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| Joachim Pense... |
 Posted: Fri Nov 06, 2009 4:00 pm |
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Nathan Sanders (in sci.lang):
[quote]In article <hd1uuv$huu$02$1 at (no spam) news.t-online.com>,
Joachim Pense <snob at (no spam) pense-mainz.eu> wrote:
Nathan Sanders (in sci.lang):
But I don't care about the formal systems but about the way humans use
them.
Then we are talking past each other. I'm talking about the formal
systems as formal systems, not what happens when humans impose their
own linguistic interpretations from the outside onto those formal
systems.
I am not interested.
Then you are apparently not interested in talking about the actual
properties of formal notation systems themselves, but rather, how any
communication system can be perverted and twisted when subjected to
external influences. That is a completely different issue.
[/quote]
I don't believe that the formal notation systems you are talking about
really exist except as idealisations.
Joachim |
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| Joachim Pense... |
| Posted: Fri Nov 06, 2009 4:08 pm |
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Nathan Sanders (in sci.lang):
[quote]In article <hd1uuv$huu$02$1 at (no spam) news.t-online.com>,
Joachim Pense <snob at (no spam) pense-mainz.eu> wrote:
Nathan Sanders (in sci.lang):
English is English, regardless of how French speakers mangle its
interpretation. Likewise, mathematical notation is mathematical
notation, regardless of how humans mangle its interpretation.
No. You seem to consider mathematical notation as a prescriptivist
considers English.
Of course. Mathematical notation, unlike language, was consciously
and intentionally designed.
[/quote]
So you think that someone wrote a handbook of mathematical notation that
formally defines it and mathematicians are supposed to stick to those
rules. That somehow must have evaded my attention.
[quote]Both systems have governing rules, but for language, we don't know
what they are, so we can only describe the system through descriptive
observation.
In the case of mathematical notation however, we know the rules,
because we designed them!
[/quote]
But not in an organized plan, but as ad-hoc-addictions and changes piling
up, and governed by taste.
[quote]So of course it should be treated
prescriptively. Anything not within those rules is not a proper part
of the system, because we already have perfect knowledge of what that
system is.
I care about mathematical notation as mathematicians use it,
For the purposes of this discussion, I only care about how it's
actually defined formally, not how it gets misinterpreted from outside
the system.
Strange attitude for a linguist.
Hardly strange at all! Linguists don't describe English by how French
speakers interpret it.
[/quote]
I care about mathematical notation as Mathematicians use it.
Joachim |
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| DKleinecke... |
| Posted: Fri Nov 06, 2009 4:13 pm |
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On Nov 6, 5:36 pm, António Marques <ento... at (no spam) gmail.com> wrote:
[quote]On Nov 7, 1:08 am, LEE Sau Dan <dan... at (no spam) informatik.uni-freiburg.de
wrote:
Nathan> Your SQL example only shows what happens when a human being
Nathan> doesn't know all the facts, so to naive humans (who are not
Nathan> truly part of the system of computer languages), the results
Nathan> do indeed seem unpredictable.
See above. The SQL example is deliberately written to allow
*unpredictable order*, so that RDBMS implementations may do any
optimizations that they see it fit.
??? The SQL example you tried to mystify NS with is not 'deliberately
written to allow' anything. SQL offers many options, and one of them
is to order results. IF no ordering is demanded, then no ordering is
done. No programmer expects any kind of ordering unless explicitly
demanded for the very simple reason that there is no 'default'
ordering to assume.
Likewise, among the various types of data structures representing
collections of elements, only a small part are expected to (and do)
exhibit ordering. Meaningful order is *not* part of their contract, so
where on earth do you get ambiguity?
(Well, maybe *you*'d like to rely on their order being meaningful, but
that's *your* misunderstanding.)
[/quote]
LSD has offered an unfortunate example of ambiguity in computer
languages. The kind of ambiguity I had in mind when I first mentioned
their ambiguity is like the C statement:
a (b) ;
This can either mean evaluate function a with argument b or define b
as a variable of type a.
