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RichardKennaway comments on Open Thread: September 2011 - LessWrong
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The point of your post was that the mathematics you are doing is creating the problem, not solving it. I haven't seen any other mathematics in this thread that is solving the problem either.
Honestly, this discussion was to long ago for me to really remember what it was about well enough to discus it properly.
I have a couple of suggestions more constructive than my earlier comments.
One is that according to a paper recently cited here, placebos can work even if you know they're placebos.
The other is that if belief doesn't work for you, how about visualisation? Instead of trying to believe it will work, just imagine it working. Vividly imagine, not just imagining that it will work. This doesn't raise decision-theoretic paradoxes, and people claim results for it, although I don't know about proper studies. We don't know how placebos work, and "belief" isn't necessarily the key state of mind.
That article was probably what caused me to notice the problem in the first place and write the OP.
Visualization is probably the most promising solution, and even if it's not as strong as placebo might b worth exploring. My main problems with it is that there's still some kind of psychological resistance to it, and that I have no clear idea of what exact concrete image I'm supposed to visualize given some abstract goal description.