Given the height of a flagpole, the angle of the sun, and the law of light propagation, you can validly deduce the length of the pole's shadow. You can also reverse the deduction: given the shadow length and sun's angle, validly deduce the pole's height. According to the covering law model, what should we conclude — and what does this reveal about the model?
ABoth deductions are valid explanations; the covering law model correctly identifies both as explanatory
BOnly the first is an explanation; the second fails because the covering law model requires that laws run in the causal direction
CBoth deductions are valid arguments, but the second (shadow explains pole height) is not a genuine explanation — revealing that the covering law model cannot distinguish causal direction
DThe second deduction is invalid because the premises don't lawfully imply the pole's height
Both deductions are logically valid and satisfy all the covering law model's requirements: they use natural laws, the premises are true, and the conclusion follows deductively. But intuitively only the first is a real explanation — the pole's height explains the shadow's length, not vice versa. The covering law model has no resources to distinguish them because it only requires logical structure, not causal direction. This asymmetry problem shows that something is missing from the model: explanations track causal structure, but the covering law model is blind to causation.
Question 2 Multiple Choice
In the inductive-statistical model, rising barometric pressure raises the probability of an approaching storm. Does the barometer's reading explain the storm? What does this case reveal?
AYes — the I-S model says that any factor that raises the probability of an event explains it
BNo — but only because the statistical correlation isn't strong enough to meet the high-probability requirement
CNo — the barometer and the storm are both caused by low pressure; the barometer doesn't cause the storm, revealing that correlation under a law is insufficient for explanation
DYes — in statistical explanation, all that matters is the probability-raising relationship, not the causal mechanism
The barometer and the storm share a common cause (low atmospheric pressure); the barometer doesn't cause the storm. Even if the correlation is high enough to satisfy the I-S model's probability requirement, citing the barometer reading does not explain the storm — it merely correlates with it. This is the irrelevance problem: the covering law model cannot rule out explanans that are statistically associated with the explanandum but causally disconnected from it. The missing ingredient is causal structure — not just any lawful probability-raising relationship, but the right kind of causal connection.
Question 3 True / False
The covering law model requires that the laws cited in an explanation run in the same direction as causation.
TTrue
FFalse
Answer: False
False. This is precisely what the covering law model lacks and what the flagpole-shadow case reveals. The model only requires that the explanation be a valid (or probabilistically strong) argument from laws plus initial conditions. It has no requirement about causal direction. The shadow-to-pole deduction is as logically valid as the pole-to-shadow deduction; the model cannot distinguish them. The absence of any causal-direction requirement is the core inadequacy, motivating causal-mechanical accounts that build directionality explicitly into the analysis of explanation.
Question 4 True / False
The inductive-statistical model requires that the explanatory premises make the explanandum highly probable — not merely possible.
TTrue
FFalse
Answer: True
True. Hempel's I-S model specifies a high-probability requirement: the statistical law plus initial conditions must make the event to be explained very likely, not merely raise its probability somewhat. This is why a 90% cure rate for penicillin treating strep can explain a patient's recovery, while a 10% survival rate for a disease does not explain a survivor's recovery. The requirement is also what introduces the reference class problem: whether the event has high probability depends on which reference class you use to describe the patient, and there is no principled way to choose without already knowing the answer.
Question 5 Short Answer
What does the flagpole-shadow case reveal about the fundamental inadequacy of the covering law model as an account of scientific explanation?
Think about your answer, then reveal below.
Model answer: The flagpole-shadow case shows that the covering law model permits explanations to run in logically valid but causally backwards directions. You can validly deduce the pole's height from the shadow length and sun angle using the same laws, but that deduction does not explain the pole's height — the height explains the shadow, not vice versa. Since the covering law model only requires a valid deductive argument from laws, it cannot distinguish genuine from spurious explanations when the same laws support both directions. This reveals that explanation requires asymmetric causal structure, which the purely logical framework of the covering law model omits.
This case motivated a major shift in philosophy of science toward causal theories of explanation (Salmon, Woodward) that treat explanation as tracking actual causal mechanisms or counterfactual dependencies, not merely lawful logical entailment. The symmetry problem, along with the barometer irrelevance problem, are the two classic challenges that the covering law model failed to handle — showing that logical form and probabilistic laws, however necessary, are not sufficient for explanation.