Contatto di riferimento: Giovanna Corsi
Partecipanti: Enrico Moriconi - Università di Pisa
In this paper we examine how the notion of semantic completeness emerged
from the entanglement of model theory and proof theory which characterized logical
investigations in the first Thirties of the last century. We emphasize the fundamental
role played in this process by K. G¨odel, who basically introduced that
notion in the form then become dominant, carving it out from the clear distinction
between syntactic and semantic analysis of a formal system. We note that
this fact can help to understand why G¨odel’s work of 1930 remained by and large
disregarded within the logic community. In the second main part of the paper we
maintain that the link to a pre-g¨odelian notion of completeness is at the root of the
introduction of the natural deduction calculi by G. Gentzen. Lastly, we emphasize
that by devising the sequent calculi Gentzen introduced still another notion of
completeness, which pertains the relationship between the rules of the system.
Per informazioni:
giovanna.corsi@unibo.it
rossella.lupacchini@unibo.it