What is the origin of the quantifier symbols ∀ and ∃?

Question

It's pretty natural how they stand for the phrases "For ∀ll" and "There ∃xists", but I was wondering who was the first to use these symbols, and if they had any related meaning before this use.

Answer 1

I haven't verified these references myself, but according to this site...

Existence (existential quantifier), $\exists$:

Peano used the symbol for existence in volume II, number 1, of his Formulaire de mathematiques, which was published in 1897 (Cajori vol. 2, page 300).

Kevin C. Klement writes, "While Peano had the backwards E for a predicate of classes, Russell was the first to use the backwards E as a variable binding operator, and there are the wonderful manuscripts printed in CPBR vol 4 in which Russell's makes large dots out of Peano's backwards epsilons to change over from the Peano-notation for existence to a more Fregean one."

For all, $\forall$:

According to M. J. Cresswell and Irving H. Anellis, the letter A appearing upside-down originated in Gerhard Gentzen, "Untersuchungen ueber das logische Schliessen," Math. Z., 39, (1935), p, 178. In footnote 4 on that page, Gentzen explains how he came to use the sign. It is the "All-Zeichen," an analogy with the symbol for existence for the existential quantifier which Gentzen says that he borrowed from Russell.