The Genealogy of '$\lor$'

TL;DR

This paper traces the historical development of the logical symbol $\ ext{\lor}$, showing its origins in Whitehead and Russell's work and its subsequent adoption by prominent logicians, highlighting its influence in formal logic.

Contribution

It provides a detailed historical analysis of the origin and dissemination of the logical disjunction symbol $\ ext{\lor}$, connecting its use to key figures and texts in logic history.

Findings

Origin traced to Whitehead and Russell's early work

Widely adopted after Principia Mathematica

Influenced by Hilbert's formal logic

Abstract

The use of the symbol $\lor$ for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol $\lor$ in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for "or", vel. We show that the origin of the symbol $\lor$ for disjunction can be traced to Whitehead and Russell's pre-Principia work in formal logic. Because of Principia's influence, its notation was widely adopted by philosophers working in logic (the logical empiricists in the 1920s and 1930s, especially Carnap and early Quine). Hilbert's adoption of $\lor$ in his Grundz\"uge der theoretischen Logic guaranteed its widespread use by mathematical logicians. The origins of other logical symbols are also discussed.