Edward Feser, the distinguished Aristotelian–Thomist philosopher, has posted an excellent commentary on C. S. Lewis’s brilliant (and under-read) essay ‘Transposition’. It is hardly too much to say that Lewis’s essay describes one of the fundamental tools of thought, and Feser does much to make clear why this is necessarily so.
Lewis’s original essay:
A taste of Feser:
By “transposition,” Lewis has in mind the way in which a system which is richer or has more elements can be represented in a system that is poorer insofar as it has fewer elements. The notion is best conveyed by means of his examples. Consider, for instance, the way that the world of three dimensional colored objects can be represented in a two dimensional black and white line drawing; or the way that a piece of music scored for an orchestra might be adapted for piano; or the way something said in a language with many words at its disposal might be translated into a language containing far fewer words, if the relevant latter words have several senses.
As these examples indicate, in a transposition, the elements of the poorer system have to be susceptible of multiple interpretations if they are to capture what is contained in the richer system. In a pen and ink drawing, black will have to represent not only objects that really are black, but also shadows and contours; white will have to represent not only objects that really are white, but also areas that are in bright light; a triangular shape will represent not only two dimensional objects, but also three dimensional objects like a road receding into the distance; and so on….
You cannot properly understand a transposition unless you understand something of both sides of it. He asks us to consider a child born to a woman locked in a dungeon, who tries to teach the child about the outside world via black and white line drawings. Through this medium “she attempts to show him what fields, rivers, mountains, cities, and waves on a beach are like” (p. 110). For a time it seems that she is succeeding, but eventually something the child says indicates that he supposes that what exists outside the dungeon is a world filled with lines and other pencil marks. The mother informs the child that this is not the case:
And instantly his whole notion of the outer world becomes a blank. For the lines, by which alone he was imagining it, have now been denied of it. He has no idea of that which will exclude and dispense with the lines, that of which the lines were merely a transposition… (Ibid.)
(Though Lewis does not note it, the parallel with Plato’s Allegory of the Cave is obvious.)
… As Lewis points out, the notion of transposition is useful for understanding the relationship between mind and matter and the crudity of the errors made by materialists.