The tacit and the ineffable: Frege and Wittgenstein on the distinction between language as a calculus and language as the universal medium (Gottlob Frege, Ludwig Wittgenstein)

The ideas of different thinkers can be examined from the vantage point of a distinction between a view of language as the universal medium (UM) and a view of language as a calculus (LC). According to a UM view, one's actual working language is universal in the sense of being an unavoidable medium between oneself and reality. Accordingly, semantic relations between language and reality cannot be expressed in language nor varied systematically. According to an LC view, language is a tool that can be varied systematically and used to express semantic relations.; Both Frege and the early Wittgenstein held variants of the UM view. Frege's position (UM1) can be considered an intermediate one, however, in that he maintained the inexpressibility of the most basic logical and linguistic categories, such as the notions of concept and object , while admitting the expressibility of the meanings of our ordinary concept and object terms. In contrast, Wittgenstein maintained in his Tractatus a full-fledged UM view (UM2). According to both Frege and Wittgenstein, the logical forms of language that provide for its meaningfulness are inexpressible in language, as is the crucial semantic notion of truth. Frege could nevertheless postulate objective meaning entities he called Sinne to mediate between signs and references.; The UM vs. LC contrast has its historical roots in the distinction between lingua characteristica and calculus ratiocinator. Developments of this contrast separate Frege's UM view from the LC views of Schroder and Hilbert. Frege's view also contrasts with Russell's variant of the UM view. Wittgenstein develops two ideas that dispose of Fregean Sinne and other avenues to the informative expression of semantic relations. One is the atomistic character of logical analysis. The other is the immediacy of the relation between linguistic symbols and what they represent. Wittgenstein exposes implications of Russell's view and radicalizes aspects of Frege's view, closing off avenues of semantic expression Frege left open. On an LC view, the tacit background structures are presupposed and provide meaning relations that are expressible in language, whereas on a full-fledged UM view these structures, should they exist, do not provide an informative semantics.