A consequence of the notional existence of an effectively calculable yet non-recursive function
Ładowanie...
Data
2021
Autorzy
Tytuł czasopisma
ISSN czasopisma
Tytuł tomu
Wydawca
Uniwersytet Papieski Jana Pawła II w Krakowie
Abstrakt
The present paper is devoted to a discussion of the role of Church’s thesis in setting limits to the cognitive possibilities of mathematics. The specific aim is to analyse the
formalized theory of arithmetic as a fundamental mathematical structure related to the theory of computation. By introducing notional non-standard computational abilities into this theory, a non-trivial enlargement of the set of theorems is obtained. The paper also indicates the connection between the inclusion of new functions through the development of axioms and the potential modification of inference rules. In addition, the paper provides an explanation of the role of inclusion of a certain interpretation of the meaning of the axioms of the theory in that theory.