You can tell which one you mean if you know what a is. But that
requires you to know another fact stated somewhere else.
Another example occurs in older C within the statement
a b (c);
which declares that b is a function of one argument returning a value
of type a. The ambiguity is whether c is the name of a type or a
variable (of type int). This one is settled by fiat - if c is the name
of a type then that interpretation is used.
So far as i know all the ambiguities in C involve type names.
A computer language should not be ambiguous. A good test is to write a
compiler and declare what the compiler does is the right answer. The
attempt to define standards (to keep the various compilers at least
more or less in line) has never been completely successful. Maybe
someday it will be but I will not hold my breath until it happens. |
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| Joachim Pense... |
| Posted: Fri Nov 06, 2009 4:19 pm |
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António Marques (in sci.lang):
[quote]On 6 Nov, 18:44, Joachim Pense <s... at (no spam) pense-mainz.eu> wrote:
Why do you think higher level
programming languages exist? They have been invented because it is easier
to write complex programs in them than it is if you write machine code
that does the equivalent job. Some programming languages are flexible in
the code they accept precisely to allow for pragmatics in the code.
I must be missing something. What exactly (in programming languages)
are you talking about?
[/quote]
Pragmatics. I had given an example before.
Joachim |
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| António Marques... |
| Posted: Fri Nov 06, 2009 4:24 pm |
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On Nov 7, 2:13 am, DKleinecke <dkleine... at (no spam) gmail.com> wrote:
[quote]On Nov 6, 5:36 pm, António Marques <ento... at (no spam) gmail.com> wrote:
On Nov 7, 1:08 am, LEE Sau Dan <dan... at (no spam) informatik.uni-freiburg.de
wrote:
Nathan> Your SQL example only shows what happens when a human being
Nathan> doesn't know all the facts, so to naive humans (who are not
Nathan> truly part of the system of computer languages), the results
Nathan> do indeed seem unpredictable.
See above. The SQL example is deliberately written to allow
*unpredictable order*, so that RDBMS implementations may do any
optimizations that they see it fit.
??? The SQL example you tried to mystify NS with is not 'deliberately
written to allow' anything. SQL offers many options, and one of them
is to order results. IF no ordering is demanded, then no ordering is
done. No programmer expects any kind of ordering unless explicitly
demanded for the very simple reason that there is no 'default'
ordering to assume.
Likewise, among the various types of data structures representing
collections of elements, only a small part are expected to (and do)
exhibit ordering. Meaningful order is *not* part of their contract, so
where on earth do you get ambiguity?
(Well, maybe *you*'d like to rely on their order being meaningful, but
that's *your* misunderstanding.)
LSD has offered an unfortunate example of ambiguity in computer
languages. The kind of ambiguity I had in mind when I first mentioned
their ambiguity is like the C statement:
a (b) ;
This can either mean evaluate function a with argument b or define b
as a variable of type a.
You can tell which one you mean if you know what a is. But that
requires you to know another fact stated somewhere else.
Another example occurs in older C within the statement
a b (c);
which declares that b is a function of one argument returning a value
of type a. The ambiguity is whether c is the name of a type or a
variable (of type int). This one is settled by fiat - if c is the name
of a type then that interpretation is used.
So far as i know all the ambiguities in C involve type names.
A computer language should not be ambiguous. A good test is to write a
compiler and declare what the compiler does is the right answer. The
attempt to define standards (to keep the various compilers at least
more or less in line) has never been completely successful. Maybe
someday it will be but I will not hold my breath until it happens.
