This paper examines one central problem in the philosophy of computer science, namely the question of whether computer programs can be verified by means of a mathematical proof. Firstly, program verification is defined and the classical debate on its feasibility is recalled under the light of a dual ontology of computational systems. Secondly, the current resurgence of the debate is analysed underlining its logical, technological, and philosophical motivations. Finally, it is shown how adopting a stratified ontology for computational systems one may recombine the different positions in the debate, arguing how program verification involves both deductive and inductive reasoning
