Peano introduced a number of logical symbols still used today:
- $∨$ (from Latin vel)
- $∧$ (inverted $∨$)
This inversion of Latin letters as symbols (and inversion of symbols to signify their 'opposite' operation) was followed by later logicians:
- $∀$ (Gentzen, 1935: inverted A from "All-Zeichen" / "Für Alle", by analogy to $∃$)
- $⊥$ (inverted $⊤$)
I had always assumed that ∃ stood for "E" in "Existential" / "there Exists" (or some cognate thereof), but Peano did not appear to use any words beginning 'e' in the paragraph this symbol was introduced:
Mais nous préférons l'indiquer par la nouvelle notation
qu'on peut lire « il y a des $a$ ».
- Formulaire de mathématiques, Peano (1897)
So why did he choose an inverted "E"?