Mathematical Symbols

Laurence Horn laurence.horn at YALE.EDU
Thu Feb 20 14:24:50 UTC 2003

```At 8:49 AM -0500 2/20/03, James A. Landau wrote:
>In a message dated 2/19/03 7:46:42 PM Eastern Standard Time,
>laurence.horn at YALE.EDU writes:
>
>>   The standard folk etymology (the one I'd always
>>   accepted) for the upside-down E is that it designates "Exists", a
>>   better translation than "Some" for the (appropriately named)
>>   existential quantifier.  (I think of it as an upside-down rather than
>>   backward E since only the former story provides a parallel with the
>>   universal.)  And the upside-down A for the universal quantifier
>>   stands for "All", as Jim notes.  The fact that the latter involves an
>>   English word ("All") supports the idea that the former should as well
>>   ("Exists"), but evidently such is not the case.
>
>An upside-down capital "E" looks exactly like a right-side-up capital E.

Again, we must be using different sorts of paper.  Here's another
test.  Put the paper on your desk, write an E.  Go the other side of
the desk, look at the paper.  You see an upside-down E (a.k.a. an
existential quantifier).  What am I doing wrong?

>
>Is there a German word "All" meaning something like the English word of the
>same spelling?

Well, there's _alle_, as in the first word of the Ode to Joy.   Of
course, the German word for 'exist' is _existieren_, so that would
preserve my intuition about the value of the two (dare I say)
upside-down vowels.

>Considering the paper in which it appeared was in German,
>which was  then the standard language for papers on mathematical logic, it
>would be a little surprising to find the authors using a symbol derived from
>English.  Russell, by the way, corresponded with German mathematicians in
>German.

So "A" (upside-down) is for "alle" rather than for "all".  Sounds plausible.

Larry

```