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timtyler comments on You cannot be mistaken about (not) wanting to wirehead - Less Wrong
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How about if X is a set of assertions that logical tautologies are true:
http://en.wikipedia.org/wiki/Tautology_(logic)
http://en.wikipedia.org/wiki/Tautology(logic)#Definitionand_examples
An example along similar lines to this post would be: you can't be wrong about thinking you are thinking about X - if you are thinking about X.
http://www.spaceandgames.com/?p=27
Now that is a overconfidence/independent statements anecdote I'll remember. The '7 is prime probability 1' part too.
Nah, these are not "independent" statements, they are all much the same:
They are "I want X" statements.
P v -p is disputed, so someone is wrong there. Also, if you have ever done a 10+ line proof or 10+ place truth table you know it is trivially (pun intended) easy to get those wrong.
I think the concept of a thought and what it is for a thought to be about something needs to be refined before we can say more about the second example. To begin with, if I see a dragonfly and mistake it for a fairy and then start to think about the fairy I saw, it isn't clear that I really am thinking about a fairy.