[/quote]
But it's not like a compiler will stop to ask you what you mean, or
make different decisions each time it's run. Whereas with language, it
really is possible to have the exact same utterance mean different
things, even in the same context, and the only way you can determine
its meaning is to ask the speaker to elaborate. Like, it's what
happens on Usenet all the time! |
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| Brian M. Scott... |
| Posted: Fri Nov 06, 2009 4:39 pm |
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On Fri, 06 Nov 2009 22:08:40 +0100, Joachim Pense
<snob at (no spam) pense-mainz.eu> wrote in
<news:hd2333$8ga$03$2 at (no spam) news.t-online.com> in sci.lang:
[quote]Nathan Sanders (in sci.lang):
In article <hd1uuv$huu$02$1 at (no spam) news.t-online.com>,
Joachim Pense <snob at (no spam) pense-mainz.eu> wrote:
Nathan Sanders (in sci.lang):
English is English, regardless of how French speakers
mangle its interpretation. Likewise, mathematical
notation is mathematical notation, regardless of how
humans mangle its interpretation.
No. You seem to consider mathematical notation as a
prescriptivist considers English.
Of course. Mathematical notation, unlike language, was
consciously and intentionally designed.
So you think that someone wrote a handbook of mathematical
notation that formally defines it and mathematicians are
supposed to stick to those rules.
[/quote]
No, he doesn't, any more than I do. And what he says is
still true: mathematical notational systems *are*
consciously and intentionally designed and have precisely
definable meanings.
[...]
[quote]In the case of mathematical notation however, we know the rules,
because we designed them!
But not in an organized plan, but as ad-hoc-addictions and
changes piling up,
[/quote]
To a degree; so what?
[quote]and governed by taste.
[/quote]
Only to a very small degree, if one expects to be
understood.
[...]
[quote]I care about mathematical notation as Mathematicians use it.
[/quote]
But apparently don't really understand how it works.
Brian |
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| Brian M. Scott... |
| Posted: Fri Nov 06, 2009 4:40 pm |
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On Fri, 06 Nov 2009 22:00:39 +0100, Joachim Pense
<snob at (no spam) pense-mainz.eu> wrote in
<news:hd22k3$8ga$03$1 at (no spam) news.t-online.com> in sci.lang:
[quote]Nathan Sanders (in sci.lang):
[/quote]
[...]
[quote]Then you are apparently not interested in talking about
the actual properties of formal notation systems
themselves, but rather, how any communication system can
be perverted and twisted when subjected to external
influences. That is a completely different issue.
I don't believe that the formal notation systems you are
talking about really exist except as idealisations.
[/quote]
Then you're ignorant of mathematical logic.
Brian |
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| LEE Sau Dan... |
| Posted: Fri Nov 06, 2009 7:52 pm |
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[quote]"Nathan" == Nathan Sanders <nsanders at (no spam) williams.edu> writes:
[/quote]
Nathan> My courses are pretty close to Utopia, I suppose! This very
Nathan> semester, I'm teaching a well-defined formal notation:
Nathan> first-order predicate logic. Every well-formed formula in
Nathan> this notation is completely unambiguous as to how it is to
Nathan> be interpreted within the system. Otherwise, I couldn't
Nathan> expect my students to provide single, consistent values to
Nathan> expressions like "V_M(S)".
So, how do you put first-order logic into practice? Prolog? If so,
it's time to look into the bells and whistles introduced into Prolog to
make it not unbearably slow. Does the cut (!) operator strictly confrom
to first-order logic?
[quote]The same happens in "i=i++;", which is grammatical, but gives
unpredictable results.
[/quote]
Nathan> Not for the *same* compiler!
Nathan> The same code given to the same compiler will produce the
Nathan> same result every time, which is what I said before: once a
Nathan> *single* interpretation algorithm (compiler) has been
Nathan> chosen, computer code is unambiguous.
The C language is not defined by the behaviour of any compiler. It is
defined in the standard.
Nathan> (Barring compilers that use random numbers to make their
Nathan> decisions, which I suppose could be done.
Yes. That's what compilers are free to do for things specified as
"undefined behaviour".
Nathan> Get a random binary digit from random.org, and that's the
Nathan> value uninitialized variables will start out with!)
