Language, Perspective, Formalism: The Philosophy of Mathematics in an Interdisciplinary Context
My research project examines the structure of discourse about mathematical objects and its relation to other forms of language. The first (historical) part of the project discusses the development of metamathematics from the 1890s to the 1930s, looking at Hilbert's formalist programme, the finitism of the middle Wittgenstein, and the early reception of the classical limitative theorems (Gödel, Church, Löwenheim-Skolem); I focus particularly on the evolution of the notion of formalized languages as multiply interpretable structures. The second (philosophical) part applies these results to recent discussions of intensionality in mathematics and the individuation of mathematical objects. The third (interdisciplinary) part assesses the relevance of these insights about mathematical language for other 'exceptional cases' in the philosophy of language: poetic language, metaphor, and fictional entities.