The tractarian operation N and expressive completeness

Synthese 123 (2):247-261 (2000)
Abstract
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 and with N as the solefundamental operation, and thus is expressivelycomplete.
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