Well I do. The following Venn diagram describes the basic concepts of the theory. As far as we are being rational, classical quality means references and romantic quality means referents. The referents are sense-data, and the references are language. You may ignore the rest of the graph for now.
The following directed graph expresses an overview of the categories the metatheory is about. Note how some of the categories are rational, and others are irrational. The different categories are created by using two binary variables. One of them denotes whether the category is internalistic or externalistic, and another one whether it is rational or irrational. The arrows denote set membership. I like to think of it as "strong emergence", but formally it suffices to say it is set membership. In the theory, these categories are called continua.
Instead of using the graph we could define these relationships with formal logic. Let us denote a continuum by so that k denotes external metaspace and l denotes rationality.
Each continuum can be split into an arbitrary amount of levels. The four continuums also form reciprocal continuum pairs, which means that the referents of each continuum are the same as the referents of some other continuum, but this continuum orders the references to those referents differently. Ordering of references is modeled as subsethood in the following directed acyclic graph:
Note that in the graph I have split each continuum into four levels. This is arbitrary. The following formula defines m levels.
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That is the structure of the theory. Now, as for theorems, what kind of theorems would you like? I've already arrived at the conclusion that knowledge by description consists of members of the rational continua, and knowledge by acquaintance (aka. gnosis) consists of members of the irrational continua. But that is mainstream philosophy. Maybe you would be more interested of a formal model of "maps" and "territories", as these concepts are used frequently by you. Yudkowsky says:
Of course, it is a severe error to say that a phenomenon is precise or vague, a case of what Jaynes calls the Mind Projection Fallacy (Jaynes 1996). Precision or vagueness is a property of maps, not territories. Rather we should ask if the price in the supermarket stays constant or shifts about. A hypothesis of the "vague" sort is a good description of a price that shifts about. A precise map will suit a constant territory.
In the LW lingo, continua are "maps" and romantic quality is the "territory". Maps that form reciprocal pairs are maps about the same territory, but the projection is different - compare it to polar coordinates as opposed to rectangular coordinates. Two maps that do not form reciprocal pairs are about different territories. The different territories could could be called natural and transcendental. Insofar as we are being rational, the former is the domain of empirical science, the latter the domain of pure maths.
The merit of this theory is that irrational things, which are called subjective or mystical, are defined in relation to rational things. The ontology of irrational things is constructed by ordering the references to the referents oppositely than they are ordered in the ontology of rational things. You can see the inversion of order from the latter graph. As you can see, subjective references consist of various kinds of beliefs, and mystical references consist of various kinds of synchronicities. These are irrational, which roughly means that no argument suffices to justify their existence, but their existence is obvious.
How do you like it?
None, unless you have compelling credentials, formal theorems, or empirical results so discussion is not wasted space & breath.
Unless I missed something, I'm only seeing one out of the three things he was stating were necessary.
I've seen there's discussion on LW about rationality, namely, about what it means. I don't think a satisfactory answer can be found without defining what rationality is not. And this seems to be a problem. As far as I know, rationality on LW does not include systematic methods for categorizing and analyzing irrational things. Instead, the discussion seems to draw a circle around rationality. Everyone on LW is excepted to be inside this circle - think of it as a set in a Venn diagram. On the border of the circle there is a sign saying: "Here be dragons". And beyond the circle there is irrationality.
How can we differentiate the irrational from the rational, if we do not know what the irrational is?
But how can we approach the irrational, if we want to be rational?
It seems to me there is no way to give a satisfactory account of rationality from within rationality itself. If we presuppose rationality is the only way to attain justification, and then try to find justification for rationalism (the doctrine according to which we should strive for rationality), we are simply making a circular argument. We already presupposed rationalism before trying to find justification for doing so.
Therefore it seems to me we ought to make a metatheory of rationality in order to find out what is rational and what is irrational. The metatheory itself has to be as rational as possible. That would include having an analytically defined structure, which permits us to at least examine whether the metatheory is logically consistent or inconsistent. This would also allow us to also examine whether the metatheory is mathematically elegant, or whether the same thing could be expressed in a simpler form. The metatheory should also correspond with our actual observations so that we could figure out whether it contradicts empirical findings or not.
How much interest is there for such a metatheory?