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...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.展开更多
基金supported by National Social Science Foundation of China,“A Truth-theoretical Study on Limits of Artificial Intelligence”(No.24AZX018)Major Interdisciplinary Cultivation Project of Philosophy and Social Sciences at South China Normal University,“Research on Frontier Issues in Epistemic Logic in Analytic Philosophy.”。
文摘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.
