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

Question

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 $a$ ».

Formulaire de mathématiques, Peano (1897)

So why did he choose an inverted "E"?

^{Earliest Uses of Symbols of Set Theory and Logic}
^{Is the symbol for set membership $\in$ derived from greek letter $\epsilon$?}
^{Math SE: What came first, the ∀ or the ∃?}

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? — Michael Bächtold, Sep 29 '20 at 14:24

score 9 · Accepted Answer · answered Jan 14 '20 at 15:40

9

When introducing the older terminology in the previous sentence, Peano describes it thus:

... signifie "il y a des a", "les a existent"...

It seems likely this is the source of the inverted "E".

answered Jan 14 '20 at 15:40

iacob

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

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