Hume's distinction inside the fairy tale
the science of mental relations, in which there really are laws, and the science of physical facts
The contrast closely resembles Hume's division between relations of ideas and matters of fact. In the Enquiry concerning Human Understanding (first published in 1748; here Peter Millican's online text following the 1777 edition), arithmetic can be established through thought, whereas denying an observed fact need not involve contradiction. Hume's examples include tomorrow's sunrise and a raised stone: considered independently of experience, its situation does not dictate downward rather than upward movement. These are particularly close comparisons with Chesterton's dawn and flying apple. Hume, §4.1–2, 4.9–13.
The comparison also exposes a difference. Hume continues to call experimentally discovered regularities laws and explains how mathematics helps apply them; he does not infer that science therefore possesses no laws. Chesterton reserves that name here for a stronger kind of necessity. His argument is consequently about what physical explanation establishes, not a demonstration that observation and calculation are useless. This is a comparison of arguments, not evidence that Chesterton borrowed directly from Hume.
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