Logicism and ramsification

Abstract

ion principles of the logical form of Hume’s Principle. The identity criteria for geometrical objects described by theories of physical space are ‘‘empirically constrained’’ in the sense that the equivalence relations in the definiens of such principles are ‘‘established experimentally’’ (39). In contrast, the central identity principle for numbers guiding the application of arithmetic is Hume’s principle. This is, as was already shown in the previous chapter, fully general and thus not constrained by empirical facts. Ramsification and scientific structuralism The second thematic focus of the book concerns contributions to the logical analysis of theoretical knowledge in work by Russell, Ramsey, and Carnap. Chapters 4–7 develop a critical discussion of the Ramsey-sentence reconstruction of theories and its structuralist underpinnings. In addition, several points of contact with the semantic conception of theories, Putnam’s model-theoretical arguments against metaphysical realism, and van Fraassen’s constructive empiricism are addressed here. Chapter 4 covers much of the ground discussed in the subsequent chapters of the book and will therefore be the focus of the present review. The chapter begins with a critical evaluation of a recent ‘‘observation’’ made by Michael Friedman regarding Carnap’s ‘‘neutralism’’ in the debate on the nature of theoretical entities. Friedman’s point—as Demopoulos presents it—is based on a comparison between van Fraassen’s constructive empiricism and Carnap’s Ramsey-sentence reconstruction of theories. A ‘‘central tenet’’ of constructive empiricism is the distinction between the truth of a theory and its empirical adequacy. As Demopoulos shows, this distinction can be trivialized, however, by a simple model-theoretical argument. Very roughly, it can be shown that an empirically adequate theory is always also true if its observational models are of the right size. Friedman’s observation is that Carnap’s own position is not affected by this trivialization argument and thus turns out to be philosophically preferable to van Fraassen’s account. Carnap’s neutralism is the view that questions concerning the ontological status of theoretical entities should really be understood as questions about the choice of linguistic frameworks. Thus, the traditional realism–instrumentalism controversy should be deflated to the dispute over whether one should adopt a language with or without theoretical terms. As a consequence, Carnap’s use of the Ramsey sentence seems to escape the above trivialization argument, simply because the distinction between truth and empirical adequacy is irrelevant in his neutralist account. Demopoulos’ main point in the paper is to present a second model-theoretical argument directed against Carnap’s alleged neutralism. The result is based on a simple mathematical toy example, namely an arithmetical theory T with one ‘‘observational’’ and one ‘‘theoretical’’ predicate. The specific theory has two important properties: First, all of its observational consequences are true in the standard or intended numerical model. Second, T itself as well as its Ramsey sentence R(T) is not true in any expansion of this intended model but only in 258 Metascience (2014) 23:255–261