Debate Discussion: "The content of belief is propositional". Gettier. Russell. Moore.
Both Gettier cases, Russell's clock, and Moore's paradox all directly involve and/or include false belief, but none of the three address that aspect as a subject matter in it's own right.
The stopped clock example shows how Russell left out a key consideration; Russell is correct to question whether or not the belief about what time it is counted as a justified belief. It's certainly true, but are we to claim that a false belief counts as good justificatory ground?
Gettier's first case shows how an accounting malpractice of a false belief can lead us astray when taking account of that false belief by virtue of using the rules of entailment. Smith believed that he would get the job and that he had ten coins in his pocket. Entailment allows us to say that he is justified in believing that the man with ten coins in his pocket will get the job, and he is. The issue here is that - when it comes to Smith's belief - "the man" has one referent and one referent only. He's talking about himself and no one else... after-all. So, because Smith's belief is about himself, and because "the man" refers to himself, the only way for Smith's belief to become true is if he got the job. He did not. Therefore, his belief about what would happen was false. This case shows us that the belief and the statement thereof have different sets of truth conditions.
It only follows that the two are not always equivalent.
Gettier's second case shows us the same as above, except it's a bit more complex. Smith believes Jones owns a Ford, and because Smith believes that he also believes that either Smith owns a Ford or Brown is in Barcelona, but he only believes that the disjunction is true because he believes Smith owns a Ford. He cannot believe it to be any other way. He does not believe that that disjunction is true as a result of the second disjunct. Rather, to quite the contrary, Smith believes the disjunction is true because he believes the first disjunct is true. So, while either disjunct can be true, and that alone makes the disjunction true as a result of either one's being so, Smith's belief is only true if Brown owns a Ford. His belief is that the disjunct is true as a result of the first disjunct being so. It is not. It is true as a result of the second. Smith's belief is false. Again, this example shows us that the belief and the statement thereof have different sets of truth conditions.
It only follows that the two are not always equivalent.
Moore's paradox shows us that we can say of another that they are in error, that they have some false belief or another, but we cannot say the same about ourselves, at least not while still believing the falsehood. That last part is what I've found to be lacking in the explanations of the problem. There are all sorts of reasons for this, self-contradiction being one. However, after becoming aware of our error, there's nothing at all stopping us from admitting that it was once raining outside and we did not believe it, or that we once believed a broken clock was working, or that we once believed that we would get the job, or that we once believed that "Either Jones owns a Ford or Brown is in Barcelona" was true because we believed that Jones owned a Ford.
All of this seems to show some inherent issues with the accounting practices...