chapter  3
Perspectives on Vagueness
Pages 22

It is a mark of the educated man and a proof of his culture that in every subject he looks for only so much precision as its nature permits. (Aristotle, Nicomachean Ethics)

Two plus two equals five-for sufficiently large values of two. (Per Eric Love, source unknown)

The first page of the 1982 Report of the Committee of Inquiry into the Teaching of Mathematics in Schools (the Cockcroft Report) included, in bold type, an assertion that:

mathematics provides a means of communication which is powerful, concise and unambiguous (DES, 1982, p. 1)

and proposed the communicative power of mathematics as a ‘principal reason’ for teaching it. There was refreshing novelty in such a claim, which seemed to be justifying mathematics teaching in much the same way that one might justify the learning of a foreign language, and it did much to promote and sustain popular interest in the place of language in the teaching and learning of mathematics. Such a view of mathematics is in contrast, however, with that expressed in a more or less contemporary pamphlet issued by the Association of Teachers of Mathematics, whose authors argued that:

Everyday speech is a highly tolerant medium. This tolerance is necessary because conversation is a form of action in the world; […] Because it is a tolerant medium, everyday language is necessarily ambiguous.