 Formalist variants of instrumentalism are a more serious alternative to realist semantics than the fiction view of theoretical entities. Formalist views in the philosophy of mathematics aim to account for mathematical concepts and objects in terms of syntactic entities and operations thereupon within a calculus. Such views have been carried over to theoretical concepts and objects in the natural sciences, with the qualification that the observational part of the calculus is interpreted in such a way that its symbols refer to physical or phenomenal objects. Cognitive access to theoretical entities is thus explained in terms of our cognitive access to the symbols and rules of the calculus in the context of an antecedent understanding of the observation terms. Formalist ideas were sympathetically entertained by Hermann Weyl (1949). He was driven towards such ideas by adherence to Hilbert’s distinction between real and ideal elements and the corresponding distinction between real and ideal propositions (Hilbert 1926). Propositions of the observation language were construed as real in the sense of this Hilbertian distinction, while theoretical propositions are construed as ideal. The content of an ideal proposition is understood in terms of the (syntactic) consistency of the whole system consisting of ideal and real propositions being asserted.