Definition:Universal Quantifier/Historical Note
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Historical Note on Universal Quantifier
The symbol $\forall$ for the universal quantifier was first used by Gerhard Karl Erich Gentzen in 1935: Untersuchungen über das logische Schließen. II (Math. Z. Vol. 39 (3): pp. 405 – 431).
He invented it in analogy with the existential quantifier symbol $\exists$ which he borrowed from Bertrand Russell.
Russell himself used the notation $\paren x$ for for all $x$. See his 1908: Mathematical Logic as Based on the Theory of Types (Amer. J. Math. Vol. 30: pp. 222 – 262).
Sources
- 1908: Bertrand Russell: Mathematical Logic as Based on the Theory of Types (Amer. J. Math. Vol. 30: pp. 222 – 262)
- 1935: Gerhard Gentzen: Untersuchungen über das logische Schließen. II (Math. Z. Vol. 39, no. 3: pp. 405 – 431)
- Earliest Uses of Symbols of Set Theory and Logic in Jeff Miller's website Earliest Uses of Various Mathematical Symbols