The purpose of this article is to give an historical sense of the intellectual developments that determined the form and content of Kenneth Arrow's path-breaking work published in 1951. One aspect deals with personal influences that helped shape Arrow's own thinking. A second aspect is concerned with the early history of the general theory of relations, which is mainly centered in the nineteenth century, and also with the essentially independent modern development of the axiomatic method in the same time period. Arrow's use of general binary relations and of axiomatic methods to ground, in a clear mathematical way, his impossibility theorem marks a turning point in welfare economics, and, more generally, in mathematical economics.