There’s a very interesting paper by Marta Sznajder in the latest Studies in History and Philosophy of Science about Carnap’s late (posthumously published) writings on inductive logic, especially his “Basic System” published by Dick Jeffrey in 1980. She focuses on Carnap’s introduction of “attribute spaces” to give structure to the semantics of the “world” to which properties are attributed; particular observations can be thought of then as points in such an attribute space, whose geometry is determined by the chosen linguistic framework (p. 70). There is an obvious continuity here with the structural characterization of the “world” in the Aufbau, a continuity Sznajder mentions (p. 65) but doesn’t develop. (I do hope someone follows this up soon – another obvious indication of the lifelong continuity, and overall unity, in Carnap’s thought that I am always banging on about!) What she does discuss very interestingly is how the shaping of the “world” by attribute spaces constrains both the choice of inductive axioms and the choice of method (within the continuum of inductive methods); “there are some values of the confirmation functions that will be determined by the framework itself. That means: given your linguistic framework, there are certain beliefs that are rational for you to hold.” Her fascinating account (section 4) gives a very straightforward explanation how this works. She further illustrates it by comparing it to a closely similar employment of “conceptual spaces” by Peter Gardenförs in the past decade or two. I’m sorry I didn’t see this paper before writing my own on “Carnapian Rationality” but as far as I can tell so far, there’s nothing in it that’s inconsistent with my interpretation.
It is very encouraging that Carnap’s inductive logic is now finally beginning to attract the same level of serious exegetical attention that first the Aufbau and then the Syntax (and eventually even the later Carnap of ESO and the Schilpp volume) have enjoyed for decades. I’m thinking especially of recent work by Teddy Groves at the University of Kent (UK) and Karine Fradet at the Université de Montreal (who unfortunately doesn’t seem to have published much on this subject yet). Please let me know of anyone I’ve missed here; there is so much new stuff coming out one loses track.
Sandy Zabell’s (continuing) work on Carnap’s inductive logic remains, of course, the gold standard in the field, a foundation which everyone will build on for generations. It derives from an unrivalled depth of knowledge in the history of mathematical statistics and related fields, combined (and this is really quite exceptional) with the intellectual and statistical creativity to develop Carnap’s ideas in directions that would have appealed to Carnap himself, yet framed in terms more acceptable than Carnap’s to mainstream statisticians. But Sandy is very explicit that he is looking at Carnap from the viewpoint of a statistician. What I find so encouraging about the work of Sznajder, Groves, and Fradet is that they are finally beginning to connect Carnap’s work on inductive logic up with his overall philosophical program. Carnap was terrible at explaining his own agenda in accessible ways, so it’s a great relief that a few people are beginning to do it for him, with respect to the project on which he spent most of the second half of his working life!