Mathematical Symbols

[Peter A. McGraw]

There's nothing English in the German term "das All-Zeichen."  The
adjective all- forms compounds with just its stem, so the only thing
different about "das All-Zeichen is its hyphenation.  There is also a noun,
das All, meaning the universe.  I don't know what the upside-down A stands
for as a mathematical symbol, and only the term "das All-Zeichen" itself is
quoted in the cites from the Gentzen paper where it apparently originated,
so I don't have enough context to tell whether it means something like 'the
symbol for the universe' or more like 'the universal symbol' or 'the symbol
for everything', but there's nothing un-German about it.  The spelling,
with the unusual hyphenation possibly used to make it possible to retain
the capitalization of both elements and thus make it clear that both parts
of the coined compound are originally nouns, seems to indicate that the
coiner meant to derive it from All rather than all-.

Peter Mc.

--On Thursday, February 20, 2003 9:24 AM -0500 Laurence Horn
<laurence.horn at YALE.EDU> wrote:

> 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.



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                               Peter A. McGraw
                   Linfield College   *   McMinnville, OR
                            pmcgraw at linfield.edu