Astronomers discovered that 'Hesperus' (the bright evening star) and 'Phosphorus' (the bright morning star) both name Venus. Kripke says 'Hesperus = Phosphorus' is necessarily true. But it was discovered empirically — couldn't it have turned out to be false?
AThe statement is contingent, since it was discovered empirically and not known a priori
BThe statement is necessarily true because both names rigidly designate Venus — the same object in every possible world — so they cannot refer to distinct things in any world
CThe statement is necessarily true only by stipulation, once we decide to treat both names as synonyms
DThe statement is a posteriori contingent — it depends on astronomical facts that could have been different
'Hesperus' and 'Phosphorus' are rigid designators: both refer to the same planet (Venus) in every possible world. If the identity holds in the actual world, then in every possible world both names pick out the same object, so the identity holds necessarily. What misleads people is conflating epistemic possibility (we could have been wrong; we discovered it empirically) with metaphysical possibility (could it have been false in some possible world?). Kripke's key insight: some truths are a posteriori necessary — empirically discovered but metaphysically necessary once known.
Question 2 Multiple Choice
Scientists discover that a substance on a distant planet looks, tastes, and functions exactly like water, but turns out to be composed of XYZ rather than H₂O. On the Kripke-Putnam account, should we call this substance 'water'?
AYes — if it plays all the same functional and experiential roles as water, it qualifies as water
BYes — 'water' is defined by its superficial properties, which the XYZ substance shares completely
CNo — 'water' rigidly designates H₂O, so a chemically distinct substance is not water, even if superficially indistinguishable
DIt depends on whether the planet's inhabitants use the word 'water' to refer to it
On the Kripke-Putnam account, 'water' rigidly designates the natural kind H₂O. The term's reference was fixed by our causal-historical connection to the actual stuff, and science revealed its essential nature to be H₂O. Since 'water = H₂O' is necessary, XYZ cannot be water — it is a watery substance, playing water's functional role, but lacking water's essential nature. The essence is determined by the underlying structure science discovers, not by the cluster of superficial properties we initially associated with the term.
Question 3 True / False
The statement 'water = H₂O' is contingent, since it was an empirical discovery that could in principle have turned out differently.
TTrue
FFalse
Answer: False
This conflates epistemic and metaphysical modality. It is epistemically possible that early scientists could have been wrong about water's composition, but once we know water is H₂O, the identity holds in all possible worlds. 'Water' rigidly designates H₂O, so no possible world contains water that is not H₂O. The discovery was empirical, but what was discovered is a necessary truth — Kripke calls this an 'a posteriori necessity.' The contingency was in our epistemic state, not in the metaphysical fact.
Question 4 True / False
Kripke's framework implies that some necessary truths can only be discovered through empirical investigation rather than through a priori reasoning alone.
TTrue
FFalse
Answer: True
This is the central philosophical consequence of rigid designation: a posteriori necessary truths. Statements like 'water = H₂O' and 'Hesperus = Phosphorus' are metaphysically necessary (true in all possible worlds) but known only through empirical discovery. Before Kripke, philosophers generally assumed necessity and a priority went together. Kripke's analysis breaks this alignment: the necessary/contingent distinction (metaphysics) crosscuts the a priori/a posteriori distinction (epistemology) in both directions.
Question 5 Short Answer
How does rigid designation provide a semantic foundation for essentialism? Explain how fixing an object's referent across possible worlds enables us to ask what properties that object necessarily has.
Think about your answer, then reveal below.
Model answer: Rigid designation fixes the reference of a name to the same individual in every possible world where that individual exists. Once we know which individual we are tracking across worlds, we can ask: what properties are true of that individual in every possible world where it exists? Whatever is true of it in all such worlds is true necessarily — those are its essential properties. Without rigid reference, the question 'what does Aristotle necessarily have?' would be ambiguous, since descriptivist names might pick out different people in different worlds. Rigidity ensures we're asking about the same individual everywhere, grounding talk of essence in the object itself rather than in our descriptions of it.
The deep connection is that rigidity and essence are two sides of the same coin. Rigidity is the semantic claim: this name picks out the same thing in all worlds. Essentialism is the metaphysical claim: this thing has certain properties in all worlds where it exists. Once you accept rigidity, the metaphysical question of essence — what is it that this individual could not lack? — becomes tractable, with an answer determined by what science discovers about the object's nature.