For many years, Charles Peirce maintained that all senses of the modal terms "possible" and "necessary" can be defined in terms of "states of information." But in 1896, he was motivated by his work in set theory to criticize that account of modality, and in 1905 he characterized that criticism as a return "to the Aristotelian doctrine of a real possibility ... the great step that was needed to render pragmaticism an intelligible doctrine." But since Peirce was a realist about (...) modality before 1896, and since he continued defining "possibility" in terms of "states of information" after that date, it is not clear exactly what he changed his mind about. In this essay I explain what it was that Peirce changed his mind about and why, in retrospect, he viewed that change as a decisive step in the development of pragmaticism. (shrink)