Questions: Possible Worlds Framework

Question 1

A property P is essential to object x according to the possible worlds framework. Which analysis is correct?

• A. P is a property x has in the actual world — essential means actually possessed
• B. P is a property x has in every possible world in which x exists
• C. P is a necessary truth that applies to all objects, not just x
• D. P is a property x would have regardless of circumstances, but only in worlds similar to the actual world

Answer: (B)

On the possible worlds framework, a property is essential to an object just in case that object has it in every world where the object exists. Option 0 confuses essential with actual — an object can have many actual properties that are merely accidental (it has them in this world but could have lacked them). An accidental property is one the object has in the actual world but lacks in some possible world. The distinction essential/accidental corresponds precisely to all-worlds vs. some-world.

Question 2

Consider the claim 'It is possibly true that 7 is even.' How does the possible worlds framework evaluate this?

• A. True — we can conceive of a world where mathematics works differently
• B. False — '7 is even' is false in every possible world, making it necessarily false rather than merely actually false
• C. True if Lewis's modal realism is correct, false if abstractionism is correct
• D. Undecidable — possible worlds semantics applies to contingent claims, not mathematical ones

Answer: (B)

On the possible worlds framework, possibility means truth in at least one possible world. '7 is even' is a mathematical claim whose negation is a necessary truth — it is false in every possible world. Therefore it is not merely actually false but necessarily false (impossible). Importantly, this is a stronger claim than 'we cannot conceive of it easily.' The framework sharply distinguishes conceivability (an epistemic notion) from genuine metaphysical possibility (truth in some world).

Question 3

On the possible worlds framework, a proposition is necessarily true if it is true in the actual world and true in most, but not most, possible worlds.

• T. True
• F. False

Answer: False

Necessity requires truth in ALL possible worlds without exception — not merely most, or many, or a preponderance. A proposition true in all but one possible world would be contingent (possibly false) rather than necessary. This is one of the framework's most important contributions: making necessary truth into a precise, fully universal quantification over possible worlds rather than a vague claim about robustness.

Question 4

The possible worlds framework enables precise, non-circular definitions of what it means for a property to be essential or accidental to an object.

• T. True
• F. False

Answer: True

Before the possible worlds framework, essential properties were often defined using primitive modal notions ('essential' means 'necessarily possessed') — circular and uninformative. The framework replaces 'necessarily' with explicit quantification over possible worlds: essential = holds in all worlds where the object exists; accidental = holds in the actual world but not all worlds where the object exists. This is not circular — it reduces the modal claim to world-quantification.

Question 5

What is the fundamental difference between Lewis's modal realism and abstractionist accounts of possible worlds, and what is each account's main tradeoff?

Model answer: Lewis holds that possible worlds are concrete, spatiotemporally isolated universes existing as fully as the actual world — 'actual' is indexical, meaning just our world. This gives a fully reductive account of modality with no primitive modal notions, but it is ontologically extravagant (infinitely many concrete universes exist). Abstractionism (Plantinga, Adams) holds worlds are abstract objects — maximal consistent sets of propositions or states of affairs — that exist necessarily but non-concretely. This is ontologically conservative but must rely on primitive modal notions like 'consistent' rather than reducing them.

The tradeoff is parsimony of ideology (Lewis) vs. parsimony of ontology (abstractionists). Lewis buys clean semantics at the cost of exotic ontology. Abstractionists avoid exotic ontology but retain modal primitives in their machinery, arguably not fully explaining what modality is.