Questions: Rigid Designators and Necessary Reference

Question 1

Ancient astronomers discovered that 'Hesperus' (the evening star) and 'Phosphorus' (the morning star) both refer to Venus. Given that both names are rigid designators, what is the modal status of the statement 'Hesperus is Phosphorus'?

• A. Contingently true — it could have turned out otherwise under different astronomical conditions
• B. Necessarily true — since both names rigidly pick out Venus in every possible world, there is no possible world where Hesperus exists and Phosphorus exists but they are distinct
• C. Necessarily false — a priori reasoning shows that evening and morning appearances are different objects
• D. Neither necessary nor contingent — modal logic does not apply to empirical identity statements

Answer: (B)

Because 'Hesperus' and 'Phosphorus' are rigid designators — each picks out Venus in every world where Venus exists — the identity statement 'Hesperus is Phosphorus' is necessarily true if true at all. There is no possible world where both names refer to different objects. This is Kripke's key result: the identity is metaphysically necessary even though it was an empirical discovery requiring astronomical observation. The tempting wrong answer (contingently true) conflates metaphysical necessity with epistemic a priority.

Question 2

In possible world W, the person who actually invented bifocals (Benjamin Franklin) became a farmer and never invented anything. What does the definite description 'the inventor of bifocals' refer to in world W?

• A. Benjamin Franklin — because he is the inventor of bifocals in the actual world
• B. No one — if Franklin never invented bifocals, there may be no inventor of bifocals in W
• C. Whoever invented bifocals in world W, which may be a different person or no one
• D. The description is rigid, so it still refers to Franklin in W

Answer: (C)

Definite descriptions are non-rigid: 'the inventor of bifocals' picks out whoever satisfies that description in each world, not Franklin across all worlds. In a world where Franklin never invented bifocals, 'the inventor of bifocals' may refer to someone else or to no one. This contrasts with the name 'Benjamin Franklin,' which rigidly picks out that same individual in every world where he exists, regardless of what he did or didn't do.

Question 3

Since 'water is H₂O' is a necessary truth on Kripke's account, a sufficiently skilled chemist could have known it through a priori reasoning alone, without any empirical investigation.

• T. True
• F. False

Answer: False

This is the confusion Kripke explicitly dismantles. 'Water is H₂O' is metaphysically necessary — there is no possible world where water is not H₂O — but it is not knowable a priori. It required empirical chemistry to discover that the substance we call 'water' has the molecular structure H₂O. Kripke's central contribution is separating metaphysical necessity from epistemic a priority: necessary truths can be empirical discoveries, and a priori truths can be contingent. The two categories do not coincide.

Question 4

A definite description like 'the tallest person alive in 2025' is a non-rigid designator because it could pick out different individuals in different possible worlds.

• T. True
• F. False

Answer: True

Definite descriptions are paradigm non-rigid designators: they pick out whoever or whatever satisfies their descriptive content in a given world, not a fixed individual across worlds. In the actual world, 'the tallest person alive in 2025' refers to whoever is tallest; in a possible world with a different population and growth patterns, it refers to a different person. This contrasts with a proper name like 'Elon Musk,' which picks out that specific individual in every world where he exists, regardless of whether he is tallest.

Question 5

Why does the rigidity of proper names imply that true identity statements between two names are necessarily true, rather than merely contingently true?

Model answer: If both 'A' and 'B' are rigid designators and 'A is B' is true, then both names pick out the same object in the actual world. Since they are rigid, each name picks out that same object in every possible world where it exists. Therefore there is no possible world in which A exists and B exists but they are distinct things — the identity holds across all worlds. Necessity follows directly from rigidity: rigid co-reference means the identity cannot fail in any possible world.

The contrast with descriptions makes this clear. 'The morning star is the evening star' could have been false — those descriptions could have picked out different objects. But 'Hesperus is Phosphorus' cannot be false in any world where both referents exist, because both names track Venus rigidly. The metaphysical necessity is a consequence of the names' semantic behavior, not of any contingent astronomical facts.