### Francesco Berto

Lundi 29 octobre, à 17h30 dans la grande salle de l'IHPST, le séminaire Philmath reçoit Francesco Berto (IHPST-CNRS-ENS):

Abstract:

Some of the strangest outcomes of paraconsistency have to do with inconsistent arithmetic and impossible numbers. Traditional-minded logicians usually get puzzled when one mentions the astonishing applications of paraconsistency in formal arithmetic. However, at the cost of some incredulous stares (which usually begin when one mentions the fact that paraconsistent arithmetics include contradictory numbers, and especially numbers which are identical to their immediate successor), one gets a world in which even well-established limitative results of ordinary metamathematics, such as Gödel’s Theorems, begin to fluctuate. In this talk I summarize some of the main results around, which are as unfamiliar to the general audience as they are innovative and interesting. The presentation is focused on *relevant* arithmetics, i.e., on formal systems for arithmetic whose underlying logic is some relevantlogic. After giving bits of relevant proof theory, I switch to a model-theoretic approach (which I find philosophically much more stimulating). I introduce a useful *collapsing filter*, which turns the so-called standard model of arithmetic into interesting inconsistent models by shrinking in an appropriate way its cardinality.