Wikipedia: List of lists of lists(en.wikipedia.org)
en.wikipedia.org
Wikipedia: List of lists of lists
https://en.wikipedia.org/wiki/List_of_lists_of_lists
17 comments
> The solution to this paradox was to use a set of axioms (most commonly the Zermelo-Fraenkel axioms) which do not allow the construction of such a contradictory set ...
Or one can adopt a non-well-founded set theory that admits such a set.
Or one can adopt a non-well-founded set theory that admits such a set.
Better yet, this iteratively deepening list of land-lake layers: https://en.wikipedia.org/wiki/Lake_island#Islands_within_lak...
This culminates in:
This culminates in:
The largest island in a lake on an island in a lake on an
island is a nameless, approximately 4.0-hectare (10-acre)
island at 66.687°N 70.479°W, situated within Nettilling Lake
on Baffin Island, Canada.`My favorite Wikipedia list is its list of unusual articles:
https://en.wikipedia.org/wiki/List_of_unusual_articles
https://en.wikipedia.org/wiki/List_of_unusual_articles
Reminds me (and I'm sure others had the thought) of the Awesome GitHub repo[0] which links to many of the other Awesome-* repos.
[0] https://github.com/sindresorhus/awesome
[0] https://github.com/sindresorhus/awesome
A lot of these “lists of lists” are just “Something A-M” and “Something N-Z”. That’s just a paginated list!
someone should add a list of lists of genes and subindex them all the way down. Just ruin that page.
so very lispy
I wished this was "Outline of outlines of outlines". I used to seek out those articles a lot in my free time when I was a student. It only made my hunger of knowledge grow.
https://en.wikipedia.org/wiki/Outline_of_computer_programming
https://en.wikipedia.org/wiki/Outline_of_computer_science
https://en.wikipedia.org/wiki/Outline_of_mathematics
https://en.wikipedia.org/wiki/Outline_of_history
https://en.wikipedia.org/wiki/Outline_of_linguistics
https://en.wikipedia.org/wiki/Outline_of_law
https://en.wikipedia.org/wiki/Outline_of_biology
https://en.wikipedia.org/wiki/Outline_of_science
All in one place: https://en.wikipedia.org/wiki/Special:PrefixIndex/Outline_of
Thank you, O great Wikipedia hacker!
(1) The page does link to itself, in which case it is wrongly present in the list of lists which do not link to themselves.
(2) The page does not link to itself, in which case it should be present in the list of lists which do not link to themselves.
Since both cases result in a contradiction, this means we cannot define the list of all lists which do not link to themselves, and thus any formal language (now called "naive set theory") which allows us to define such a set is logically inconsistent.
The solution to this paradox was to use a set of axioms (most commonly the Zermelo-Fraenkel axioms) which do not allow the construction of such a contradictory set, while also maintaining all the expressive power of naive set theory.
To anyone interested in this stuff (plus Gödel) I highly recommend the graphic novel Logicomix.