Do the Self-Knowing Machines Dream of Knowing Their Factivity?

The Gödelian Arguments represent the effort done to interpret Gödel’s Incompleteness Theorems in order to show that minds cannot be explained in purely mechanist terms. With the purpose of proving the limits of mechanistic theses and investigate aspects of the ChurchTuring Thesis, several results obtained in the formal setting of Epistemic Arithmetic (EA) reveal the relation among different properties of knowledge of machines, including self-awareness of knowledge and factivity of knowledge. We discuss the main principles behind the Gödelian Arguments and extend the results obtained in EA. In particular, we define a machine that, in a specific case, knows its own code and the factivity of its own knowledge, thus providing new insights for the analysis of the Gödelian Arguments.