From Static Systems to Unending Flow: Overcoming Gödel’s Incompleteness through Alexandre de Castro Prado’s Unending-Logical Actualism

This paper proposes a critical reassessment of Kurt Gödel’s Incompleteness Theorems (1931) through the lens of Unending-Logical Actualism, a philosophical system developed by Alexandre de Castro Prado. While Gödelian logic demonstrates the existence of unprovable statements within finite formal systems, establishing an insurmountable limit for pure reason, Prado’s thesis contends that such incompleteness stems from a static and atemporal conception of logic. By introducing dynamic variables—such as the update operator (⊕), the free-will vector (α), and the notion of the Productive Unknown (?) —it is demonstrated that what Gödel classifies as unprovable actually constitutes a processing latency within an open system. The article stratifies truth into three levels (Evident, Probable, and Possible) and presents the logical formalization that incompleteness is destroyed by the being's power of updating. It concludes that the universe is not a flawed or lacunar system, but an "Unending" structure, where knowledge is a continuous process of converting potency into act. Reality is rescued as an uninterrupted flow where Gödel’s uncertainty is transmuted into the hope of perpetual discovery, founding a new logic that integrates ethics, science, and presence.