On Wed, 10 May 2006 10:25:18 -0600, Burton Samograd
<kruhft@gmail.com> wrote:
> Chris Croughton <chris@keristor.net> writes:
>
>> On Tue, 9 May 2006 20:26:30 -0400, Pavel314
>> <Pavel314@NOSPAM.comcast.net> wrote:
>> More to the point, the rest of us have limited fonts as well (I would be
>> surprised if Unicode doesn't have the backward E and upside-down A, but
>> I don't have any font which could cope).
>
> Try looking at LaTeX (actually TeX, but LaTeX is a much easier to
> manage subset of the TeX language). It was designed for creating print
> ready documents and is the standard tool for mathematicians
> typesetting equations, papers and documents. It's generally not
> WYSIWYG, but when combined with the emacs editor and specific LaTeX
> packages, you can get a very powerful document and equation editor.
I know LaTeX (and InfoTeX, and MusiTeX), but it isn't a font which can
be used with a news client, which was the point. Messages could be
posted in Unicode (or preferably UTF-8) which could convey the
appropriate characters but few people would be able to display them (and
my Xterms will only handle Latin-1 anyway).
> Although this doesn't help in the general case of writing by everyone,
> it does help in the specific case of creating documents for reading by
> others.
I would be surprised if the major technical text preparation packages
(I'm not includinf MS Word in those!) couldn't handle the extra
characters, and for most people they are easier than the TeX variants.
>>> Google "universal quantifier" to get some links to the
>>> subject. I remember doing lots of fun things with these. For example, your
>>> statement might translate as:
>>>
>>> A(x) [ RV(x) ==> BI(x) & BL(x) ] ==> E(x) [ BI(x) & BL(x) & RV(x) ]
>>
>> The sad thing is that I read that straight off and understood it, and I
>> haven't done symbolic logic for almost 30 years. It seams that I do
>> still use it internally even though I've forgotten most of the names of
>> things (I am frequently annoyed at the number of people who think that
>> [A => B] => [B => A])...
>>
>>> There were formal rules for manipulating the quantifiers and qualifiers,
>>> most of which I've forgotten long ago. Try asking for help on sci.logic or
>>> sci.math.symbolic.
>
> Pick up a book discreet mathematics, they cover all of these things
> and they are pretty cheap since they're a standard course in most
> science curriculums.
Depends where you are whether you can get textbooks cheaply. In the UK
they tend to be a lot more expensive than fiction books of the same
size...
>> Converting a natural language into symbolic logic, which seems to be
>> what the OP is wanting to do, is however not generally possible. In
>> natural language it is possible, even easy, to say things which make no
>> sense, like the canonical "This sentence is a lie" which caused a lot of
>> computers in Star Trek to blow up, which are not possible to express in
>> symbolic logic without an obvious error. And there are ambiguities like
>> "time flies like an arrow" which can't be parsed mechanically without
>> extra information (although not all languages are as bad, that phrase in
>> an inflected language like Latin is not ambiguous).
>
> Yes, it's very easy to create meaningless (as in having no true or
> false value) sentances using any language (even symbolic logic and
> mathematics).
The thing is that "time flies like an arrow" is not meaningless, its
syntax is just ambiguous, because English syntax (and that of other
natural languages) has grown organically and hasn't been designed.
Lojban and a few other created languages are unambiguous, but few people
speak those and even fewer do so in normal conversation or writing.
> Mathematics is about finding and eliminating those
> practices in the search of obtaining 'truth' (or at least truthful
> axioms from which a 'real' version of truth can be built). Of course,
> there is always a measure of faith (see Godel's Incompleteness
> Theorem, The Halting Problem, or the various other limits to logical
> truth and knowledge that have been found in other fields of study)
> that is required before truth is accepted though, so really, nothing
> can be proven to be true.
"In [pure] mathematics we never know what we are talking about nor
whether what we say is true." Mathematics has no direct connection to
things in the Real World(tm), at best it is a model of RW events but
since we don't have total information on the RW events it is an
idealised model. That's not saying that it has no use, even flawed and
incomplete models can be very useful, but the mathematicial always has
an 'out', and excuse, that the model is not the Real World(tm) thing
which it emulates...
Chris C
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