Questions: The Modal Status of Identity Statements

Question 1

Before astronomers discovered that Hesperus and Phosphorus were the same planet, it seemed possible they were distinct. According to Kripke, in what sense was this 'possible'?

• A. It was both epistemically and metaphysically possible — the identity was contingent before discovery
• B. It was epistemically possible (compatible with what was known) but never metaphysically possible (there was always only one object)
• C. It was metaphysically possible because Venus could have been in a different orbit
• D. It was neither epistemically nor metaphysically possible — the identity was analytically true from the meaning of the names

Answer: (B)

Kripke's key move is distinguishing epistemic from metaphysical possibility. Epistemic possibility is about what is compatible with our knowledge: before the discovery, we couldn't rule out that they were distinct, so it was epistemically open. But metaphysical possibility is about what could have been the case in reality: 'Hesperus' rigidly designates Venus, 'Phosphorus' rigidly designates Venus, so in every possible world they refer to the same object. There is no metaphysically possible world where Hesperus ≠ Phosphorus. Option A is the mistake Kripke is correcting.

Question 2

Kripke argues that 'Hesperus = Phosphorus' is necessarily true. What is the key reason?

• A. The sentence is true by definition — the two names were introduced to mean the same thing
• B. Both names are rigid designators picking out the same object (Venus) in every possible world, so the identity cannot fail in any world
• C. Identity statements are always necessarily true, regardless of what the names designate
• D. The discovery was made by scientists, and scientific discoveries are necessarily true

Answer: (B)

The argument turns on rigid designation: 'Hesperus' picks out Venus in every possible world (not just the actual one), and so does 'Phosphorus.' Since both names rigidly designate the same object, there is no possible world in which they designate different objects, and so no world in which the identity fails. Option A is wrong because the names were introduced independently with no definitional link. Option C is too strong — 'the morning star = the evening star' uses descriptions, not rigid designators, and is not necessarily true.

Question 3

According to Kripke, most necessary truths are knowable a priori — if something is true in most possible worlds, we can know it without empirical investigation.

• T. True
• F. False

Answer: False

False — this is precisely what Kripke refutes. 'Water = H₂O' is necessarily true (water is H₂O in every possible world, since 'water' rigidly designates the substance that actually has that chemical structure) yet it is a posteriori: we had to do chemistry to discover it. Kripke breaks the traditional alignment of necessity with a prioricity, showing that these are independent dimensions: some truths are necessary AND a posteriori, others are contingent AND a priori.

Question 4

If 'water = H₂O' is a necessary truth, then there is no possible world in which water is not H₂O.

• T. True
• F. False

Answer: True

True, on Kripke's account. 'Water' rigidly designates the substance that, in the actual world, has the chemical structure H₂O. Since rigid designators pick out the same thing across all worlds, 'water' picks out H₂O-stuff in every possible world. So there is no world where water exists but lacks that chemical structure. A world with a clear drinkable liquid that isn't H₂O would have a different substance — call it 'XYZ' — but it wouldn't be water. This is counterintuitive precisely because it feels like water could have turned out to be something else, but that's an epistemic intuition, not a metaphysical one.

Question 5

Explain in your own words why 'water = H₂O' is both a posteriori and necessarily true, and what this shows about the relationship between necessity and a prioricity.

Model answer: It is a posteriori because we had to do empirical chemistry to discover it — there was no way to figure out that water is H₂O by analyzing the concept of water alone. It is necessarily true because 'water' is a rigid designator that picks out H₂O in the actual world, and therefore picks it out in all possible worlds. What this shows is that necessity and a prioricity are independent dimensions: something can be necessary (true in all possible worlds) while also being discoverable only through experience. The old assumption that necessary = a priori and contingent = a posteriori is wrong.

The deeper point is the epistemic/metaphysical distinction. Before chemistry, it was epistemically possible that water wasn't H₂O — our concepts didn't rule it out. But the metaphysical structure was fixed: there was always one substance with that chemical makeup. 'Possible' in the epistemic sense and 'possible' in the metaphysical sense come apart, and Kripke's account of rigid designation explains why.