Steins Theory: A New Axiomatic System Concerning Identity

In the philosophy of language, Frege's (1892) distinction between sense and reference provided the foundational framework for identity statements, while Putnam's (1975) 'Twin Earth' thought experiment, with its remarkable insight, pushed externalism to its extreme, successfully challenging the internalist model of meaning and setting the agenda for subsequent decades of debate on the determination of reference. However, despite the highly illuminating nature of these seminal works, an intriguing phenomenon is that the ensuing debates—such as those surrounding core cases like the Ship of Theseus and identical particles—seem to have reached an impasse. This paper argues that this impasse may not stem from the depth of the problem itself, but rather from an unexamined deep presupposition shared by these otherwise highly persuasive theories: namely, the belief that there exists some single, decisive level (whether microphysical structure or historical causation) that can definitively answer the question of identity once and for all. This paper proposes that instead of continuing to seek a superior single answer under this presupposition, a more productive approach might be to question the presupposition itself. To this end, we develop a level-relativity analytical framework (Steins Theory). Interestingly, this framework demonstrates that the aforementioned seemingly opposing outstanding 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 does not aim to negate previous work, but rather seeks to clarify its valid scope of application, thereby offering a new path to resolving a series of philosophical puzzles arising from level confusion.