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A standard understanding of abstraction principles elicits two opposite readings: Intolerant Reductionism, where abstractions are seen as reducing talk of abstract objects to talk about non-problematic domains, and Robust Abstractionism, where newly introduced terms genuinely refer to abstract objects. Against this dichotomy between such "austere" and "robust" readings, Dummett suggested ways to steer intermediate paths. We explore different options for intermediate stances, by reviewing metaontological strategies (metaontological minimalism, Rayo's trivialism, and Linnebo's notion of thin objects) and semantic ones (tolerant reductionism and Dummett's notion of thin reference). Based on Dummett's and Picardi's understanding of the Context Principle, the paper acknowledges that Frege's Grundlagen are open to several interpretations of contextual definitions, and argues that the prospects for broadly Fregean intermediate views are all but foreclosed.

DOI: 10.1007/978-3-319-95777-7_7

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