Which came first, the ##\exists## or the ##\forall##?

1MileCrash · Jul 27, 2013

I've always imagined that some mathematician or logician was looking for a cool way to write these quantifiers, and one of the following scenarios happened:

1.)

"Hey, I know, for "For All," I'll just take the letter "A" and flip it vertically, giving me this lovely ##\forall##. Then I'll just do the same thing with the letter "E" for "There Exists."

But wait, the letter "E" is vertically symmetric, it'll look the same!" *flips it horizontally instead.

2.)

"Hey, I know, for "There Exists," I'll just take the letter "E" and flip it horizontally, giving me this lovely ##\exists##. Then I'll just do the same thing with the letter "A" for "For All."

But wait, the letter "A" is horizontally symmetric, it'll look the same!" *flips it vertically instead.

So the question is, what came first, the ##\forall## or the ##\exists##?

micromass · Jul 27, 2013

From wiki:

Peirce's approach to quantification also influenced William Ernest Johnson and Giuseppe Peano, who invented yet another notation, namely (x) for the universal quantification of x and (in 1897) ∃x for the existential quantification of x. Hence for decades, the canonical notation in philosophy and mathematical logic was (x)P to express "all individuals in the domain of discourse have the property P," and "(∃x)P" for "there exists at least one individual in the domain of discourse having the property P." Peano, who was much better known than Peirce, in effect diffused the latter's thinking throughout Europe. Peano's notation was adopted by the Principia Mathematica of Whitehead and Russell, Quine, and Alonzo Church. In 1935, Gentzen introduced the ∀ symbol, by analogy with Peano's ∃ symbol. ∀ did not become canonical until the 1960s.

http://en.wikipedia.org/wiki/Quantification

1MileCrash · Jul 27, 2013

Another mystery dispelled by wikipedia.

AlephZero · Jul 27, 2013

1MileCrash said: ↑

But wait, the letter "E" is vertically symmetric, it'll look the same!" *flips it horizontally instead.

But wait, the letter "A" is horizontally symmetric, it'll look the same!" *flips it vertically instead.

True but probably irrelevant. Both symbols are rotated through 180 degrees.

Before computer typesetting, using metal type "upside down" was an easy way to get new symbols.

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Which came first, the ##\exists## or the ##\forall##?

1MileCrash

micromass

1MileCrash

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