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 astonishing insight, pushed the externalist position to its extreme, successfully challenging the internalist model of meaning and setting the basic agenda for debates on referential determinacy for the subsequent decades. However, despite the highly inspirational nature of these pioneering works, an intriguing phenomenon is that the debates they sparked—such as discussions around core cases like Theseus's ship and identical particles—seem to have fallen into a kind of impasse. This article attempts to argue that this impasse may not stem from the depth of the problem itself, but precisely from an unexamined deep presupposition shared by these otherwise highly convincing theories: namely, the belief that there exists some single, decisive level (whether microscopic physical structure or historical causation) that can once and for all answer the identity question. This article proposes that, rather than continuing to seek a superior single answer under this presupposition, a more productive approach may be to reflect on this presupposition itself. To this end, we develop an analytical framework of hierarchical relativity. Interestingly, this framework shows that those seemingly opposing excellent theories can actually be understood as special cases of this framework at different levels; the difficulties they encounter become inevitable precisely when they attempt to make assertions across levels. Therefore, this framework is not intended to negate the work of predecessors, but aims to provide a new path for resolving a series of philosophical puzzles arising from category mistakes by clarifying the valid scope of application of those works.