From the Notebooks to the Investigations and Beyond

TL;DR

This paper investigates how Wittgenstein's meaning-as-use can be formalized for predicate logic by leveraging the Wittgenstein Nachlass. It argues that explanations of consequences can be modeled as movements within language via reduction rules and a dialogical/game-theoretic semantics, contrasting with verificationist approaches. The author sketches a program that aligns with natural deduction, Gentzen-style inversion, and proof-theoretic semantics while drawing on Lorenzen/Hintikka-style games and Peirce-inspired interaction. These insights aim to ground a pragmatist semantics for logic and connect Wittgenstein's use-based view to modern proof-theoretic and dialogical frameworks. The work suggests future development of a full formal semantics incorporating usage and purpose across the Nachlass.

Abstract

The use of the open and searchable Wittgenstein's Nachlass (The Wittgenstein Archives at the University of Bergen (WAB)) has proved instrumental in the quest for a common thread of Wittgenstein's view on the connections between meaning, use and consequences, going from the Notebooks to later writings (including the Philosophical Investigations) and beyond. Here we take this as the basis for a proposal for a formal counterpart of a 'meaning-as-use' (dialogical/game-theoretical) semantics for the language of predicate logic. In order to further consolidate this perspective, we shall need to bring in key excerpts from Wittgenstein oeuvre (including the Nachlass) and from those formal semanticists who advocate a different perspective on the connections between proofs and meaning. With this in mind we consider several passages from Wittgenstein's published as well as unpublished writings to build a whole picture of a formal counterpart to 'meaning is use' based on the idea that explanations of consequences via 'movements within language' ought to be taken as a central aspect to Wittgenstein's shift from 'interpretation of symbols in a state of affairs' to 'use of symbols' which underpins his 'meaning is use' paradigm. As in the Investigations "every interpretation hangs in the air together with what it interprets, and cannot give it any support. Interpretations by themselves do not determine meaning", as well as in a remark from his transitional period (1929-30): "Perhaps one should say that the expression 'interpretation of symbols' is misleading and one should instead say 'the use of symbols'." Significantly, we wish the present examination of the searchable Nachlass can make a relevant step towards a formal counterpart to the 'meaning is use' dictum, while highlighting an important common thread from Wittgenstein's very early to very late writings.