Benacerraf’s Problem and the Accessibility of Frege’s ‘Third Realm’

This paper extends Benacerraf’s problem – concerning the tension between Platonism of mathematical objects and epistemological access of mathematic truth – to Frege’s ‘third realm’ of thoughts, identifying key flaws in Frege’s theory: the language-independence, epistemological inaccessibility, and structural incoherence of thoughts. It proposes a revised account that construes thoughts as linguistically mediated, intersubjective entities, which resolves Frege’s predicaments while retaining his core anti-psychologism and addressing the accessibility challenge posed by Benacerraf’s problem.