Logic of ER II - Comparative Ontology via Frame Classes: Presentism, Eternalism, Growing Block, and Existential Realism

Debates in temporal ontology—most prominently between presentism, eternalism, and the growing block theory—are often conducted via intuitive and linguistic contrasts that leave the underlying structural commitments underspecified. Existential Realism (ER) proposes a two-tier distinction: existence is present-bound, while reality extends beyond the present to include (at least) causal traces of the past and structured anticipations of the future. This paper offers a model-theoretic comparison of ER with its major rivals within a single, shared fixed-domain semantic environment. We introduce a unified first-order tense language with an ER-style existence predicate and a reality predicate; define a neutral class of temporal frames; characterize presentism, eternalism, growing-block theory, and ER as subclasses determined by explicit frame conditions; and prove representation results. We then establish separation results showing that ER is frame-theoretically distinct from presentist, eternalist, and growing-block rivals, and prove that the reality predicate R cannot be conservatively eliminated over ER frames. A key technical component is a non-definability result (with an explicit countermodel) showing that ER’s reality predicate is not eliminable in favor of tense and existence alone, together with a bisimulation-based robustness discussion.

Series note. This installment extends the two-tier framework and logical core of Formal Logic for Existential Realism by treating temporal ontologies as frame classes and proving comparative model-theoretic results, while taking soundness/completeness/conservativity results from the core system as background.