Propositional Attitudes

Let's say that there is someone, S, who believes a proposition, P. So there are two ways that S can believe a proposition:

(1) S believes P.
(2) S believes that P.

It is debated what the two differences are between (1) & (2), but one of the differences is that in (2) we would consider it referentially opaque. To illustrate what it means to be referentially opaque take the following example.

(3) Lois Lane loves Superman.
(4) Superman = Clark Kent.
(5) Lois Land does not love Clark Kent.

We could further elaborate on (3) & (5) into the following:

(3') Lois Lane believes that - 'I love Superman' - in English.
(5') Lois Lane believes that - 'I don't love Clark Kent' - in English.

Now we have a problem because Lois Lane has conflicting beliefs. She both loves and doesn't love Superman. How do we explain this? Usually we describe this as intensional beliefs. Although Superman and Clark Kent are members of the Kal El extension, they both present different intensional beliefs. So, 'Superman' is a different intension than 'Clark Kent'. Even though Superman = Clark Kent, since intensional attitudes are referentially opaque we cannot substitute Clark Kent and Superman.

However there is the Millian position that claims that a name exhausts its referent. So for the Millian one could take the name either 'Superman' or 'Clark Kent' and substitute them for each other. Although Lois Lane may not know that Clark Kent = Superman, Lois Lane does love the referent of 'Superman' and it just so happens that the referent of 'Superman' is the referent of 'Clark Kent'.

So, I will post more on this latter on how it relates to the gospel and belief in Jesus.