Formalizing God: The Silvestre Dilemma Between Agnostic Neutrality and Monotheistic Coherence

Ricardo Sousa Silvestre’s 2021 paper, "A Formal-Logical Approach to the Concept of God," proposes an ambitious formalization of the monotheistic concept of God uti- lizing the Simplest Quantified Modal Logic (SQML). The project aims to reconcile the singularity of the concept (SA) with the plurality of its descriptions (PG), while adhering to an "Extensional Agnostic Assumption" (AAE)—a methodological com- mitment to neutrality regarding the actual existence of God. This paper provides a critical proof-theoretical analysis of Silvestre’s system, demonstrating that its orig- inal formulation is technically incapable of sustaining this neutrality. We establish that Postulate C7 (∀x(♢I(x, g) → I(x, g))) functions as an axiomatic implementa- tion of the S5 Modal Ontological Argument, necessitating Theorem T2 (♢∃x → ∃x) and logically precluding the agnostic position. Furthermore, we identify a structural bind, termed the "Silvestre Dilemma": C7 is shown to be requisite for deriving Theo- rem T5 (Trans-World Monotheism), apparently forcing a choice between agnosticism and monotheism. However, departing from purely destructive critiques, we propose a constructive modification to the system. We introduce a weakened postulate of Trans- World Uniqueness (C7*) which effectively decouples uniqueness from existence. We demonstrate that this modification preserves the system’s monotheistic integrity (AM) while restoring its agnostic neutrality (AAE), thereby validating the feasibility of Sil- vestre’s broader project.