The Liar Paradox: A Structural Dissolution Through Recursion, Interruption, and Completion

The Liar Paradox arises from a sentence that says of itself: “This sentence is false.” If true, it is false; if false, it is true. Standard solutions tend to modify logic, restrict self‑reference, or introduce new truth values. This paper suggests that the paradox may be better understood as a structural artifact of how we process recursive patterns. It proposes that the paradox emerges from three operations: recursion (the ongoing pattern generated by self‑reference), interruption (the truncation of that pattern at a chosen step), and completion (the inductive inference that the truncated part represents the whole). These operations appear in both the Liar and its stable counterpart, “This sentence is true.” The difference is not in the structure, but in the outcome of the induction. This points to a possible candidate for logic’s unexamined foundation: induction itself. The paradox may not be a problem to be solved—it may be a diagnostic of the frame that logic assumes.