Carnap’s conventionalism in geometry

Grazer Philosophische Studien 88 (1):123-138 (2013)
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Against Thomas Mormann's argument that differential topology does not support Carnap's conventionalism in geometry we show their compatibility. However, Mormann's emphasis on the entanglement that characterizes topology and its associated metrics is not misplaced. It poses questions about limits of empirical inquiry. For Carnap, to pose a question is to give a statement with the task of deciding its truth. Mormann's point forces us to introduce more clarity to what it means to specify the task that decides between competing hypotheses and in what way such a task may be both in practice and/or in principle impossible to carry out
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