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", by analogy to ∃)
- ⊥ (inverted ⊤)
I had always assumed that ∃ stood for "E" in "Existential" / "there Exists", but Peano wrote and introduced this symbol in French, not using any words beginning 'E':
Mais nous préférons l'indiquer par la nouvelle notation
Ǝa
qu'on peut lire « il y a des a ».
- Formulaire de mathématiques, Peano (1897)
So why did he choose an inverted "E"?
Earliest Uses of Symbols of Set Theory and Logic
What came first, the $\forall$ or the $\exists$?