What is stated by a sentence is what is logically possible or impossible. A sentence which is not true in any possible world is analytically false. It is hard to give a precise characterization of analyticity or related notions. But we take it as basic and undefined. The belief that p is incorrigible for S if and only if it is logically impossible that S believes that p and p is false.
Truth follows from incorrigibility.
But a problem arises with statements which are logically necessary. Any proposition of arithmetic would be incorrigible, yet we want to say that the person could have been mistaken. The incorrigibility has nothing to do with the believing. The first condition is the infallibility condition and the second is the irresistibility condition. The second condition fixes the counterexample in cases of large numbers.