On Wittgenstein’s Dispensation with “ = ” in the Tractatus and its Philosophical Background. A Critical Study

Abstract

In this essay, I critically analyze Wittgenstein’s dispensation with “ = ” in a correct concept-script. I argue inter alia (a) that in the Tractatus the alleged pseudo-character of sentences containing “ = ” or = -sentences remains largely unexplained and propose how it could be explained; (b) that at least in some cases of replacing = -sentences with equivalent identity-sign free sentences the use of the notion of a translation seems inappropiate; (c) that in the Tractatus it remains unclear how identity of the object as that which is expressed by identity of the sign should be understood specifically; (d) that there are = -sentences which have no obvious equivalent in Wittgenstein’s novel notation; (e) that Wittgenstein’s adherence to (non-relational) identity, although he dispenses with “ = ”, is probably motivated by his desire to ensure that the expressive power of an identity-sign free concept-script of first-order is on a par with standard first-order logic containing “ = ”. In the concluding section, I critically discuss some claims in Lampert and Säbel (The Review of Symbolic Logic, 14, 1–21, 2021) and defend Wehmeier’s account of pseudo-sentences in the Tractatus (2012) against the objections they raise.