A standards-compliant C compiler could also generate code to trigger the
circuits to detonate an atomic bomb in case of "undefined behaviour".
Nathan> "Hurdles for the reader" have nothing to do with the
Nathan> interpretation of mathematical notation within the system of
Nathan> mathematical notation itself.
What level of "interpretation" do you want?
Abstraction level is important!
If you ignore abstraction level, then perhaps you shouldn't intepret "0"
and "1" as merely "zero" and "one". Strictly speaking, you should dig
deeping into the definition of them. E.g. Richard Dedekind defines "0"
as the empty set {}, and "1" as the set {0} = {{}}. 2 = {0,1} {{},{{}}}, etc.
So, do you ALWAYS want to think about "0" and "1" that way?
Nathan> What quantifiable role does topicalization play in a
Nathan> computer language?
[quote]The computer doesn't care about this difference.
[/quote]
Nathan> Bingo.
[quote]But human beings reading the code do!
[/quote]
Nathan> Likewise, human beings are not proper computer code
Nathan> compilers.
I didn't say they are. But that doesn't mean human beings must not
interpret computer code written in a high level language. There is a
need for programmers to communicate details of various APIs,
implementations, etc. And they do so via the codes. Even researchers
need to exchange algorithms, and they do so via pseudocode. In either
cases, the code IS used for human communication.
[quote]Maybe, to you, the SOLE purpose of programming languages is for
human begins to specify instructions to the COMPUTERS.
[/quote]
Nathan> I'm not talking about purpose. I'm talking about proper
Nathan> interpretation within a system.
Which system. Communication between two programmers?
And why do you think pseudo-code ever existed, if only computers are
supposed to read and interpret program code?
--
Lee Sau Dan §õ¦u´° ~{ at (no spam) nJX6X~}
E-mail: danlee at (no spam) informatik.uni-freiburg.de
Home page: http://www.informatik.uni-freiburg.de/~danlee |
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| LEE Sau Dan... |
| Posted: Fri Nov 06, 2009 8:08 pm |
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[quote]"Nathan" == Nathan Sanders <nsanders at (no spam) williams.edu> writes:
Why do you assume that the notation system mathematicians use are
well-defined and formal?
[/quote]
Nathan> It's not an assumption; it's an observation.
Then, you have not made enough observations, or your observations are
too shallow.
[quote]Not "the notation system". Some author's will change their usage,
others won't.
[/quote]
Nathan> Those that don't change are bad authors writing bad
Nathan> notation.
There is no "the notation system". Is that ambiguous?
Just flip open a well-written book on maths or algorithms and check it's
front matter or back matter (sometimes conveniently on the inside
front/back-cover). They'll have a table or list explaining the set of
notations used in that book. Why would they need that?
[quote]The author may think that in the particular context of his paper,
the readers will understand it anyway.
[/quote]
Nathan> See my post responded to LSD. Readers are irrelevant to the
Nathan> interpretation of mathematical notation within the system of
Nathan> mathematical notation.
Then, why do people write anything according to that system?
Nathan> You didn't write an ambiguity. You wrote a string that,
Nathan> when interpreted within the confines of mathematical
Nathan> notation, would not be interpreted the way you wanted it to
Nathan> be interpreted.
Unfortunately, such "confines" do not exist outside your ivory tower.
[quote]but (even though I was aware of the ambiguity) I did not bother
because I thought that the meaning was clear to everyone who
understands complex numbers.
[/quote]
Nathan> Readers are irrelevant to the interpretation of mathematical
Nathan> notation within the system of mathematical notation.
If readers are irrelevant, then why would people even bother to write
them?
[quote]There is an example where ambiguity is _not_ ungrammatical but by
design. In the database language SQL, you can write
select * from A where x > y
(Assuming that you have a table named A that has two number
columns x and y.) Now this will produce a list of all rows where
the x entry is bigger than the y entry, but the order in which
the rows appear is unpredictable. (The database system will use
table statistics, recent buffered query results and whatever to
decide which order it can produce in the shortest time).
