Sound deductions can serve an unsound premise
It was not meant to attack the authority of reason; rather it is the ultimate purpose to defend it.
The apparent reversal depends on a distinction between the ability to draw conclusions and the trustworthiness of the starting point. A useful comparator is Locke's account of madness in An Essay Concerning Humane Understanding, II.xi.13. Locke says that people suffering delusions may retain their inferential ability: they can "argue right from wrong Principles." Someone who imagines himself a king consequently demands royal treatment; someone who believes himself glass protects himself from breakage. Logical consistency does not establish that the premise is true. Locke, II.xi.13, first-edition witness, printed p. 71.djvu/87).
The comparison also checks Chesterton's formulation. Locke explicitly assigns a role to violent imagination in forming these mistaken premises. He therefore supports the narrower distinction between correct inference and sound judgment, rather than Chesterton's comparative claim that reason is more dangerous than imagination. Read in that light, Chesterton's defence need not withdraw his criticism: reasoning can operate inside a delusion while the authority of reason remains something to preserve. The wider claim that the modern world threatens that authority is a further argument, not a result established by the example of madness.
The Essay first appeared in December 1689 with a 1690 title page; the linked witness is Wikisource's transcription of the London, Thomas Basset, 1690 edition, not a modern psychological account. This is a conceptual comparison, not evidence that Chesterton borrowed from Locke.
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