Steins Theory: A New Axiomatic System for Identity

In the philosophy of language, Frege’s (1892) distinction between sense and reference provided a foundational framework for identity statements, while Putnam’s (1975) Twin Earth thought experiment, with its remarkable insight, pushed externalism to its limits, successfully challenging the internalist model of meaning and setting the agenda for decades of debate on the determinacy of reference. However, despite the groundbreaking nature of these works, a curious phenomenon persists: the debates they sparked—such as those surrounding the Ship of Theseus or identical particles—seem to have reached an impasse. This paper argues that this stalemate may not stem from the depth of the problem itself but rather from a shared, unexamined assumption underlying these otherwise compelling theories: the belief that there exists a single, decisive level (whether microphysical structure or historical causation) capable of conclusively resolving the identity question. This paper proposes that, rather than continuing to seek a superior singular answer under this assumption, a more productive approach lies in critically examining the assumption itself. To this end, we develop a hierarchical relativity framework (Steins Theory). Intriguingly, this framework reveals that these seemingly opposing theories can be understood as special cases within our framework at different levels; their difficulties arise inevitably when they attempt to make assertions across levels. Thus, this framework does not aim to negate prior work but seeks to clarify its valid scope of application, offering a new path to resolve a series of philosophical puzzles born of category mistakes.