 One kind of non-syntactic logicist reading of inductive probability takes each support function \(P_{\alpha}\) to be a measure on possible states of affairs. The idea is that, given a fully meaningful language (associated with support function \(P_{\alpha}\)) ‘\(P_{\alpha}[A \pmid B] = r\)’ says that among those states of affairs in which B is true, A is true in proportion r of them. There will not generally be a single privileged way to define such a measure on possible states of affairs. Rather, each of a number of functions \(P_{\alpha}\), \(P_{\beta}\), \(P_{\gamma}\),…, etc., that satisfy the constraints imposed by axioms 1–7 may represent a viable measure of the inferential import of the propositions expressed by sentences of the language. This idea needs more fleshing out, of course. The next section will provide some indication of how that might go.