Kripke argues that 'water is H₂O' is necessarily true. Which of the following best explains why this identity is necessary rather than contingent?
AScientists confirmed through repeated experiment that water reliably has the composition H₂O, making it a well-established law of nature
B'Water' is a rigid designator — it refers to the same substance (H₂O) in every possible world, so any world containing water contains H₂O, and anything with a different structure simply would not be water
CThe molecular structure of water cannot change because chemical bonds are governed by immutable physical laws
DMathematical truths about molecular bonding make it logically impossible for H₂O to have a different structure
Kripke's argument turns on rigid designation. Natural kind terms like 'water' pick out the same substance in every possible world — whatever has the actual molecular structure H₂O. A world with a liquid that looks, tastes, and flows like water but has a different molecular structure would not be a world containing water; it would be a world containing a water-like impostor. Therefore, in every possible world where water exists, it is H₂O. The necessity is metaphysical, not logical or empirical. Crucially, this necessity was discovered empirically (option A describes how it was found, not why it is necessary), which is Kripke's key point: necessary a posteriori.
Question 2 Multiple Choice
Before Kripke, philosophers typically assumed that necessary truths are always knowable a priori. Which pair of examples correctly represents Kripke's challenge to this assumption?
ANecessary a priori: 'All bachelors are unmarried.' Necessary a posteriori: 'Water is H₂O.'
BNecessary a priori: 'Water is H₂O.' Contingent a posteriori: 'Hesperus is Phosphorus.'
CNecessary a priori: 'Hesperus is Phosphorus.' Contingent a posteriori: 'All bachelors are unmarried.'
DNecessary a priori: 'Napoleon was exiled to Saint Helena.' Contingent a posteriori: '2 + 2 = 4.'
'All bachelors are unmarried' is the paradigm case of necessary a priori: true in all possible worlds and knowable by analysis of the concept alone, without empirical investigation. 'Water is H₂O' is Kripke's paradigm of necessary a posteriori: true in all possible worlds (because 'water' rigidly designates H₂O), but discoverable only through empirical chemistry. The other options scramble these categories. Option B wrongly makes 'water is H₂O' a priori and 'Hesperus is Phosphorus' contingent — both are necessary a posteriori on Kripke's view.
Question 3 True / False
According to Kripke, the fact that 'Hesperus is Phosphorus' was an empirical astronomical discovery shows that this identity statement is merely contingent — true in the actual world, but false in some possible world.
TTrue
FFalse
Answer: False
False, and this is exactly the confusion Kripke's account of rigid designation resolves. 'Hesperus' and 'Phosphorus' are both proper names that rigidly designate Venus — the very same planet in every possible world where it exists. Once we discover (empirically) that both names pick out the same object, the identity 'Hesperus = Phosphorus' holds necessarily: there is no possible world where Venus is both Hesperus and not Phosphorus. The discovery was empirical (a posteriori), but what was discovered is a necessary truth. Epistemic status (how we came to know it) and modal status (whether it could have been otherwise) are independent dimensions.
Question 4 True / False
A proposition is contingent if it is true in the actual world but false in at least one other possible world.
TTrue
FFalse
Answer: True
True — this is the standard definition within possible worlds semantics. 'Napoleon was exiled to Saint Helena' is true in the actual world but false in worlds where the Battle of Waterloo ends differently or where Napoleon dies earlier. 'Water is H₂O' is not contingent on Kripke's view, because it is true in every possible world where water exists. The possible-worlds framework makes precise what it means to say something 'could have been otherwise': there exists an accessible world where it is not the case.
Question 5 Short Answer
What does it mean for a truth to be 'necessary a posteriori,' and why is this concept philosophically significant? Use 'water is H₂O' as your example.
Think about your answer, then reveal below.
Model answer: A necessary a posteriori truth is one that holds in every possible world (necessary) but can only be known through empirical investigation rather than pure reason (a posteriori). 'Water is H₂O' is necessary because 'water' rigidly designates the substance with that molecular structure — any possible world containing water thereby contains H₂O. But we could not know this from the armchair; it required empirical chemistry to discover. Before the discovery, someone could coherently imagine water turning out to be XYZ rather than H₂O. After the discovery, we know that was impossible. The philosophical significance is that Kripke broke the traditional alignment between necessity and a priority, showing that the structure of reality constrains what is possible in ways that go beyond what we can know by pure reason.
Before Kripke, the dominant view was that the necessary/contingent distinction mapped neatly onto the a priori/a posteriori distinction — necessary truths are known by reason, contingent truths by experience. Kripke showed these are independent dimensions: the modal question (true in all possible worlds?) and the epistemic question (knowable without experience?) come apart. This transformed metaphysics by revealing that empirical science can discover not just what is actually the case, but what must be the case — a much stronger claim than was previously recognized.