Repository | Journal | Volume | Articles
(2014) Philosophia Scientiae 18 (3).
We argue that Gödel's completeness theorem is equivalent to completability of consistent theories, and Gödel's incompleteness theorem is equivalent to the fact that this completion is not constructive, in the sense that there are some consistent and recursively enumerable theories which cannot be extended to any complete and consistent and recursively enumerable theory. Though any consistent and decidable theory can be extended to a complete and consistent and decidable theory. Thus deduction and consistency are not decidable in logic, and an analogue of Rice's Theorem holds for recursively enumerable theories: all the non-trivial properties of them are undecidable.
Publication details
DOI: 10.4000/philosophiascientiae.968
Full citation:
Salehi, S. (2014). Gödel's incompleteness phenomenon—computationally. Philosophia Scientiae 18 (3), pp. 23-37.
This document is available at an external location. Please follow the link below. Hold the CTRL button to open the link in a new window.
