Idea for resolving Liar’s Paradox:
In logic, sentences should be assigned circuits* instead of truth values.
Firstly, processing circuits, which execute the action described by the sentence.
“Proof” that there exists a suitable circuit for sentences such as “2+2=4“ “2+2=5” and “9^9=387420489”, exists in the form of calculators.
Secondly, circuits for checking if a truth value assignment is consistent. They receive “True” or “False” as an input, hereafter referred to as “I”, and output “True” if the assignment is consistent. This can be done by having both the processing circuit and “I” as inputs to a gate which returns “True” if they are both equal. (An equals gate.)
This is like turning the problem of evaluating the truth value of “2+2=4” into constructing a circuit that “represents” “2+2==4”.
These are necessitated by the existence of sentences which may be assigned multiple truth values. “This sentence is true.” Assigning ‘true’ would be consistent, as would ‘false’. (This sentence is unusual in that the consistent assignment circuit has the input, “I”, go into both the processing circuit, and the equals gate.)
*Several things work here. In addition to being a good place to hold a lot of technical/logical questions, circuits can be implemented fairly easily.
I came up with this when thinking through something I saw someone write on the resolving the LP (on their blog, they also wrote a book). Now I’m trying to find it again.*
What they said, paraphrased (from memory): You attempt to assign a truth value as follows: you suppose it is true. If it were true, then it would be false. So you suppose it is false. But then it would be true. At this point, they rejected this line of thinking on the grounds that, what it means for something to be true, is for there to exist something in reality that corresponds to it, and there is no operator that satisfies this criteria. So the LP is false. (This is similar to the answer that it’s “not true or false, but nonsense” (from xkcd forums results on google search, when I tried to find their blog). The author took the additional step of combining the notions of “falsehood” and “nonsense” under the label of “false”.)
When I was thinking through that, while I got their point, it sounded like a NOT-gate. That is, I figured you could assign to a sentence a circuit which takes the truth value you would assign to it, and returns what it would be if that were so. This made sense for both of the self-referential sentences I considered (LP and “This sentence is true.”), and valid assignments were fixed points. What makes LP “paradoxical” is that trying to assign it a truth value is a process that corresponds to trying to find the fixed point of a function which doesn’t have any fixed points. (It’s opposite behaves the opposite way: it has all the fixed points.) When I thought about other sentences that weren’t self-referential, this didn’t make as much sense, and that was when I came up with the other two types of circuits/(ways of thinking about this).
*EDIT: It’s fakenous.net.
Thanks to this question, I recently started thinking about how progress on open problems in math  could be made faster, at least with regard to low hanging fruit. I made a comment there about modeling the problem (how can progress be made faster) and a possible solution.
This brings me to a few questions:
Modeling the problem.
Solving the problem.
Is this a big enough deal that people want it solved? Or are people only interested in something like
a) More narrow areas with obvious value being improved?
b) The creation of a platform where people can put money on specific things that they want solved being solved/progress being made.
c) Something else?
How to test all of the above (and implement where applicable).
Meta: Should these all be posted as separate Questions? What should they be called? Have any of these questions already been asked?
 They have a certain formal/empirical quality which makes things simpler. It also might be easier to use this as a metric for ‘how good is our X  at advancing research (progress)’?
 Anything that could make a difference—a Platform, Organization, Program, a set of Math courses...
Two models of how feedback is useful, for making corrections.
1) Post quality*:
Write an article.
Re-write the article (if necessary).
Say a thing/write a post.
If responses indicates prior message was unclear, respond and explain the unclear part/revise post or ‘change future posts.’**
*Intended generally. May also apply to books, etc.
** This is a subset of (possible) responses, because it is still about communicating the same idea/s, rather than doing something new.
Some ideas on structure:
“Posts” are usually “about themselves”. For example, SSC has posts with no comments section. For counter-examples, see posts like Reasonable Explanations—the author is interested in comments that fit a certain format, the body of the post has the rules for (top-level) comments, and the author posts a comment (that fits the format) as a starter.
This is a format for a “Discussion”. If an author includes both the rules and the starter in the “post” body, it’s still a “Discussion”. If the OP expounds an idea, and includes examples (usually of a certain form) and suggests people comment other things they think might be examples, that is both a “Post” and a “Discussion”.
The Monthly threads are of course “Discussion”-like, though they’re more free form—a “Discussion” with no rules*.
*Since this is LessWrong, both LessWrong’s rules apply, and ways people here prefer things be discussed—this is why “The Sequences” are emphasized. The second type, not being laid out in a short explicit set of rules are at times “broken”, leading to conflict.
The value of structure, including linearity. (A lens.)
Some (if not all) sites are about ideas. This site does it by “one-off” methods for presenting ideas. These may be contrasted with systems that present an idea, but (may) continually change the presentation (non-automatically), such as wikis. What might a site look like if it tried for more integration?
(Bending the format:)
What if comments sections, rather than staying fixed in their attachments to (a) post, roamed around?
ETA: What is an actually good way of getting combinations of ideas/comparing how similar problems are solved in different fields?
From the other direction—Ideas are in posts. This is part of why re-runs exist—to send the idea out again, to reflect, and to bring comments on the idea to life again.
When a post is run the first time there are comments. When a post is re-run (unchanged), the idea may already be out there (it’s possible all the readers have read it), but there are new comments. In this way, the comments section on the re-run is still about the same thing, absent changes resulting from time, it’s just comments 2.0. It’s also fresh—when I read The Sequences, I did not read all the comments.
(Bending the format.)
Setting up a comments section so that is possible would require a redesign, and probably work against the reasons they were set up the way they are. (Which is why The Sequences were made into a book instead.) I haven’t seen a lot of sites do this intentionally. There are blogs with no comments sections anywhere, but making a set readable by making it empty is trivial.
Things that becomes “finished” (‘Posts’) versus Things that don’t (‘Lists’):
Finished: Posts/Comments are (individually) created, then submitted.
Common Exceptions: “Update” may be appended to the end, followed by content. Alternatively, changes may be made, and described in a section added to the end marked “Edit”.
Un-Finished: All Posts, All Questions, All Sequences (The Library). These lists keeps changing.
While a List may come to an end, if all Lists die (and stay dead), that’s a sufficient condition for the site to be considered dead.
That’s not to say the site would be dead if there stopped being new posts for a time—if people started revising their posts, and submitting those changes, discussion of ideas (and the life of the site) could continue—but then the currently existing posts would “living lists” while “all posts” would be dead.
The pattern seem to be “Lists”, which can go on forever, contain “items” which have a short life.
Two ways on looking at things:
1) See what this website calls, say, “Posts”. Look for patterns. (Practice → Theory.)
2) Consider different Ideas, and look at what ‘implements’ them. (Theory → Practice.)
This is why what the site designates “comments” are often referred to by users as “posts”—they implement the same idea.
(This is a list.)
Since bookmarking comments hasn’t been implemented yet, I think I’ll put them here.
(Without votes so they don’t clog up space on recent discussion.)
Also, comments on these might better go on the page where they are.
Not a comment, but similar idea:
My own (long?):
https://www.lesswrong.com/posts/9FNHsvcqQjxcCoJMJ/shortform-vs-scratchpad-or-other-names#GKuKJFnvDuinjWGYd Some names.
Google docs are good for saving content on the fly.