Fixing Montague's Problem
-----
The study of computability is traditionally taken to produce absolute truths. According to this standard view, results in computability theory do not depend on contingent cultural practices, such as denoting numbers by Arabic numerals. However, the standard view faces what Grabmayr calls Montague's Problem. This problem purports to show that computability is inherently relative to notation. Montague's Problem has led philosophers to argue that classic computability-theoretic results are relative to contingent matters, as opposed to the absolute nature of other mathematical truths. The aim of this talk is twofold. First, Grabmayr will show that Montague's Problem generalises to the case of arithmetical definability. Hence, a similar attack can be raised against the standard view that important (un-)definability results express absolute mathematical truths. Second, Grabmayr will defend the standard view from Montague's Problem. In doing so, Grabmayr will introduce absolute notions of computability and definability for important classes of objects.
-----