I've been thinking further about Carnap, as I've just read Michael Friedman's A Parting of the Ways, and also because I've been thinking about my dissertation, in which I borrow heavily from Carnap. Friedman's discussion of the Kantian influences on Carnap's thinking has led me to return to a thought I've had before. Carnap of course subscribes to what Quine called the "linguistic doctrine of logical truth," logical and mathematical truths for Carnap are established by implicit linguistic conventions. They are prescriptions of language, chosen for pragmatic reasons.
Though Carnap wrote very little about ethics, he shared the general positivist enthusiasm for expressivist meta-ethical views; when he presents his own view of ethics in response to one of the papers in his Schilpp volume, the view is clearly expressivist. In particuar, normative ethical claims generally involve the expression of commands or prescriptions. Naturally, this is not to say that there are no reasons for them; there can of course be pragmatic reasons for expressing particular endorsements.
Though I cannot think of any expressivists who have made this connection explicitly, I see a fascinating parallel here. Many philosophers have, of course, maintained that ethics is an a priori discipline. Sometimes this is claimed because of a feeling that the a priori is more secure, or more universal, or somehow more exalted, but not infrequently another reason that is given is the more prosaic observation that it's hard to think of what could possibly count as empirical evidence for or against basic ethical principles. Certainly with respect to my own normative views (utilitarian, of course, as regular readers of the blog will know), I cannot think of any evidence I could give someone who didn't already find happiness valuable to convince them that they were mistaken.
So, the conventionalist maintains that logic and mathematics are expressions of the norms and prescriptions of our linguistic practices. This is the conventionalist's account of the paradigm cases of a priori knowledge; to the extent that a conventionalist can be said to have a theory of the a priori, that is how the conventionalist thinks a priori knowledge works. The expressivist maintains that moral claims are expressions of the norms and prescriptions of our moral practices. Would that not make ethics a priori, in the conventionalist sense of that notion?
This must have occurred to Carnap, even if it seems to have escaped many of the other positivists. One of the main goals of his efforts to construct ever more sophisticated logical devices was to facilitate mutual understanding; he dreamed of universal languages which would insofar as was possible remove barriers to communication by enabling everyone to express themselves accurately in ways comprehensible to everyone else. I cannot imagine how he could have missed the parallels to the Kantian project of finding a universal morality to remove barriers to cooperative effort. Further, there seems no necessity for imagining Carnap to have been that dense, as despite the silence of his published work on the topic, his letters and other private communications of which I am aware suggest strongly that he did believe that there was just such a connection.
Analytic philosophy is commonly accused of having become immersed in dry technical details and having lost touch with the purpose of philosophy in connecting to life. Carnap no doubt made himself more vulnerable to such charges by his efforts to avoid making any explicit statements about the political or personal consequences of his views in his writings. No doubt this was wise; he was associated with communism anyway, and would likely simply have been dismissed on the basis of his socialist views had he explicitly drawn the connections he believed to obtain between his logical system-building and his socialist ideals. However, he clearly believed such connections to exist, and I tend to agree. As Stephen Colbert says, reality has a well known liberal bias. Getting technical issues and matters of methodology right will have a natural tendency to advance the cause of the good. Further, focusing on such issues, rather than merely engaging in partisan preaching, will help shield one from charges of bias. Perhaps Carnap's approach still has some merit in modern times.