 Historically, the state-space approach emerged from work by Evert Beth, John von Neumann, and Hermann Weyl, and has important parallels with Przełęcki (1969) and Dalla Chiara Scabia and Toraldo di Francia (1973) (on the history of the approach see: Suppe 1977; van Fraassen 1980, 65–67; Lorenzano 2013; advocates of the approach include: Beatty 1981; Giere 1988, 2004; Giere, Bickle, and Mauldin 2006; Lloyd 1983, 1994 [1988], 2013 In Press; Suppe 1977, 1989; Thompson, 1989, 2007; van Fraassen 1980, 1989, 2008; for alternative early analyses of models see, e.g., Braithwaite 1962; Hesse 1966, 1967). Interestingly, van Fraassen (1967, 1970) provides a potential reconstruction of state spaces via an analysis of “semi-interpreted languages.” Weisberg (2013), building on many insights from Giere’s work, presents a broad view of modeling that includes mathematical structures that are “trajectories in state spaces” (29), but also permits concrete objects and computational structures such as algorithms to be deemed models. Lorenzano (2013) calls Giere’s (and, by extension, Weisberg’s and even Godfrey-Smith’s 2006) approach “model-based,” separating it out from the state-space approach. A more fine-grained classification of the state-space approach is desirable, particularly if we wish to understand important lessons stemming from the Pragmatic View of Theories, as we shall see below.