Moore, Open Questions and ...is good. Imagine a situation where we do not know whether or not a speaker is being honest/speaking sincerely. We have much different expectations from sincerity than insincerity. This cannot be properly accounted for and thus grasped by virtue of focusing upon truth conditions alone.
Sincere speech does not match the world if it is mistaken. Insincere speech does not match the world, unless it is mistaken. We all know this, and our expectations and understanding regarding what we will find when we check differs accordingly.
When someone believes that there is a beer in the fridge and says "There is a beer in the fridge", they are speaking sincerely. The sincerity aspect is determined by the speaker's belief, not by whether or not what they say is true. If we know that they are sincere, and we go look in the fridge and discover that there is no beer, then we know that they were mistaken.
When someone does not believe that there is a beer in the fridge and says "There is a beer in the fridge", they are speaking insincerely. The sincerity aspect is determined by the speaker's belief, not by whether or not what they say is true. If we know that they are insincere(say we know that it is a joke), and we go look in the fridge and discover that there is no beer, then we know that they were not mistaken, because they did not believe that there was any beer to begin with.
If all we focus upon is what it takes for the statement to be true, we learn nothing about the sincerity aspect, for we've separated the statement from the speaker. That is an ill-advised move.
So the examples above were cases when we knew the sincerity/insincerity aspect. Sometimes we do not. When we're mulling through ways to check, we posit what should or should not be the case for sincere/insincere speech. What should or should not be discovered.
When a sincere speaker says "There is a beer in the fridge", unless s/he is mistaken, when we go check - there ought be a beer in fridge.
When an insincere speaker says "There is a beer in the fridge", unless s/he is mistaken, when we go check - there ought not be a beer in fridge.