Lugano Philosophy Colloquia. Balthasar Grabmayr
Multiuso, Theology building (USI West Campus)
Via Giuseppe Buffi 13
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We are pleased to announce that on Friday, December 1 at 17:30 (CET), Balthasar Grabmayr (University of Tübingen) will give the talk On the Limits of Mathematics and Their Philosophical Consequences as part of the Lugano Philosophy Colloquia Fall 2023 organised by the Institute of Philosophy (ISFI) at USI.
This hybrid talk will take place in the Multiuso room, Theology Building, USI West Campus and online via Zoom. If you are interested in joining it online, please write to [email protected]
For more information: https://www.usi.ch/en/feeds/25721
Here is the abstract of the talk:
There is a well-known gap between metamathematical theorems and their philosophical interpretations. Take Tarski's Theorem. According to its prevalent interpretation, the collection of all arithmetical truths is not arithmetically definable. However, the underlying metamathematical theorem merely establishes the arithmetical undefinability of a set of specific Gödel codes of certain artefactual entities, such as infix strings, which are true in the standard model. That is, as opposed to its philosophical reading, the metamathematical theorem is formulated (and proved) relative to a specific choice of the Gödel numbering and the notation system. Similar observations apply to Gödel and Church's theorems, which are commonly taken to impose severe limitations on what can be proved and computed using the resources of certain formalisms. The philosophical force of these limitative results heavily relies on the belief that these theorems do not depend on contingencies regarding the underlying representation choices. The main aim of this talk is to put this belief under scrutiny by exploring the extent to which we can abstract away from specific representations in the formulations and proofs of several metamathematical results.
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