The symbol ∄, denoting "there does not exist" (i.e., the negation of the existential quantifier ∃), was first introduced by Gerhard Gentzen. While Gentzen is primarily credited with popularizing the sans serif versions of the existential (∃) and universal (∀) quantifiers in his 1935 paper Untersuchungen über das logische Schließen ("Investigations into Logical Deduction"), he also establishe...

Short answer: there is no known “inventor” in the way there is for ∃, and the slashed existential ∄ appears to be a late 20th‑century typographical convenience rather than a symbol introduced by a specific logician. Historically, logicians wrote negation in front of the quantifier (¬∃x … or ~∃x …), not as a precomposed slashed symbol.

What we do know

• Early logic texts never use ∄. Peano (late ...

The symbol ∄ (meaning "there does not exist") appears to be a relatively modern addition to mathematical notation, though pinpointing its exact first use is challenging due to limited documentation.

Based on available historical records:

1. The existential quantifier ∃ came first: As you correctly noted, Giuseppe Peano introduced a serifed version of ∃ in his 1889 work "Arithmetices principi...

Excellent question that delves into the fine-grained history of mathematical notation. You are correct in your summary of the origins of the existential quantifier ∃. The story of its negation, ∄, appears to have a different, later origin.

Based on historical analysis of mathematical texts, the introduction and popularization of the "does not exist" sign (∄) is most strongly attributed to the **B...

I need to approach this systematically. First, I recall that the "there exists" symbol ∃ was ...

Origin of the "Does Not Exist" Symbol (∄)

The question about who first introduced the "does not exist" symbol (∄) is an interesting one in the history of mathematical notation.

From what I can determine, the symbol ∄ is a relatively modern addition to mathematical notation compared to its positive counterpart ∃. While we know that:

• Giuseppe Peano introduced the serifed existential quantifie...

A short answer is: nobody in the classical period of symbolic logic seems to have “invented” the slashed‐existential ∄ as a proper logical symbol; it simply crept into print as a typographical convenience sometime in the mid–20th century. In every one of the founders’ texts—Peano’s Formulaire (1897 ff.), Whitehead & Russell’s Principia (1910–13), Hilbert & Ackermann (1928), Gentzen (1935), Kleene...

Short answer
So far the earliest appearance that can be located in print of a struck-through existential quantifier – the sign ∄ used to mean ‘there does not exist’ – is in the first volume of Nicolas Bourbaki’s Éléments de Mathématique, Théorie des ensembles, Fascicule I (Paris: Hermann, 1939). In that text one already finds statements such as

  ∄ x (x ∈ ∅)

on page 10. Every edition of th...

Searching the literature in which the existential quantifier first appears (from Peano in the 1890’s up to the middle of the twentieth century) shows a fairly clear picture:

• Peano (from the Formulario, 1899-1908) used his “serif” ∃, but for a set–former, not for an existential quantifier, and he never put a bar through it.

• Whitehead & Russell, Principia Mathematica (1910–13) are the first ...