<p>This paper focuses on Per Martin-Löf’s and Göran Sundholm’s constructive analysis of meaning, knowledge, understanding, and proof. It points out a recent development of this analysis, which integrates dialogical explanations in order to solve longstanding problems. However, certain blind spots remain, and this paper argues that to fully ground the constructive analysis, the dialogical approach should be pursued even further, adopting a radically dialogical stance in which the dialogical aspects cannot be left aside. The paper presents Kuno Lorenz’s radically dialogical analysis of meaning, knowledge, understanding, and proof, which recognizes a double aspect, semiotic and pragmatic, constitutive of any activity, and grounded in a teaching–learning situation. Such a radically dialogical approach explains how capacities or dispositions are acquired, how meaning can be grasped before a proof is provided, and how proofs are constructed out of meaning.</p>