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Flatland’s critique of analogy is reminiscent of Thomas Reid, writing in 1767. Reid noted both the utility and frequency of analogical thinking, and the way in which it was particularly common in figuring thought itself as a material parallel to make clear the abstract: ‘The second, and the most common way in which men form their opinions concerning the mind and its operations we may call the way of analogy. There is nothing in the course of nature so singular, but we can find some resemblance, or at least some analogy, between it and other things with which we are acquainted. The mind naturally delights in hunting after such analogies, and attends to them with pleasure.’ Thomas Reid, An Inquiry into the Human Mind on the Principles of Common Sense, ed. by Derek R. Brookes (Edinburgh: Edinburgh University Press, 1997), p. 203.

Reid argued that philosophers were not immune from such a tendency and that until Descartes philosophy was liable to ‘materialize the mind and its faculties.’  (209) He doubted that many were capable of the rigorous reasoning required to reach concepts by other means: ‘If one attentively examines the systems of the ancient philosophers, either concerning the material world or concerning the mind, he will find them to be built solely upon the foundation of analogy.’ (204)

Intriguingly, in the same text from which these lines are taken Reid set out a thought experiment in which a race of two-dimensional beings he called Idomenians, confined to the surface of a sphere and having only the sense of sight, were unable to conceive of a three-dimensional geometry.

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