# Why is the existential quantifier symbol ∃ a backwards "E"?

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

$$Ǝa$$

qu'on peut lire « il y a des $$a$$ ».

So why did he choose an inverted "E"?

• Comments are not for extended discussion; this conversation has been moved to chat.
– Danu
Apr 17 '20 at 21:57
• According to Jeff Millers page it was Russel and Heyting who introduced $\wedge$ and $\vee$. Could you add sources to your claim that it was Peano? Sep 29 '20 at 14:24