Frege and Penand

Frege's theory and its classical destruction by Russell were briefly discussed, and the intriguing contradiction that the sot of all ordinary sets in both ordinary and not ordinary was given to expose the dangers of using sets. The Peano postulates probably provided the audience with a theory nearer to what they had expected as the answer to the original question. The two fundamental concepts are the existence of 1 and the succession of rational numbers. Transfinite numbers were briefly mentioned: these are numbers so large that they have little individual meaning to most people through ministers of finance are expected.

After a few philosopher's definitions and an admission that the question remained unanswered a lively discussion took place. Professor Watson-Munro queried the necessity for postulating multiplication separately. Professor Peddy refused to tacitly assume the Peano postulates and the comments helped clarify some ideas. The discussion continued over supper but the question remained, for many a case of confusion worse confounded.

It appears that to grasp the full significance of number theory one must reject what we think we know and treat numbers us abstract Ideas rather than symbols. The lecture was too short to go far. Prof. Campbell said he had collected sufficient material for a scries of lectures, but it did indicate that the mathematician means by "a number" and suggested the lines of present-day thought on the subject.

—P.T.A.