Lois Lane believes Superman can fly. Superman is Clark Kent. What can we correctly conclude?
ALois Lane believes Clark Kent can fly, because Superman and Clark Kent are the same person
BWe cannot conclude that Lois Lane believes Clark Kent can fly, because the belief context is opaque to reference
CThe sentence 'Superman is Clark Kent' must be false, since it leads to a contradiction about Lois's beliefs
DLois Lane is irrational for having inconsistent beliefs about the same individual
The belief context 'Lois Lane believes...' is referentially opaque: substituting 'Clark Kent' for 'Superman' can change the truth value even though they refer to the same person. In extensional contexts, co-referential terms are interchangeable. But beliefs are about how one *represents* an individual, not merely which individual it is. Lois represents 'Superman' and 'Clark Kent' under different modes of presentation — which is why she can believe one thing about the superhero without believing it about the mild-mannered reporter.
Question 2 Multiple Choice
Which of the following contexts is extensional — that is, allows free substitution of co-referential terms without changing truth value?
A'It is necessarily true that the number of planets is greater than 7'
B'Maria knows that the morning star is visible at dawn'
C'The evening star is a planet' (given that the evening star = the morning star, which is a planet)
D'John hopes that Hesperus will be bright tonight'
Option C is a simple extensional context: no propositional attitude verb, no modal operator. If the morning star is a planet and the morning star = the evening star, substitution preserves truth — the evening star is also a planet. Options A, B, and D are all intensional: 'necessarily' creates a modal context (what is necessarily true of 9 is not necessarily true of 'the number of planets,' a contingent fact), 'knows' and 'hopes' create propositional attitude contexts. In all three, substituting co-referential terms can fail.
Question 3 True / False
Intensional contexts like 'believes that' are opaque because expressions within them lack determinate truth values.
TTrue
FFalse
Answer: False
Opacity has nothing to do with truth values being undefined. 'Lois Lane believes Superman can fly' has a perfectly determinate truth value — true or false depending on Lois's mental states. What opacity means is that the truth value of the whole sentence depends on more than just the referents of the terms within it; it depends on the sense or mode of presentation under which those referents are given. Intensional semantics is required not because meaning breaks down, but because purely referential semantics is insufficient to capture what these sentences are about.
Question 4 True / False
The discovery that 'Hesperus = Phosphorus' (both refer to Venus) is informationally trivial, just like 'Hesperus = Hesperus.'
TTrue
FFalse
Answer: False
This is Frege's original motivating example for the sense-reference distinction. 'Hesperus = Hesperus' is trivially true — it follows from the logical law of identity. But 'Hesperus = Phosphorus' was a genuine astronomical discovery: ancient astronomers tracking the evening star and the morning star did not initially know they were the same object. The two names have the same reference (Venus) but different senses — different modes of presentation. Informativeness is a function of sense, not reference, which is why identity statements can be both true and surprising.
Question 5 Short Answer
Explain why an adequate semantic theory for natural language cannot be purely extensional, and what intensional semantics must add to handle belief and necessity contexts.
Think about your answer, then reveal below.
Model answer: A purely extensional semantics assigns meanings as referents — objects for names, truth values for sentences, sets for predicates — and predicts that co-referential expressions are always interchangeable. But belief and necessity contexts show this fails: 'Lois believes Superman can fly' and 'Lois believes Clark Kent can fly' can differ in truth value even though 'Superman' and 'Clark Kent' co-refer. Intensional semantics must assign meanings sensitive to mode of presentation — what Frege called 'sense' — or treat meanings as functions from possible worlds to extensions rather than bare extensions, allowing two co-referential names to differ in meaning.
The formal apparatus of intensional semantics — possible worlds, intensions as functions from worlds to extensions, senses as modes of presentation — reflects a genuine feature of natural language: we do not only describe the world as it is, but describe how agents represent the world, and what holds across possible scenarios. The failure of extensionality in belief and modal contexts is a window into the difference between reference (what a term picks out) and meaning (how a term presents what it picks out).