Re: help with an unknown character

From: Philippe Verdy <verdy_p_at_wanadoo.fr>
Date: Fri, 11 Jan 2013 20:01:14 +0100

2013/1/11 Jukka K. Korpela <jkorpela_at_cs.tut.fi>

> The page http://en.wikipedia.org/wiki/**Contradiction<http://en.wikipedia.org/wiki/Contradiction>(which isnít particularly convincing or otherwise important) refers to the
> LaTeX Symbol List
> ftp://ftp.funet.fi/pub/TeX/**CTAN/info/symbols/**
> comprehensive/symbols-a4.pdf<ftp://ftp.funet.fi/pub/TeX/CTAN/info/symbols/comprehensive/symbols-a4.pdf>
> which describes, in clause ď3 Mathematical SymbolsĒ, some notations used
> for contradiction. None of them resembles much the symbol in the image.
> What comes closest is \blitza, but itís still rather different, and there
> is no information of what it might be in Unicode terms.
>
In fact what is expressed is not a contradiction, but a symbol for FALSE
(opposed to TRUE).

But mathemetics also include assertions that are neither FALSE or TRUE but
UNDECIDABLE (and it can be PROVEN that such assertion is undecidable,
within a logic system with its axioms, whiuch means that you can derive two
distinct logic systems where the undecidable assertion is arbitrarily set
as TRUE or FALSE).

There's also the need to express cases where assertions have any other
probability of being TRUE or FALSE (instead of just 0% and 100%), and
you'll need a symbol to express this probability, because it is sometimes
computable, within the logic system itself. Sometimes this probability is
not absolute and could be within a range (the UNDECIDABLE state means that
the probability range is [0%..100%] inclusively). This includes cases like
the results of some operations supposed to return any number, where you'll
need the concept of "NaN" (not a number), and even some more ranges of NaN
values indicating the cause of this undecidability.

Mathematics have a lot of logic (and numeric) systems (in fact their
possible number is most probably infinite). For each of them, you need more
symbols to express your assertions. How many symbols will you need ? Each
mathemetical theory studying one of them will then need to create its own
symbols
Received on Fri Jan 11 2013 - 13:03:50 CST

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