I gave a talk in Chicago on using Ideological Turing Tests to avoid some mindkill-y problems and have better, more interesting arguments. The video is now up.

In an Ideological Turing Test, you answer one set of questions honestly and another as your best model of your ideological opponent. It's a nice way to spot and burn strawmen and to get curious about why your opponent thinks the thing zer does instead of just angry that they won't concede. Other material included: tips on skipping generic argument scripts and cribbing from LARPing to build a line of retreat.

Very interesting list, thanks Louie!

I just randomly clicked on a few links for online courses, and it seems there's at least one issue: The "Probability and Computing" part points to "Analytic Combinatorics, Part I" coursera course, which is not about probability at all. The MIT and CMU links for this part seem wrong too. Someone should carefully go through all the links and fix them.

Awesome summary, thanks!

The funny thing is, that the rationalist Clippy would endorse this article. (He would probably put more emphasis on clippyflurphsness rather than this unclipperiffic notion of "justness", though. :))

You just say: 'For every relation R that works exactly like addition, the following statement S is true about that relation.' It would look like, '∀ relations R: (∀x∀y∀z: R(x, 0, x) ∧ (R(x, y, z)→R(x, Sy, Sz))) → S)', where S says whatever you meant to say about +, using the token R.

I would change the statement to be something other than 'S', say 'Q', as S is already used for 'successor'.

Mainstream status:

This is meant to present a completely standard view of semantic implication, syntactic implication, and the link between them, as understood in modern mathematical logic. All departures from the standard academic view are errors and should be flagged accordingly.

Although this view is standard among the professionals whose job it is to care, it is surprisingly poorly known outside that. Trying to make a function call to these concepts inside your math professor's head is likely to fail unless they have knowledge of "mathematical logic" or "model theory".

Beyond classical logic lie the exciting frontiers of weird logics such as intuitionistic logic, which doesn't have the theorem ¬¬P → P. These stranger syntaxes can imply entirely different views of semantics, such as a syntactic derivation of Y from X meaning, "If you hand me an example of X, I can construct an example of Y."

I can't actually recall where I've seen someone else say that e.g. "An algebraic proof is a series of steps that you can tell are locally licensed because they maintain balanced weights", but it seems like an obvious direct specialization of "syntactic implication should preserve semantic implication" (which is definitely standard). Similarly, I haven't seen the illustration of "Where does this first go from a true equation to a false equation?" used as a way of teaching the underlying concept, but that's because I've never seen the difference between semantic and syntactic implication taught at all outside of one rare subfield of mathematics. (AAAAAAAAAAAAHHHH!)

The idea that logic can't tell you anything with certainty about the physical universe, or that logic is only as sure as its premises, is very widely understood among Traditional Rationalists:

... as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.

--Albert Einstein

(Audiatur et altera pars is the impressive Latin name of the principle that you should clearly state your premises.)

That's not what I thought it means. My understanding was that it's something like: "all parties should be heard", and it's more of a legal thing...

http://en.wikipedia.org/wiki/Audi_alteram_partem

I'm really itching to try this out! ;)

(Consider this as a word of encouragement. I'll to think about my predictions and will post them here if I come up with anything useful. But, in the time being I wanted to say at least this much.)

Who is the intended audience for this?

If someone has a good grasp of Bayes, it's not that informative. (Though I liked the original idea and the story. :)) But, if one doesn't already understand the math behind this, then it's just a bunch of magic numbers, I am afraid. The second half of it for sure.

The link to the "Hamlet" is broken. Not that it's hard to find, but you might still want to fix it.