Questions: The Deductive-Nomological Model of Explanation

Question 1

A biologist explains a population decline: 'All species losing more than 30% of their habitat decline within 50 years (law). This bird species has lost 40% of its habitat (initial condition). Therefore, this population is declining.' Which statement best evaluates this as a D-N explanation?

• A. This is not a D-N explanation because D-N applies only to physics and chemistry
• B. This fits the D-N form — it has a universal law plus initial conditions that deductively entail the explanandum, though the strength depends on whether the 'law' is genuinely universal
• C. This is a D-N explanation only if the conclusion is stated as a probability, not a certainty
• D. This cannot be D-N because biological systems are too complex for deductive logic

Answer: (B)

The D-N model applies across all sciences. This argument has the required structure: (1) a universal law (all species losing >30% habitat decline), (2) true initial conditions (this species lost 40%), and (3) the explanandum (population decline) logically follows. The D-N model simply requires this formal structure. The genuine concern is empirical — whether the 'law' is truly exceptionless — but structurally this is a D-N argument. Hempel's point was that this logical structure is what makes an explanation genuinely explanatory rather than mere description.

Question 2

You can derive a flagpole's shadow length from the flagpole's height, sun angle, and laws of optics. You can also derive the flagpole's height from its shadow length, the sun angle, and the same laws. Both are formally valid D-N arguments. What does this reveal about the D-N model?

• A. Both arguments are equally good explanations — the D-N model is symmetric and complete
• B. The D-N model correctly shows that explanation and prediction are the same logical act
• C. The D-N model misses causal direction — we explain shadows from flagpoles, not flagpoles from shadows, even though both derivations are logically valid; formal deducibility alone cannot capture what makes an explanation genuinely explanatory
• D. The shadow-to-flagpole derivation is invalid because shadows cannot cause flagpoles

Answer: (C)

The flagpole case is the canonical counterexample to the D-N model. Both derivations are formally valid D-N arguments, but intuitively only one explains: the shadow is explained by the flagpole's height and the sun angle, not vice versa. The D-N model cannot distinguish them because it captures only logical structure, which is symmetric. What is missing is causal direction: explanation tracks causation — effects are explained by their causes — and causation runs from flagpole to shadow, not the reverse. This asymmetry motivates causal and unification models of explanation.

Question 3

According to the D-N model, every successful scientific explanation could, in principle, have served as a prediction of the event before it occurred.

• T. True
• F. False

Answer: True

This is the D-N model's symmetry thesis: explanation and prediction have the same logical structure. Both consist of universal laws plus initial conditions from which an event follows deductively. If you had the laws and conditions before the event, you could predict it; using those same premises after the event to show it was to be expected is explanation. The D-N model collapses explanation and prediction into the same formal act, distinguished only by temporal perspective. This was seen as a virtue — tying explanation to predictive power — but the flagpole and other cases show it also generates problems.

Question 4

The D-N model can fully account for most scientific explanations, including probabilistic, causal, and mechanistic explanations, because it is based on universal logical principles.

• T. True
• F. False

Answer: False

The D-N model handles deterministic explanations from universal laws, but faces serious limitations beyond that domain. Probabilistic laws require a different model (the Inductive-Statistical model, also Hempel's). The model cannot account for causal asymmetry (the flagpole problem). Many biological and historical explanations that scientists regard as legitimate — explaining why a species evolved a particular trait, why an empire fell — do not fit the D-N structure. The model captures something real about explanation (the role of laws and entailment) but is not a complete theory.

Question 5

What is the core insight of the D-N model of explanation, and what important feature of scientific explanation does it fail to capture?

Model answer: The core insight is that to explain an event is to show it was to be expected — that it follows as a logical consequence from true universal laws and true initial conditions. This ties explanation to lawfulness and logical necessity, and implies that explanation and prediction are symmetric (same structure, different temporal vantage). What the model fails to capture is causal direction: the D-N model cannot distinguish explaining a shadow from the flagpole's height (genuinely explanatory) from 'explaining' the flagpole's height from its shadow length (which is not explanatory). Real scientific explanation follows causal structure — causes explain effects, not vice versa — but the D-N model captures only formal deducibility, which runs symmetrically in both directions.

This gap motivated subsequent work on causal models (explaining via causal mechanisms) and unification models (explaining by subsuming phenomena under fewer, more general principles). The D-N model remains historically important as the first rigorous formal account of explanation.