The text of The Tractatus supports incompatible interpretations of a number of key philosophic positions. For example, the book is neither obviously nominalistic nor obviously realistic. Another difficulty is presented by the apparent. incompatibility of Wittgenstein's theses that propositions are logical pictures of facts, and that propositions are truth-functions of elementary propositions. There are several places in The Tractatus where these two doctrines meet head on, but the central one is the set of passages 5.54-5.5422. This paper is an exegesis (...) of these passages and a sketch of Wittgenstein's theory of judgement.In Tractatus 5.54 - 5.5422, Wittgenstein argues that statements of belief, judgement, thoughts and the like are not incompatible with the principle of finite extensionality. The passages contain a brief but obscure reductio on the possibility of non-extensional contexts, and several no less obscure corollaries. In this paper I shall explicate the content of the reductio, criticise a common but mistaken view of these passages, and draw out the consequences of some major doctrines in the Tractatus for Wittgenstein's Theory of Judgement. (shrink)