Necessity of identity and Tarski's T‐schema

Abstract

It is argued that Tarski's T-schema and the thesis of the necessity of identity cannot both be true.We show that the thesis of the necessity of identity 1 and Tarski's T-schema 2 cannot both be true.For, given the necessity of identity, it follows that: A: If Socrates = the teacher of Plato, then necessarily Socrates = the teacher of Plato.And hence, B: Necessarily Socrates = the teacher of Plato. But clearly.C: The statement 'Socrates = the teacher of Plato'. is not necessarily true.However, given Tarski's T-schema, (B) and (C) cannot both be true.1 Kripke (1971: 136-7), Kripke (1980: 3).2 Informally, Tarski's T-schema states that a statement is true if and only if what it states is the case. See Tarski (1949: 54-55).This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

On the Argument for the Necessity of Identity

“…See note 4. 6 This follows from Blum (2023). The argument depends crucially on the validity of Tarski's Tschema which may be stated informally: 'A statement is true if and only if what it states is the case'.…”

Tarski's T‐schema and necessity of identity

“…Blum (2023) has recently argued that ‘Tarski's T‐schema and the thesis of the necessity of identity cannot both be true’. The argument can be formalized in a modal logic that contains the familiar modal axiom : Assume that If , then necessarily (by the thesis of the necessity of identity) Then, necessarily ( modus ponens 1,2) Necessarily ‘’ is true if and only if (by the necessity of Tarski's T‐schema) Therefore, necessarily ‘’ is true (by axiom and modus ponens 3,4) However, ‘clearly’ it is not necessary that ‘’ is true Contradiction. …”