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There are two ways of thinking about the problem.
1. You see the problem as decision theorist, and see a conflict between the expected utility recommendation and the dominance principle. People who have seen the problem this way have been led into various forms of causal decision theory.
2. You see the problem as game theorist, and are trying to figure out the predictor's utility function, what points are focal and why. People who have seen the problem this way have been led into various discussions of tacit coordination.
Newcomb's scenario is a paradox, not meant to be solved, but rather explored in different directions. In its original form, much like the Monty Hall problem, Newcomb's scenario is not well stated to give rise to problem with a calculated solution.
This is not a criticism of the problem, indeed it is an ingenious little puzzle.
And there is much to learn from well defined Newcomb like problems.
Without a theory of focal points, it is very hard to analyze this interaction.
One point, however, is very clear - the slight change away from symmetry reveals two agents arguing over what should be focal, without the slightest interest in a Nash equilibrium/
Could become the new model to replace peer reviewed paper journals.
This is not a prisoner's dilemma. The nash equilibrium (C,C) is not dominated by a pareto optimal point in this game.
Although an interesting game, it requires interpersonal comparisons of utility to make your point that the Nash equilibrium is not as good as another outcome.
Generally, we assume that comparisons already show up in the utility functions of each player.
BTW, I think your non-standard notation is confusing.
Alright, I am going to bite on this.
E writes: "The proliferation of modal logics in philosophy is a good illustration of one major reason: Modern philosophy doesn't enforce reductionism, or even strive for it."
The usual justification for skepticism about reductionism as a methodology had to do with the status of the bridge laws: those analytic devices which reduced A to B, whether A was a set of sentences, observations, etc. Like climbing the ladders in the Tractatus, they seemed to have no purpose, once used.
They weren't part of the reductive language, yet the they were necessary for the reductive project.
Carnap was probably the last philosopher to try for a systemic reduction, and his attempts floundered on well known problems, circa 1940.
E writes: "Consider the popular philosophical notion of "possible worlds". Have you ever seen a possible world? Is an electron either "possible" or "necessary"?"
Kripke's essay on possible worlds makes it clear that there is nothing mysterious about possible worlds, they are simply states of information. Nothing hard.
E writes: " If there was a repository of philosophical work along those lines - not concerned with defending basic ideas like anti-zombieism, but with accepting those basic ideas and moving on to challenge more difficult quests of naturalism and cognitive reductionism - then that, I might well be interested in reading."
Professional philosophers are not scientists, but rather keep alive unfashionable arguments that scientists and technicians wrongly believe have been "solved", as opposed to ignored.
You are not suited for philosophical abstraction because you primarily want to build something. Get on with it, then and stop talking about foundations -which may not exist. Just do it.
Eliezer Yudkowsky writes: "I think that's the closest I've ever seen life get to imitating a Raymond Smullyan logic puzzle."
You might find this interesting, then:
http://www.bizop.ca/blog2/due-diligence/what-is-too-goo.html
I think much of our signaling life needs to be informed by Smullyan puzzles.
You guys really need to get a competent commenting system: so far, your reliance on typepad plain sucks.
There are a number of good plugins which will allow you to have a serious commenting system, further your own academic goals, and not piss off most people trying to get something out of being here.
Just saying ...
Sorry, have you argued someplace else for either reduction or eliminative materialism?
Your use of your blog is very similar to mine. In my previous life as an academic, I never submitted papers until they were perfect - and even when they were accepted I wanted them to be even better. Good way to have to change careers. I find that by writing simple little ideas on my blog, collecting examples, and refining several big picture points, I am far more productive. It also helps that the blogging readers are not complete sticklers for correct grammar!