Hempel, like Ayer, was a representative of a younger generation of philosophers influenced by logical positivism in the 1930s. He was not quite 30 when he wrote this, and Ayer was about 25 when his paper was published. By contrast, both Schlick and Neurath were in their mid-50s at this time, and Carnap was in his mid-40s. (In age, Quine was between Hempel and Ayer and had similar associations with logical positivists early in his career. Although he is usually thought of mainly as a critic of logical positivism, you may notice some similarity between his views and the views that Hempel ascribes to Neurath.)
The paper can be divided into two parts. In the first (pp. 49-54), Hempel describes three stages in a movement from the sort of correspondence theory of truth that might be found in Wittgenstein’s Tractatus (or in Ramsey) to what Hempel sees as a sort coherence theory proposed by Neurath and Carnap. The second part (54-59) is a critique of an alternative form of logical positivism adopted by Schlick. This can be divided further into a criticism of Schlick’s own “theory of truth” (pp. 54-56) and a response to a criticism of the Neurath-Carnap coherence theory that might be attributed to him (pp. 56-59).
Let me call your attention to two specific points that it might be easy to pass over.
• Neurath’s metaphor of the ship under repair at sea has come to be well-known, largely because of Quine’s repeated use of it to explain his own similar views.
• Although Hempel does not speak of Ramsey’s deflationism, he gets somewhat similar results from Carnap’s distinction between the “formal mode” and “material mode” of speech—i.e., between explicit statement of some aspect of language (a formal mode statement) and an indirect statement of the same feature that appears to concern something extra-linguistic (a material mode statement).
(You will find a typo in the paper: the final 2 lines of the first full paragraph of p. 53 were intended for, and also appear in, the paragraph at the middle of the page, and some text from the first paragraph has dropped out.)