A consequence of the notional existence of an effectively calculable yet non-recursive function

Autor

DOI:

https://doi.org/10.15633/acr.5306

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.

Bibliografia

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Opublikowane

2021-12-31

Numer

Dział

Filozofia