsic truth in Boolean systems of self-referential sentences under Kleene’s strong valuation scheme. To achieve this, we first present a known result about the definability of three-valued functions within Kleene’s strong logic. Then, by reducing the problem of determining the fixed points to a calculation problem in propositional logic, we demonstrate a truth-functional characteristic for the intrinsic truths in Boolean systems. We thus find an effective method for constructing intrinsic truths in a first-order language for Peano arithmetic. We also discuss the applicability of our findings to Kleene’s weak valuation scheme.

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Ming Hsiung, Zhaolong Yuan, Kripke's Intrinsic Truths in Boolean Systems, Studies in Logic, Vol. 18, No. 6 (2025): 19–42.

Report: YUAN Zhaolong

Initial Review: HU Yang

Secondary Review: WU Su

Final Review: HSIUNG Ming