This hybrid talk will take place in Room Multiuso, FTL Building (USI West Campus) and online via Zoom. If you are interested in joining online, please write to events.isfi@usi.ch.  

Here is the abstract of the talk:  

The existence of non-standard models of first-order Peano-Arithmetic threatens to undermine the claim of the moderate mathematical realist that non-mysterious access to the natural number structure is possible on the basis of our best arithmetical theories. The move to logics stronger than FOL is denied to the moderate realist on the grounds that it merely shifts the indeterminacy “one level up” into the meta-theory by -- illegitimately -- assuming determinacy of the notions needed to formulate such logics. This paper argues that the challenge can be met by showing that the notion “infinitely many” is uniquely determinable in a naturalistically acceptable fashion and is thus available to the moderate realist in the formulation of a theory of arithmetic. If there is time, I will discuss how the approach can be extended to other important mathematical theories and compare it with Field's alternative proposal and the popular strategy of invoking a second-order formalism, arguing that it is more robust than either of these.

For more information: https://www.ftl.usi.ch/it/feeds/14780