Formal Logic for Existential Realism: Modeling Time, Causality and Observability

In both philosophy and science, standard logics struggle to model a key insight of Existential Realism (ER): that existence is a strictly present, empirical notion, whereas reality spans beyond the present. Classical first-order logic and even temporal modal logics tend to conflate being real with existing simpliciter, making it difficult to formally distinguish something that exists now from something that is real but not present. This paper introduces a formal two-tier logical framework tailored to ER’s ontology. We motivate this framework by showing how orthodox systems—from classical predicate logic to temporal modal logic—fail to capture ER’s core distinction between present existence and temporally extended reality. We then develop a layered logic with explicit operators or quantifiers for “existence-now” versus “reality-over-time,” including formal axioms that preserve ER’s asymmetries: only present entities exist (in the fullest sense), yet past and future entities can be real (ontologically significant) without existing. The logic adopts a modal-style treatment of time to model the collapse of potential into actual (present-becoming), and explicitly encodes causal asymmetry — where the past influences the present, but not the reverse. We illustrate the framework with symbolic representations, including an iconic “ER equation” capturing the relationship between reality and existence. To demonstrate its versatility, we apply the logic to examples from quantum physics (e.g. wavefunction collapse and delayed-choice experiments), cognitive neuroscience (memory traces and anticipatory processing), ethics (moral duties to future persons and the reality of future outcomes), and AI (agents modeling counterfactual or temporally extended scenarios). Finally, we show how the formalism sheds new light on classic metaphysical debates such as the truthmaker problem for past truths, persistence and identity over time, and the ontology of merely possible or future entities. Throughout, our presentation maintains a rigorous yet accessible tone, consistent with prior ER works, with technical clarity and footnoted references. The result is a self-contained preprint that extends T.C. Trepp’s Existential Realism into a formal logical system, demonstrating its broad applicability across science, philosophy, and practical reasoning.