From Incompleteness to Practice: An Epistemological Reconstruction — An Isomorphic Analysis of Philosophy, Mathematics, and Physics Based on the Cognitive Model

This paper takes "information collapse" as its core operational concept to provide a unified epistemological explanation for both Russell's Paradox and Gödel's Incompleteness Theorems. The former originates in the operational idling caused by a secondary collapse after a cognitive product has been reified; the latter originates in the structural predicament wherein the subject cannot fully objectify its own ongoing operation. The "surplus" revealed by both is not a cognitive failure but the very impetus that allows cognition to continue occurring, and it illuminates the underlying structure in which cognition and Being share an "inexhaustible" foundation. Based on this, practice is established as the sole path for breaking through the boundaries of closed theories. This framework further dissolves traditional philosophical dualisms and provides a unified explanation for core mathematical structures and frontier dilemmas in physics. The paper concludes with reflexivity, acknowledging itself also as a cognitive model, aiming to invite the reader to illuminate the boundaries of the cognitive operation itself.