In earlier chapters we saw how the domains of mathematics and logic had been taken care of (albeit differently) by Wittgenstein and Carnap. Most positivists were willing to go along with one or the other of them on those topics; but they were far more interested in empirical knowledge. Once again, as in the case of mathematics, the leading questions were semantic and foundational: What does science say, and what kinds of reasons do we have for believing what it says? These two questions were the kernel of what was misleadingly called at the time the “problem of induction.” A variety of ways of looking at it had been taking shape for decades. Their proponents finally confronted one another in Vienna in the early 1930s. The showdown was, as usual, inconclusive, but it greatly sharpened the conflicting positions and helped reveal their respective virtues and vices. Moreover, beneath the wide variety of responses, one may detect further evidence of the methodological shift toward the transcendental approach adumbrated in Chapter 10.