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 $a$ ».

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 ∃?

  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – Danu
    Apr 17 '20 at 21:57
  • $\begingroup$ 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? $\endgroup$ Sep 29 '20 at 14:24

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".


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