William Gibson of Oxford Brookes University says that I haven't quite got the hang of reductio ad absurdum (Letters, 28 August) and that I can't cry foul if he reduces to absurdity my principles by applying these to examples I had not thought of myself. But I must cry foul because this is not what a reductio ad absurdum is.
A reductio ad absurdum is the refutation of an assumption by deriving a contradiction or other necessarily false conclusion from it. The refutation must then follow logically from the point being made.
But nothing in what I said about variant spellings necessarily leads to the conclusion that my argument could be applied to mathematics or history, and no reasonable person would conclude that it did. The proof of this is that a number of such variant spellings already exist in the English language without entailing the consequences Gibson describes.
The statement of absurd conclusions, without any attempt to show that these follow logically from the argument being made, is therefore not a reductio ad absurdum; it is simply an absurd argument. It is therefore Gibson who has got this wrong.
Ken Smith, Bucks New University.