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It is a pity that, in an article subscribing to the very necessary view that mathematics in use must be made real, Mr Conway falls into the all too common error of condemning, from a practical point of view, what he calls “abstraction for abstraction's sake”. I do not want to disagree with the spirit of change which inspires the article, but I do want to put a viewpoint on ‘abstraction’ which should show that there is a danger of throwing the baby out with the bathwater.

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