The Genealogy of '$\lor$'

Landon D. C. Elkind; Richard Zach

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arXiv · 2012.06072

The Genealogy of '$\lor$'

Landon D. C. Elkind·Richard Zach

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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.

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Landon D. C. Elkind, Richard Zach. 2020-12-11. The Genealogy of '$\lor$'. https://arxiv.org/abs/2012.06072

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