Logical segmentation and generality in Wittgenstein’s Tractatus

Abstract

Abstract This chapter argues that Wittgenstein’s understanding of quantification is rooted in the interaction between two kinds of structure: the picturing structure of elementary sentences, and the iterative structure of repeated applications of truth-operations. Quantificational generality is a matter of applying a truth-operation to a sentence-function. The chapter argues that multiply embedded first-order quantification poses no difficulties for this view. However, since sentence-functions can take only expressions contained in elementary sentences as arguments, this view cannot accommodate higher order quantification. For this we must turn to formal generality, where the bases for a truth-operation are the members of a form-series determined by a formal law. By means of form-series Wittgenstein can simulate predicative, but not impredicative, higher-order quantification. The chapter concludes with some remarks on Wittgenstein's view of the application of logic and on the general form of sentences, and urges that the general form of sentences should be understood schematically.

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