Meaning, Relation, Identity and Generality in the Tractarian

Abstract

In this article, the author examines the theory of representation (representationalism) in Tractatus Logico-Philosophicus, considering it as a means of access to the Tractarian architectonics. The researcher focuses on the introduction of a new formalism specific to Wittgenstein, designed to establish conceptual writing on different foundations than those of Frege–Russell, to avoid inherent paradoxes and to eliminate the cumbersome techniques used to counter them. In this regard, the author analyzes and interpret Wittgenstein’s new formalism for eliminating metalanguage and the theory of types, comparing Frege’s theory of sense and reference with Wittgenstein’s proposal, which separates meaning from the way an object appears and distinguishes between syntax and semantics—a critique that also applies to Russell. Wittgenstein’s approach to “cutting through” these issues is to assert that the propositional sign cannot state or show anything about itself. By following the logicality of the image and the concrete way it is constituted, Wittgenstein constructs his formalism of general forms concerning relations, operations, propositions, and logical functions. Through this framework, he defines, in a logicist manner, the concept of the general form of a proposition, logical operations, and natural numbers. All these are intensional forms, obtained by highlighting their internal structures. In this way, the Austrian philosopher exposes an entire series of metaphysical expressions associated with foundational theories of numbers, constructions, and calculative conventions, as well as with the logicist foundations of mathematics (set, function, number, conventional signs). It becomes evident that mathematics and logic share the same internal structures, and logical discoveries are reflected at the level of mathematical language. As part of this process, Wittgenstein eliminates the concept of identity as expressed by the equality sign, replaces the universal quantifier with the existential one (using negation and an additional variable), and introduces his own formal notation. Through these modifications, he attempts to eliminate the “pseudopropositions” that undermine the logicist edifice of mathematics. This article also examines how Wittgenstein reformulates Russell’s concept of relation from Principia Mathematica, assimilating it into an empirical framework. In this case, Wittgenstein reduces the symbolism of relations to states of affairs, with the direction being from objects to relations rather than vice versa. The author emphasizes that Wittgenstein equates relations with the concept of logical operations, thereby ensuring the necessary generality and reconstructing the general form of the concept aRb. The author synthesizes the general forms presented in the Tractatus: relation, proposition, series of forms, natural number, and the derivation of one term from another based on the internal relation of a series of forms. The central aim of this study is a comparative reconstruction of how Wittgenstein proposes replacement theories for the formalisms of Frege and Russell/Whitehead, as well as a new reading of the Tractatus Logico-Philosophicus from the perspective of the theory of meaning and general forms, with a focus on the sentences contained in sections 5.53–5.54.