The slogan which forms the title of this note was coined in the 1960s by the opponents of large scale university expansion. It was maintained that an increase in student numbers could only lower academic standards. The purpose of this note is to show that more can mean better or worse according to the criterion used. The theorems proved in the main part of the paper give formal statements of intuitively obvious results, but the amount of misunderstanding generated on this topic suggests that such an exposition is worthwhile. The conclusion of the note must be that comparisons of academic achievement, based on varying proportions admitted to higher education, should be interpreted with great care.