A surprising fact is not a logical contradiction
when it suddenly becomes illogical, it has found, so to speak, an illogical truth
The lunar observer's mistake is to turn a visible pattern into an unrestricted rule. Two arms do not logically entail two hearts: the apparent deduction imports an unproved premise about universal symmetry. The hedges 'so to speak' and 'if one may say so' therefore matter. Chesterton's analogy defends truths that defeat an expectation, rather than statements that are simultaneously true and false in the same respect. Later in this chapter he expressly says that the opposed passions are not really inconsistent (the paragraph beginning 'Paganism declared that virtue was in a balance'). Chesterton, Orthodoxy, chapter VI.
A useful theological comparison is Aquinas, Summa theologiae I, question 1, article 8. He allows reasoning from revealed principles and holds that genuine demonstration cannot establish the contrary of a truth of faith; reason can also clarify doctrine and answer objections. This supports the distinction between exceeding ordinary expectations and licensing contradiction. It does not establish that Chesterton derived this image from Aquinas. Aquinas's medieval discussion is inspected here in New Advent's English transcription, not in a medieval manuscript or Chesterton's own copy. Article 8, answer and reply to objection 2.
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