The First-Order Logic of the Tractatus

Kai F. Wehmeier (Irvine) gives a talk at the MCMP Colloquium titled "The First-Order Logic of the Tractatus". Abstract: First-order logic with identity, while not isolated as a logical system in its own right until the end of the 1920s, is arguably a natural fragment of the logic envisaged by Wittgenstein in the Tractatus Logico-Philosophicus. We will discuss two distinctive features of the system sketched there, namely the abolition of the equality sign and the use of a (purportedly) single logical constant, the so-called N-operator. Building on early work by Hintikka, we identify three possible variable conventions that Wittgenstein might have used to eliminate the equality sign without loss of expressive power, and we adduce textual, historical and systematic evidence for one of these as the intended convention. With respect to the N-operator, we show that an effective notation for variable scope is implicit in the Tractatus when taken in its historical context, thus bolstering the case made by Geach against Fogelin's claim of expressive inadequacy. We close by showing how both conventions can be simultaneously implemented in perfectly workable tableau calculi.