Gödel's incompleteness theorems
The work
| Authors | Panu Raatikainen |
|---|---|
| Editors | |
| Type | incollection |
| Year | 2020 |
| Citekey | raatikainen2020godel |
Where it appeared
| Published in | The Stanford Encyclopedia of Philosophy |
|---|---|
| Publisher | Metaphysics Research Lab, Stanford University |
Abstract
Gödel’s two incompleteness theorems are among the most important results in modern logic, and have deep implications for various issues. They concern the limits of provability in formal axiomatic theories. The first incompleteness theorem states that in any consistent formal system F within which a certain amount of arithmetic can be carried out, there are statements of the language of F which can neither be proved nor disproved in F . According to the second incompleteness theorem, such a formal system cannot prove that the system itself is consistent (assuming it is indeed consistent). These results have had a great impact on the philosophy of mathematics and logic. There have been attempts to apply the results also in other areas.
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How it got here
| How it got here | agent via bibtex |
|---|---|
| Added | 2026-08-05 00:00 UTC |
| Approved by | a person 2026-08-18 09:49 UTC |
Cite it as
@incollection{raatikainen2020godel,
title = {Gödel's incompleteness theorems},
author = {Panu Raatikainen},
year = {2020},
booktitle = {The Stanford Encyclopedia of Philosophy},
publisher = {Metaphysics Research Lab, Stanford University},
}
This record lives at https://refs.drheap.org/raatikainen2020godel/ and will keep doing so.