A philosopher claims: 'It is necessarily true that water is H₂O.' How does possible worlds semantics represent this claim?
AThe claim is true in our world but stipulated to be false in some hypothetical worlds
BThe claim is true in all possible worlds — there is no accessible world where water is not H₂O
CThe claim is verified by the fact that we can conceive of a world without H₂O
DThe claim means only that H₂O is the empirically correct description in the actual world
In possible worlds semantics, 'necessarily P' means P is true in all accessible worlds. For metaphysical necessity (where the accessibility relation is universal), 'necessarily water is H₂O' means there is no possible world where water is something other than H₂O. This is distinct from conceivability — one can conceive of XYZ oceans, but conceivability doesn't settle metaphysical possibility. Kripke argued that true identity statements like this are necessarily true.
Question 2 Multiple Choice
Which of the following best captures the difference between modal realism and ersatzism about possible worlds?
AModal realists think possible worlds are useful fictions; ersatzists think they are real
BModal realists (Lewis) hold that other possible worlds are concrete entities like the actual world; ersatzists hold they are abstract representations
CModal realists define necessity in terms of what we can imagine; ersatzists use formal logic
DModal realism is a view about physics; ersatzism is a view about mathematics
David Lewis's modal realism holds that possible worlds are concrete, spatiotemporally isolated universes — as real as our world, just causally inaccessible to us. Ersatzism (held by most philosophers) treats possible worlds as abstract objects — sets of propositions, maximal consistent descriptions — that represent ways things could be without being concrete realities. The debate concerns ontological status, not the utility of possible worlds as a formal tool.
Question 3 True / False
Accepting possible worlds semantics as a formal framework commits a philosopher to modal realism — the view that other possible worlds are concrete entities.
TTrue
FFalse
Answer: False
This is the central misconception to avoid. Possible worlds semantics assigns truth conditions to modal statements — 'possibly P' is true iff P is true in some accessible world — and this works equally well whether worlds are Lewisian concrete universes or abstract ersatz representations. Many philosophers use possible worlds semantics while remaining committed ersatzists. The metaphysical question of what worlds ARE is separate from the semantic question of how modal claims are evaluated.
Question 4 True / False
In possible worlds semantics, 'possibly P' is true if and only if P is conceivable — that is, we can coherently imagine a world where P holds.
TTrue
FFalse
Answer: False
Conceivability and metaphysical possibility come apart. Conceivability is an epistemic notion — what a mind can entertain without apparent contradiction. But something can be conceivable yet metaphysically impossible: one can conceive of water that is not H₂O (before knowing chemistry), but Kripke argues such a world is not genuinely possible if water's identity with H₂O is necessary. Possible worlds semantics tracks metaphysical possibility, not the limits of human imagination.
Question 5 Short Answer
Explain how the possible worlds framework can function as a useful tool for analyzing modal claims without requiring any commitment to a particular view of what possible worlds really are.
Think about your answer, then reveal below.
Model answer: Possible worlds semantics provides truth conditions: 'necessarily P' is true iff P holds in all accessible worlds; 'possibly P' is true iff P holds in some accessible world. These conditions allow evaluating modal arguments, checking validity in Kripke models, and analyzing counterfactuals — regardless of whether 'worlds' are concrete Lewisian universes or abstract ersatz representations. The framework specifies the role possible worlds must play without specifying their intrinsic nature. The metaphysics matters only when seeking a fully reductive account of modality.
An analogy: a mathematician can use the real number line to solve equations without settling what numbers ultimately are (Platonic objects? Structuralist positions? Fictionalist tools?). Similarly, philosophers use possible worlds to evaluate modal reasoning without settling foundational questions about their ontology. The semantic tool works for its purpose regardless of the metaphysical background theory.