[/quote]
Nathan> "And whatever"? Is it really undefined and random?
Yes. The spec. says clearly that the order of the results rows are in
an unspecified order. i.e. you as a programmer should not make any
assumption on the ordering of the resulting rows. An implementation is
allowed to use any order, and the order does not have to be consistent a
second time you use an identical query.
The order is arbitrary, unpredictable. Whether it is random is up to
the implementation. (Not that "random" is just one possibility to
realize "undefined", and it differs from "arbitrary".)
Is that hard to understand? Is that ambiguous?
Nathan> My hunch is that given the same database with the same table
Nathan> statistics and query results, you'll get the same sort order
Nathan> every time.
No. You're wrong. And you're a bad programmer by not checking the
specs. and by simply making wrong assumptions about the behaviours of
the system.
What prevents the RDBMS from reorganizing the data blocks around over
night so as to (hopefully) improve the the performance for the next day?
The blocks could be even hosted on different (physical) sites and the
moving could have changed the site where a block is located. And then
when answering the same query the next day, the RDBMS may fetching the
last row the first because it has to moved to a nearby location. And
then, it might decide to print out this row first. Nothing in the specs
disallows this.
Nathan> Your SQL example only shows what happens when a human being
Nathan> doesn't know all the facts, so to naive humans (who are not
Nathan> truly part of the system of computer languages), the results
Nathan> do indeed seem unpredictable.
See above. The SQL example is deliberately written to allow
*unpredictable order*, so that RDBMS implementations may do any
optimizations that they see it fit.
[quote]Well, that's just as naive as if someone said that the sentence
"Paul is only a year older than John, but they look like twins"
was equivalent to "Paul is a year older than John, but they look
like twins" and "Paul is only a year older than John, and they
look like twins" because they express the same facts.
[/quote]
Nathan> Except that, *within the system of English itself*, those
Nathan> sentences are not equivalent!
But they mean the same thing.
--
Lee Sau Dan §õ¦u´° ~{ at (no spam) nJX6X~}
E-mail: danlee at (no spam) informatik.uni-freiburg.de
Home page: http://www.informatik.uni-freiburg.de/~danlee |
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| LEE Sau Dan... |
| Posted: Fri Nov 06, 2009 8:13 pm |
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[quote]"Nathan" == Nathan Sanders <nsanders at (no spam) williams.edu> writes:
That is indeed a crucial point. We use *OUR* language capacity
to interpret formal systems; we don't ordinarily use the defined
interpretation algorithms from within the formal systems
themselves.
[/quote]
Nathan> In fact, this is precisely one of the biggest problems I
Nathan> face when I teach logic. Students quite frequently ignore
Nathan> parts of the definition of well-formed formulas, because as
Nathan> humans, they see no meaningful difference between "(P & Q &
Nathan> R)" and "(P & Q) & R".
Maybe, you could try using the postfix notation instead to see if that
helps stopping them from thinking so. When people see something
unfamiliar (postfix notation in this case), they may refrain from
generalizing their past knowledge into the new field.
Nathan> But there *is* a meaningful difference *within* the logical
Nathan> system itself! Because "&" is strictly defined as a binary
Nathan> connective, the first string is not well-formed and cannot
Nathan> be assigned an interpretation, but the second string is
Nathan> fine.
It depends. One can *define* that "P&Q&R" means "(P&Q)&R", but
specifying that "&" is left-associative (or is it right-associative?).
Take a course in compiler design theory and you'll learn those
subtleties.
--
Lee Sau Dan §õ¦u´° ~{ at (no spam) nJX6X~}
E-mail: danlee at (no spam) informatik.uni-freiburg.de
Home page: http://www.informatik.uni-freiburg.de/~danlee |
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| Brian M. Scott... |
| Posted: Fri Nov 06, 2009 8:26 pm |
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On Sat, 07 Nov 2009 09:08:58 +0800, LEE Sau Dan
<danlee at (no spam) informatik.uni-freiburg.de> wrote in
<news:87r5sbi1jp.fsf at (no spam) informatik.uni-freiburg.de> in
sci.lang:
[quote]"Nathan" == Nathan Sanders <nsanders at (no spam) williams.edu> writes:
Why do you assume that the notation system mathematicians use are
well-defined and formal?
