Please register and log-in to create and edit pages

### User Tools

Please register and log-in to create and edit pages

### Site Tools

Click categories to expand

A-Z listingplugin-autotooltip__plain plugin-autotooltip_bigA-Z listing

This is an alphabetical index of all content pages.

Other categories

Utilities

Also see

Wikenigma supports:

Feeds etc
sitemap file
A-Z listing (archived)

# Gödel's incompleteness theorems

“Gödel proved that, within any axiomatic framework for mathematics there are mathematically true statements that we will never be able to prove are true within that framework.”

Source: Marcus du Sautoy, What We Cannot Know: Explorations at the Edge of Knowledge

Gödel developed two theorems dealing with the subject :

“The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of the natural numbers. For any such formal system, there will always be statements about the natural numbers that are true, but that are unprovable within the system.
The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.”

Further info at Wikipedia

Note: This item is one of a special case Known Unknowables i.e. in an area where it can be proved that we will never be able to resolve an answer.

## Dear reader : Do you have any suggestions for the site's content?

Ideas for new topics, and suggested additions / corrections for old ones, are always welcome.

If you have skills or interests in a particular field, and have suggestions for Wikenigma, get in touch !

Or, if you'd like to become a regular contributor . . . request a login password. Registered users can edit the entire content of the site, and also create new pages.

( The 'Notes for contributors' section in the main menu has further information and guidelines etc.)

Show another (random) page

### Page Tools

DOKUWIKI IMPLEMENTATION DESIGN BY UNIV.ORG.UK AUGUST 2021