Temporal Perspective: Interpretation of Gödel's Incompleteness Theorems and the Connotation of Scientific Spirit

Gödel’s incompleteness theorems reveal the inherent limitations of closed formal systems by means of self-referential propositions. For a long time, they have mostly been interpreted within a static framework, often leading to cognitive dilemmas. This paper introduces the dimension of time sequence and reinterprets the theorems from the perspective of cognitive evolution: acknowledging a proposition as unprovable within the current system at a past stage itself endows the proposition with a truth value, thus completing its confirmation. Through natural transition in the temporal dimension, the logical tension in traditional interpretations is dissolved, enabling a more transparent understanding of the theorems. On this basis, this paper clarifies the internal consistency between Hilbert’s Program and Gödel’s incompleteness theorems. Combined with the century-long solutions to Hilbert’s 23 problems and their representative achievements, it extracts the underlying scientific spirit. While adhering to logical rigor, this paper accomplishes theoretical sublimation, providing a plain yet profound approach to interpreting classic results in mathematical logic.