Logical segmentation and generality in Wittgenstein’s Tractatus

How does Wittgenstein understand quantification in the Tractatus? In particular, what becomes of higher-order quantification? Higher-order quantification is central to Frege’s and Russell’s universalist conception of logic, the conception that Russell vividly encapsulates in Introduction to Mathematical Philosophy: ‘logic is concerned with the real world just as truly as zoology, though with its more abstract and general features’ (Russell 1919: 169). In particular, it is by means of quantification of predicate as well as singular term positions that the principles of logic abstract from the content that distinguishes the propositions of the special sciences. Logical principles get applied here in that their higher-order variables as well as their first-order variables may be instantiated by vocabulary from any science. This view of logic and its application implicates many features of the ‘old’ logic that Wittgenstein rejects in the Tractatus: a need for general principles to mediate specific inferences in argumentation (5.132), general validity as the mark of a logical law (6.1231), an important distinction between logical axioms and the truths derivable from them (6.127), to name a few. The alternative the Tractatus offers to Frege’s and Russell’s universalist conception displaces higher-order quantification from the central role it had occupied. What happens to higher-order quantification itself in the Tractatus scheme? Frege’s and Russell’s views of quantification are linked to their views of logical segmentation. On their views, there is no great divide as regards logical segmentation between atomic sentences and logically compound sentences. This comes out strikingly in Frege’s view that every sentence is multiply analyzable as the completion of an incomplete expression by type-appropriate completers, and in his assimilation in logic of the grammatical predicates of colloquial language to his first-level incomplete