As computational systems burgeon with advancing artificial intelligence (AI), the deterministic frameworks underlying them face novel challenges, especially when interfacing with self-modifying code. The Executioner Paradox, introduced herein, exemplifies such a challenge where a deterministic Executioner Machine (EM) grapples with self-aware and self-modifying code. This unveils a self-referential dilemma, highlighting a gap in current deterministic computational frameworks when faced with self-evolving code. In this article, the Executioner Paradox is proposed, highlighting the nuanced interactions between deterministic decision-making and self-aware code, and (...) the ensuing challenges. This article advocates for a re-evaluation of existing deterministic frameworks, emphasizing the need for adaptive decision-making mechanisms in computational systems. By dissecting the Executioner Paradox, the aim is to foster a robust discussion on evolving deterministic frameworks to accommodate the dynamic nature of self-modifying code, thereby contributing a forward-looking lens to the discourse on computational systems amidst advancing AI. (shrink)