EDIT: This post has been superceeded by this one.

The doomsday argument, in its simplest form, claims that since 2/3 of all humans will be in the final 2/3 of all humans, we should conclude it is more likely we are in the final two thirds of all humans who’ve ever lived, than in the first third. In our current state of quasi-exponential population growth, this would mean that we are likely very close to the final end of humanity. The argument gets somewhat more sophisticated than that, but that's it in a nutshell.

There are many immediate rebuttals that spring to mind - there is something about the doomsday argument that brings out the certainty in most people that it must be wrong. But nearly all those supposed rebuttals are erroneous (see Nick Bostrom's book Anthropic Bias: Observation Selection Effects in Science and Philosophy). Essentially the only consistent low-level rebuttal to the doomsday argument is to use the self indication assumption (SIA).

The non-intuitive form of SIA simply says that since you exist, it is more likely that your universe contains many observers, rather than few; the more intuitive formulation is that you should consider yourself as a random observer drawn from the space of possible observers (weighted according to the probability of that observer existing).

Even in that form, it may seem counter-intuitive; but I came up with a series of small steps leading from a generally accepted result straight to the SIA. This clinched the argument for me. The starting point is:

A - A hundred people are created in a hundred rooms. Room 1 has a red door (on the outside), the outsides of all other doors are blue. You wake up in a room, fully aware of these facts; what probability should you put on being inside a room with a blue door?

Here, the probability is certainly 99%. But now consider the situation:

As an exercise, I take a scrap of argumentation, expand it into a tree diagram (using FreeMind), and then formalize the argument (in Automath). This towards the goal of creating  "rationality augmentation" software. In the short term, my suspicion is that such software would look like a group of existing tools glued together with human practices.

About my choice of tools: I investigated Araucaria, Rationale, Argumentative, and Carneades. With the exception of Rationale, they're not as polished graphically as FreeMind, and the rigid argumentation-theory structure was annoying in the early stages of analysis. Using a general-purpose mapping/outlining tool may not be ideal, but it's easy to obtain. The primary reason I used Automath to formalize the argument was because I'm somewhat familiar with it. Another reason is that it's easy to obtain and build (at least, on GNU/Linux).

Automath is an ancient and awesomely flexible proof checker. (Of course, other more modern proof-checkers are often just as flexible, maybe more flexible, and may be more useable.) The amount of "proof checking" done in this example is trivial - roughly, what the checker is checking is: "after assuming all of these bits and pieces of opaque human reasoning, do they form some sort of tree?" - but cutting down a powerful tool leaves a nice upgrade path, in case people start using exotic forms of logic.  However, the argument checkers built into the various argumentation-theory tools do not have such upgrade paths, and so are not really credible as candidates to formalize the arguments on this site.

Most propositional knowledge (knowledge of facts) is pretty easy to come by (at least in principle).  There is only one capital of Venezuela, and if you wish to learn the capital of Venezuela, Wikipedia will cooperatively inform you that it is Caracas.  For propositional knowledge that Wikipedia knoweth not, there is the scientific method.  Procedural knowledge - the knowledge of how to do something - is a different animal entirely.  This is true not only with regard to the question of whether Wikipedia will be helpful, but also in the brain architecture at work: anterograde amnesiacs can often pick up new procedural skills while remaining unable to learn new propositional information.

One complication in learning new procedures is that there are usually dozens, if not hundreds, of ways to do something.  Little details - the sorts of things that sink into the subconscious with practice but are crucial to know for a beginner - are frequently omitted in casual descriptions.  Often, it can be very difficult to break into a new procedurally-oriented field of knowledge because so much background information is required.  While there may be acknowledged masters of the procedure, it is rarely the case that their methods are ideal for every situation and potential user, because the success of a procedure depends on a vast array of circumstantial factors.

I propose below a general strategy for acquiring new procedural knowledge.  First, saturate by getting a diverse set of instructions from different sources.  Then, distill by identifying what all or most of them have in common.  Finally, improvise within the remaining search space to find something that works reliably for you and your circumstances.

The strategy is not fully general: I expect it would only work properly for procedures that are widely attempted and shared; that you can afford to try multiple times; that have at least partially independent steps so you can mix and match; and that are in fields you have at least a passing familiarity with.  The sort of procedural knowledge that I seek with the most regularity is how to make new kinds of food, so I will illustrate my strategy with a description of how I used it to learn to make meringues.  If you find cookies a dreadfully boring subject of discourse, you may not wish to read the rest of this post.

To begin, here are some Fun Psychology Facts:  

People who were asked to describe a face after seeing it are worse at recognizing the same face later.

People who are asked to describe a wine after drinking it are worse at recognizing the same wine later.

People who are asked to give reasons for their preferences among a collection of jellies are worse at identifying their own preferences among those jellies.

This effect, known as Verbal Overshadowing, occurs primarily when a principally non-verbal process is disrupted by a task which involves verbalization.  The above generalizations (and Verbal Overshadowing effects more generally), do not occur among what we can term "Verbal Experts": individuals who are as good at verbalizing the relevant process as they are at doing it implicitly or automatically.  This seems like it will be very important to keep in mind when cultivating our own Rationality.