Carnap (1891-1970), like other members of the Vienna Circle, was influenced both by the positivism of people like the physicist Ernst Mach (1838-1916) by Wittgenstein. Wittgenstein’s influence came first from the Tractatus, but also from the somewhat different views he held after his return to philosophy in the late 1920s and that he conveyed in meetings with the Vienna Circle when he returned to Vienna for visits after he’d taken up a fellowship at Cambridge.
Carnap had published two major books before this article, his Der Logische Aufbau der Welt (The Logical Construction of the World) in 1928 and the Logische Syntax der Sprache (Logical Syntax of Language) in 1934. This article reflects the point of view of the latter work. Around the time it was published Carnap delivered a series of lectures in London. These were later published as Philosophy and Logical Syntax (London: Keagan Paul, Trench, Trubner & Co., 1935); you can also find a short account of them in C. A. M. Maund and J. W. Reeves, “Report of Lectures on Philosophy and Logical Syntax, Delivered on 8 10 and 12 October at Bedford College in the University of London, by Professor Rudolf Carnap,” Analysis, vol. 2 (1934), pp. 42-48 (on JSTOR).
• The most characteristic view of positivists is the rejection of metaphysics. Carnap presents his form of this on pp. 5-8. It can be traced back through positivists like Mach and Auguste Comte (1798-1857) to Hume. But, by contrast with earlier positivists, Carnap, like Wittgenstein, rejected metaphysics not as speculative but as meaningless. He suggests a difference between his views and Wittgenstein’s in his comments on the quotations from the Tractatus (4.112 and 6.54), but the difference is less when what Carnap says is compared to Wittgenstein’s views of the late 1920s and early 1930s. At that time, Wittgenstein, too, saw philosophy as concerned with syntax, and it’s easy to think of the views Carnap presents here as his own way of developing ideas he learned from Wittgenstein.
He probably was influenced by Wittgenstein in another respect. The standard grounds for holding metaphysics to be meaningless on the part of the Vienna Circle and others at the same time with similar views—the term “logical positivist” tends to be used for such people—is the “principle of verification” according to which the meaning of a claim is to be found in its “mode of verification.” Metaphysics was meaningless because it claimed to go beyond experience so its claims could, in principle, have no verification in experience. This idea can be traced back to the British empiricists, and especially Hume, but in the form advanced by the logical positivists, it seems to have been due to Wittgenstein around 1930.
The idea is not explicitly stated in this article but appears prominently in the report of Carnap’s lectures (ibid., pp. 42f):
Linguistic utterances which can be verified are representative and have theoretical sense. A proposition P, which may be individual or general, can be verified either directly, by present perception, or indirectly, by direct verification of propositions deduced from P and other already verified propositions. If P is not directly verifiable, it is an hypothesis; as such it cannot be certain since the number of propositions necessary for its complete verification is infinite. To say that P is an hypothesis is to say something about its logical character; it is not to say that the probability of its truth is low. No statement which is not in principle directly or indirectly verifiable has sense. It follows that all propositions of metaphysics, that is, all propositions which pretend to represent something over and beyond experience, all doctrines such as Realism, Idealism, etc., usually called epistemological and taken to assert or to deny the reality of something, all propositions of normative ethics, are unverifiable; accordingly, they have no sense. Empirical propositions asserting reality have sense, since they assert something about part of a system, e.g. that things of such and such a sort are to be found in the world, they do not assert something about the system as a whole.
• One of Carnap’s own contributions lies in his distinction between the formal and “inhaltlich” modes of speech. The latter term is an adjectival form of the German term equivalent to content and thus has no direct translation in English, though the invented term “contentual” is sometimes used. The use of the term “connotative” in this translation was not followed by others, and Carnap’s distinction is now known by the pair of terms formal mode and material mode, terms which he seems to have used himself in his London lectures. Getting a sense of this distinction and its significance is your chief task in digesting this article.
• You should notice how Carnap uses the distinction of formal and material modes as a way of overcoming or undermining philosophical controversies. This aim is characteristic of Carnap and appears also in the other chief distinction of the article, that between “assertions” and “proposals.” This distinction is closely related to the ideas in 6.341 of the Tractatus. That is, assertions can be made only within a given framework but one might propose one framework or another on what the logical positivists called “pragmatic” grounds—i.e., as a simpler or more convenient framework within which to make assertions about a given subject matter.