“if x and y are the same object, then x and y have the same properties" — frank

Superman is not Clark Kent. — T Clark

He's not? — frank

Lois Lane believing Clark Kent can or cannot fly is not a property of Clark Kent. It's not a property at all. — T Clark

A little more formally, the rule of inference =E can be stated as:

Identity Elimination Schema

Major: t1 = t2

Minor: ϕ(t1)

Conclusion: ϕ(t2)

Here t1 and t2 are expressions which refer to entities (for example, proper names of people or cities). ϕ(t1) is a sentence containing at least one occurrence of t1, and ϕ(t2) is a sentence that results from replacing at least one occurrence of t1 in ϕ(t1) with an occurrence of t2, eliminating the “=” of t1 = t2. Recurring ti presumes that ti is univocal throughout, and recurring ϕ presumes that the sentential context ϕ is not altered, syntactically or semantically, by the replacement. If these uniformity conditions are not met, then the inference scheme is being misapplied, and it is no wonder that false conclusions are derivable. For example, in the inference “The man behind Fred = the man in front of Bill; the man behind Fred saw him leave; therefore, the man in front of Bill saw him leave,” the context “saw him leave” is not uniform, since substitution of “the man behind Fred” by “the man in front of Bill” changes the reference of “him” (Fine 1989:222–3; Linsky 1967:104).

In discussing the problem with apparent substitution-failure by using =E, many examples will be drawn from the fictional story of Superman, treated as if it were true. In the story, a child from the planet Krypton, Kal-El, is sent to Earth, where physical conditions cause him to acquire superpowers. Wearing specific clothing (red cape, blue jumpsuit), Kal-El prevents disasters, rescues endangered innocents, and foils would-be perpetrators of crimes, such as Lex Luthor. People call Kal-El “Superman” when talking about Kal-El’s actions of this kind.

But Kal-El also takes a day job as a reporter, using the name “Clark Kent.” A coworker, Lois Lane, treats him with indifference in the office, but has a pronounced crush on, as she would put it, Superman, unaware they are the same individual.

The problematic examples discussed below involve ascriptions of mental states to Lois (or occasionally Lex), arrived at by applying the rule =E to the major premise “Superman is Clark” and a carefully chosen minor premise. Lois has a crush on Superman (minor premise), so, by =E, Lois has a crush on Clark. But this latter seems false, and would certainly be rejected by Lois herself. Also, Lois believes that Superman can fly, but does not seem to believe that Clark can; she hopes to see Superman again soon, but seems not much to care when she next sees Clark; she would like a date with Superman, but apparently has no interest in one with Clark; and so on — IEP

a. The number of planets = 3 squared
b. It is contingent that the number of planets = 9
c. ∴ It is contingent that 3 squared = 9. — IEP

He's Jor-el. — T Clark

Referential opacity occurs between contexts. Indeed, it can be considered part of what defines a context. Getting the scope right clears up the mess. — Banno

a. Superman is Clark Kent. Major
b. Lois believes that Superman can fly. Minor
c. ∴ Lois believes that Clark Kent can fly. a, b =E — IEP

Perhaps a slower reading of the article is called for? — Banno

You stipulated that she does. I trust you. If you now want to bring that in to doubt, go ahead, but I don't much see the point in doing so. — Banno

I don't think it's a stipulation in that context. We know what Lois believes because we know the story. It's from the narrator's point of view. That isn't available in real life. — frank

“if x and y are the same object, then x and y have the same properties"

A typical example involves Lois Lane believing that Superman can fly, but she doesn't believe Clark Kent can. Yet Superman=Clark Kent.

a. Superman is Clark Kent. Major
b. Lois believes that Superman can fly. Minor
c. ∴ Lois believes that Clark Kent can fly. a, b =E
— IEP — frank

Allow me to risk being idiotic, but perhaps part of the solution lies in thinking "Lois believes that Superman can fly" is not a property of Superman. It's a fact that you can say, but it's not a property as such.

Seems more like that statement is about a property of Lois lane — flannel jesus

There's a magical thing about belief: that it causes referential opacity. — frank

Wouldn't it be more a cause for wonderment if it created referential transparency?

Then the Superman of Lois' beliefs could be relied on to share all his properties with the actual fictional one? — bongo fury

Normally, we understand such ascriptions in the way that does not, which is why we reject (2b), but if cajoled enough (“look, she does believe Clark can fly, she just wouldn’t say it like that”), we may switch to a reading that allows substitution. In the usual terminology, this is called the de re reading, contrasting with the more common de dicto reading, which disallows substitution. Other terminology for this reading is relational, contrasting with notional; transparent, contrasting with opaque; and wide scope, contrasting with narrow scope. We turn now to explaining what distinction these labels attempt to mark. — IEP

Wouldn't it be more a cause for wonderment if it created referential transparency?

Then the Superman of Lois' beliefs could be relied on to share all his properties with the actual fictional one?

Granted that would spoil story-telling, and perhaps also Davidson's proposed intentionality test. — bongo fury

the de re reading, contrasting with the more common de dicto reading, [...] relational, contrasting with notional; transparent, contrasting with opaque; and wide scope, contrasting with narrow scope. — IEP