Steins Theory: A New Axiomatic System Concerning Identity

In the philosophy of language, Frege’s (1892) distinction between sense and reference provides a foundational framework for identity statements. Geach’s (1967) relative identity breaks out of the framework of absolute identity and opens another perspective for us. Putnam’s (1975) “Twin Earth” thought experiment, with its striking insight, pushes externalism to the extreme, successfully challenging the internalist model of meaning and setting the basic agenda for decades of subsequent debate on the problem of reference determination. However, despite the inspirational value of these groundbreaking works, a noteworthy phenomenon is that the debates they triggered—such as discussions around core cases like the Ship of Theseus and identical particles—seem to have reached a certain impasse. This paper argues that this impasse may not stem from the depth of the problems themselves, but precisely from a deep, unexamined presupposition shared by these otherwise highly persuasive theories: namely, that there exists a single, decisive category (whether microscopic physical structure or historical causality) capable of once and for all answering the question of identity. Instead of continuing to seek a better single answer under this presupposition, a more productive approach may be to reflect on the presupposition itself. To this end, we attempt to analyze the problem from a different angle. Interestingly, this angle shows that the aforementioned seemingly opposed excellent theories can actually all be understood as special cases of this theory under different categories; the difficulties they encounter become inevitable precisely when they attempt to make assertions across categories. Therefore, this paper is not intended to negate previous work, but to clarify the valid scope of its application, thereby providing a new path to resolve a series of philosophical difficulties arising from category mistakes.