Correa Moylan Walsh (1862–1936) was a monetary economist of the early twentieth century, mostly remembered for his contributions to the theory of index numbers. Francis Ysidro Edgeworth (1845–1926) was a renowned mathematical economist, remembered as one of the great masters of the discipline. Walsh was an adamant defender of a deterministic, test approach to the theory of index numbers, whereas Edgeworth favored probabilistic approaches and thought index-number theorists should not close themselves to alternative methods. Holding contrasting views about the making of index numbers, they engaged in a fierce debate in the first half of the 1920s—a period marked by several quarrels on the subject. The main points in dispute between Walsh and Edgeworth were the existence of an ideal formula for index numbers and the use of probability in the measurement of price variations. The goal of this article is to explore this debate and its underpinnings. It is argued that the main points of contention between them relate to their conflicting perspectives on the nature of index numbers.