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  1. The tractarian operation N and expressive completeness.Leo K. C. Cheung - 2000 - Synthese 123 (2):247-261.
    The purpose of this paper is threefold. First, I visit the Fogelin–Geach-dispute, criticizeMiller''s interpretation of the Geachian notationN(x:N(fx)) and conclude that Fogelin''s argumentagainst the expressive completeness of the Tractariansystem of logic is unacceptable and that the adoptionof the Geachian notation N(x:fx) would not violate TLP5.32. Second, I prove that a system of quantificationtheory with finite domains and with N as the solefundamental operation is expressively complete. Lastly, I argue that the Tractarian system is apredicate-eliminated many-sorted theory (withoutidentity) with finite domains (...)
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  • Tractarian First-Order Logic: Identity and the N-Operator.Brian Rogers & Kai F. Wehmeier - 2012 - Review of Symbolic Logic 5 (4):538-573.
    In theTractatus, Wittgenstein advocates two major notational innovations in logic. First, identity is to be expressed by identity of the sign only, not by a sign for identity. Secondly, only one logical operator, called “N” by Wittgenstein, should be employed in the construction of compound formulas. We show that, despite claims to the contrary in the literature, both of these proposals can be realized, severally and jointly, in expressively complete systems of first-order logic. Building on early work of Hintikka’s, we (...)
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  • Incompatibility, inconsistency, and logical analysis in Tractatus Logico-Philosophicus.Ivan Welty - 2021 - Synthese 199 (3-4):8171-8186.
    Statements of degree appear to falsify basic doctrines in Tractatus Logico-Philosophicus. I offer a fresh formulation of the challenge and assess a solution proposed on Wittgenstein’s behalf by Sarah Moss. I find that Moss’s proposal fails. The proposal rides in part on novel interpretations of pronouncements by Wittgenstein on the nature of the elementary proposition. I find that the interpretations cannot be sustained but that Moss’s textual case hints at important and overlooked features of the Tractarian program. I develop Wittgenstein’s (...)
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  • Analysis of Quantifiers in Wittgenstein’s Tractatus: A Critical Survey.Dale Jacquette - 2001 - History of Philosophy & Logical Analysis 4 (1):191-202.
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  • The Expressive Power of the N_-Operator and the Decidability of Logic in Wittgenstein’s _Tractatus.Rodrigo Sabadin Ferreira - 2023 - History and Philosophy of Logic 44 (1):33-53.
    The present text discusses whether there is a tension between aphorisms 6.1-6.13 of the Tractatus and the Church-Turing theorem about the decidability of predicate logic. We attempt to establish the following points: (i) Aphorisms 6.1-6.13 are not consistent with the Church-Turing theorem. (ii) The logical symbolism of the Tractatus, built from the N-operator, can (and should) be interpreted as expressively complete with respect to first-order formulas. (iii) Wittgenstein’s reasons for believing that Logic is decidable were purely philosophical and the undecidability (...)
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