# A new reading and comparative interpretation of Gödel’s completeness (1930) and incompleteness (1931) theorems

*Логико-Философские Штудии*13 (2):187-188 (2016)

**Abstract**

Peano arithmetic cannot serve as the ground of mathematics for it is inconsistent to infinity, and infinity is necessary for its foundation. Though Peano arithmetic cannot be complemented by any axiom of infinity, there exists at least one (logical) axiomatics consistent to infinity. That is nothing else than a new reading at issue and comparative interpretation of Gödel’s papers (1930; 1931) meant here. Peano arithmetic admits anyway generalizations consistent to infinity and thus to some addable axiom(s) of infinity. The most utilized example of those generalizations is the complex Hilbert space. Any generalization of Peano arithmetic consistent to infinity, e.g. the complex Hilbert space, can serve as a foundation for mathematics to found itself and by itself.

**Keywords**

**Categories**

**PhilPapers/Archive ID**

PENANR

**Upload history**

Archival date: 2020-05-28

View other versions

View other versions

**Added to PP index**

2020-05-28

**Total views**

17 ( #55,471 of 55,806 )

**Recent downloads (6 months)**

8 ( #50,461 of 55,806 )

How can I increase my downloads?

**Downloads since first upload**

*This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.*