Re: \neg



On Mon, 5 Sep 2005, Donald Arseneau wrote:

> "DBThompson" <drdbthompson@xxxxxxxxx> writes:
>
> > That would be correct. It is the logical "not" operator.
>
> There is some interesting history that is peripherally related to
> TeX...
>
> Why is the tilde symbol used in several computer languages as
> a logical negation? A tilde should mean "approximate", if any
> interpretation is to be made.
>
> Well there was (is) a logical not symbol in the ebcdic character
> set, and it was used for its intended meaning on computer systems.
> There was no tilde in ebcdic. Ascii contains a tilde but no not.
> When the powers that be (or were) made up mappings between the
> two character sets, they decided to map between those two vaguely
> similar characters.
>
>
> --
> Donald Arseneau asnd@xxxxxxxxx
>

What year are we talking about here? I would have thought that the story
of tilde as negation must go back further than this, and probably had
something to do with what symbols were available on Bertrand Russell's
typewriter or something. Many older intro logic textbooks going back at
least to the 50s, ones that use a period for and, (x) for \forall x, and a
horseshoe instead of an arrow, use a tilde instead of the sideways L sort
of negation. Many introductory books still do use that horrible notation
.... I think because the people writing these things are basing the
notation on what was in the textbooks when they were grad students instead
of what logicians typically use nowadays. I don't have my copy of
Principia Mathematica right at hand, and haven't cracked the thing open
for years, but maybe tilde was used as the negation sign as far back as
that.

Dave DeVidi
University of Waterloo
.

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