Moore's Paradox

In second grade, I received a poor evaluation on a particular homework assignment. We were given a worksheet, which featured sentences such as:

A) It is raining outside
B) "I like chocolate."
C) "That girl is beautiful."

The teacher told us to ignore whether or not the statements were true, but to focus on whether or not each fell into the purview of fact or opinion. I sincerely believed that A and B were facts, and that C was an opinion. (B was apparently an opinion).

I'm still a bit stubborn about that answer. Can't a lie detector determine, within a certain margin of error, whether or not the anonymous kid indeed enjoys chocolate cake? I suppose this semantic confusion can be avoided with clearer instructions about which aspect of the sentence to evaluate, or with a less hopelessly literal third grader (The girl in the sentence is stating her opinion. Get over it, kid).

In his new communal blog, Less Wrong, Eliezer Yudkowsky mulls over Moore's paradox, Wittgenstein's favorite reflection on assertion versus belief: "It's raining outside but I don't believe that it is." Yudkowsky expounds on this contradiction to differentiate between belief and endorsement. He says,

"It's not as if people are trained to recognize when they believe something. It's not like they're ever taught in high school: "What it feels like to actually believe something - to have that statement in your belief pool - is that it just seems like the way the world is. You should recognize this feeling, which is actual (unquoted) belief, and distinguish it from having good feelings about a belief that you recognize as a belief (which means that it's in quote marks)."

I think that the mix-up largely stems from failing to juxtapose the concepts of truth/falsehood with fact (be it true or false)/opinion . Beauty is neither truth nor falsehood. It's just opinion- until we are given a more specific, working definition (i.e. "Beauty is the democratic consensus").

As Yudkowsky mentions, we use the word "believe" to express a lot of different concepts. For example, we say,

1) "I believe she is beautiful"- If we ignore the fussiness of my third-grade self, we'll call this an opinion, neither true nor false. Perhaps in need of clearer criteria, but certainly not irrational.

2) "I believe it is raining" -A statement concerning fact, which can be proven as true or false", and

3) "I believe in life after death"- A statement concerning fact, which cannot, however, be reasonably proved or disproved.

We also use the word "believe" ways that are difficult to categorize- say, "I believe in liberal/conservative political policy."
Is this statement purely an endorsement that requires no need for evidence (Example 1)?, Or, given clear-cut, agreed-upon goals, can evidence show that one ideology is likely superior (Example 2)? Or is this divide, with its necessary "whole world as laboratory" scientific design so hopelessly flawed and impossible that it is akin to attempting to prove "life after death."(Example 3)?
2 plus? 3 minus?

Is the term "belief" better used to make assertions regarding facts, or is the word better spared for expressions of mere opinion? My problem is that, despite having passed third grade, I'm still not always sure about the category in which my pronouncements belong.