Questions: Counterfactual Conditionals and Similarity

Question 1

Why does treating 'If the match had been struck, it would have turned into a fish' as a material conditional fail to capture its falsity?

• A. Because material conditionals require both parts to be empirically verifiable
• B. Because the antecedent 'the match was struck' is false in the actual world, which makes a material conditional vacuously true — so the fish conditional would come out true, which is absurd
• C. Because material conditionals do not allow modal language
• D. Because the consequent describes a physically impossible event

Answer: (B)

A material conditional is false only when its antecedent is true and its consequent is false. When the antecedent is false, the material conditional is vacuously true — regardless of the consequent. Since counterfactuals have false antecedents by definition (they describe what didn't happen), every counterfactual would be vacuously true under the material conditional analysis. This gives us 'If the match had been struck, it would have turned into a fish' as true, which is clearly wrong. The Lewis-Stalnaker closest-worlds analysis is designed precisely to avoid this vacuity, by asking what holds in nearby worlds where the antecedent is true.

Question 2

Historians debate: 'If Napoleon had won at Waterloo, France would have dominated Europe for another generation.' According to the Lewis-Stalnaker analysis, how should this counterfactual be evaluated?

• A. By asking whether Napoleon's character, had it been different in relevant ways, would have led to such dominance
• B. By finding the closest possible worlds to actuality where Napoleon wins at Waterloo, and checking whether France dominates Europe in those worlds
• C. By consulting historical experts about what the most probable outcome of a Napoleon victory would have been
• D. By treating the conditional as equivalent to the material conditional and noting that the antecedent is false

Answer: (B)

The closest-worlds analysis evaluates a counterfactual by fixing the actual world as the reference point, identifying worlds where the antecedent holds (Napoleon wins at Waterloo), ordered by similarity to actuality, and checking whether the consequent holds in the nearest such worlds. The similarity ordering keeps past history largely fixed and allows the counterfactual consequence to unfold into the future from the point of divergence. Option A describes the backtracking reading — tracing back in time to what must have been different — which Lewis's account treats as non-standard.

Question 3

On Lewis's account of counterfactuals, the standard reading of 'If Nixon had pressed the button, something in his past should have been different' is the preferred interpretation.

• T. True
• F. False

Answer: False

This is the non-standard 'backtracking' reading of counterfactuals. Lewis's similarity ordering explicitly privileges the forward-looking reading: the closest worlds where Nixon presses the button are those where a small divergence from actual history (a 'local miracle') causes him to press it, but the past remains as it actually was. The counterfactual consequence then unfolds forward from that moment of divergence. The backtracking reading — in which we infer that something in the past must have been different to cause the pressing — is non-standard and requires special context to become the intended interpretation.

Question 4

Counterfactual conditionals play a central role in the philosophical analysis of causation, not just in the semantics of modal language.

• T. True
• F. False

Answer: True

Counterfactual theories of causation analyze 'C caused E' as 'if C had not occurred, E would not have occurred.' This makes the semantics of counterfactuals directly relevant to the metaphysics of causation. The same analysis underlies the distinction between laws of nature and accidental regularities: a genuine law supports counterfactuals (if this were copper, it would conduct electricity) in a way that an accidental generalization does not. So the machinery of possible-worlds semantics for counterfactuals is not a philosophical curiosity — it underpins fundamental questions in metaphysics and the philosophy of science.

Question 5

What work does the notion of 'world similarity' do in the Lewis-Stalnaker analysis of counterfactuals, and why is it philosophically controversial?

Model answer: World similarity is the ordering relation that determines which possible worlds are 'closest' to actuality when evaluating a counterfactual. A counterfactual 'If P, then Q' is true if Q holds in the closest worlds where P is true. Similarity does the work of distinguishing good counterfactuals from bad ones — it explains why 'the match would have lit' is true but 'the match would have become a fish' is false, even though both have false antecedents. It is controversial because 'similarity' between possible worlds is not a natural or unambiguous notion: Lewis had to impose a complex priority ordering (match of laws, then match of particular facts) to avoid counterintuitive results, and critics argue this ordering is ad hoc or itself depends on causal intuitions, making the analysis partly circular.

The core philosophical worry is that world-similarity is doing enormous theoretical work but is not independently well-defined. Lewis tried to formalize it using a hierarchy: large violations of actual laws make a world farther; matching particular facts matters but less than matching laws; small 'miracles' confined to the antecedent event are tolerated. But why should this ordering reflect genuine metaphysical closeness? And why does it produce the right temporal asymmetry (forward, not backtracking)? Critics argue that Lewis's similarity ordering was reverse-engineered to match our pre-theoretical judgments about counterfactuals, rather than providing an independent analysis. This is a live dispute in the semantics and metaphysics of modality.