Abstract

Heyting is considered to be the first individual to place the previously informal logic of the Intuitionist movement on a rigorous formal foundation; he is probably the most likely candidate one might select for a book about Intuitionism. The first edition appeared in 1956, and the revisions have been brief. Only the seventh of eight sections deals with the Intuitionistic formulation of sentential and predicate logics; the first chapter is in the form of a dialogue among an Intuitonist [[sic]], Logicist, Formalist, and several supporting characters; this discussion is predominantly philosophical and deals with various views concerning the foundations of mathematics. The five succeeding chapters consider first arithmetic, spreads and species, algebra, plane pointspecies, measure and integration. The last chapter considers two controversial subjects—infinitely proceeding sequences and negationless mathematics. There is a bibliography containing references of recent as well as classical articles, an index and glossary of symbols. The reader with a classical mathematical intuition will have sticky going in certain sections and should take care not to conflate his own notions with those of the author; Intuitionism and its attendant mathematics are not merely formal systems or philosophies of mathematics, they are a way of thinking.—P. J. M.