Nathan> It's not an assumption; it's an observation.
Then, you have not made enough observations, or your
observations are too shallow.
[/quote]
Or yours are simply wrong.
[quote]Not "the notation system". Some author's will change their usage,
others won't.
Nathan> Those that don't change are bad authors writing bad
Nathan> notation.
There is no "the notation system". Is that ambiguous?
[/quote]
There are, as Nathan has already acknowledged, notational
systems. All are well-defined.
[quote]Just flip open a well-written book on maths or algorithms
and check it's front matter or back matter (sometimes
conveniently on the inside front/back-cover). They'll
have a table or list explaining the set of notations
used in that book. Why would they need that?
[/quote]
Because there is more than one well-defined system of
notation, and a careful author specifies the one that he's
using.
[quote]The author may think that in the particular context of his paper,
the readers will understand it anyway.
Nathan> See my post responded to LSD. Readers are irrelevant to the
Nathan> interpretation of mathematical notation within the system of
Nathan> mathematical notation.
Then, why do people write anything according to that system?
[/quote]
That's a remarkably pointless question, unless you imagine
that the meaning of musical notation would change if
everyone suddenly went deaf.
[quote]Nathan> You didn't write an ambiguity. You wrote a string that,
Nathan> when interpreted within the confines of mathematical
Nathan> notation, would not be interpreted the way you wanted it to
Nathan> be interpreted.
Unfortunately, such "confines" do not exist outside your ivory tower.
[/quote]
They certainly do. And I speak as a practising
mathematician.
[quote]but (even though I was aware of the ambiguity) I did not bother
because I thought that the meaning was clear to everyone who
understands complex numbers.
Nathan> Readers are irrelevant to the interpretation of mathematical
Nathan> notation within the system of mathematical notation.
If readers are irrelevant, then why would people even bother to write
them?
[/quote]
More muddy thinking: once again you are confusing the
interpretation of a notation with people's reasons for using
it.
[...]
[quote]Well, that's just as naive as if someone said that the sentence
"Paul is only a year older than John, but they look like twins"
was equivalent to "Paul is a year older than John, but they look
like twins" and "Paul is only a year older than John, and they
look like twins" because they express the same facts.
Nathan> Except that, *within the system of English itself*, those
Nathan> sentences are not equivalent!
But they mean the same thing.
[/quote]
Not precisely, no.
Brian |
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| LEE Sau Dan... |
| Posted: Fri Nov 06, 2009 10:35 pm |
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[quote]"Nathan" == Nathan Sanders <nsanders at (no spam) williams.edu> writes:
[/quote]
Nathan> English is English, regardless of how French speakers mangle
Nathan> its interpretation. Likewise, mathematical notation is
Nathan> mathematical notation, regardless of how humans mangle its
Nathan> interpretation.
Wrong analogy. The correct one should have read:
English is English, regardless of how *English readers* mangle its
interpretation. Likewise, ..., regardless of how *mathematicians*
mangle its interpretation.
Now, do you find it absurd?
[quote]I care about mathematical notation as mathematicians use it,
[/quote]
Me too.
Nathan> For the purposes of this discussion, I only care about how
Nathan> it's actually defined formally, not how it gets
Nathan> misinterpreted from outside the system.
Um... you're a prescriptivist?
--
Lee Sau Dan §õ¦u´° ~{ at (no spam) nJX6X~}
E-mail: danlee at (no spam) informatik.uni-freiburg.de
Home page: http://www.informatik.uni-freiburg.de/~danlee |
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| LEE Sau Dan... |
| Posted: Fri Nov 06, 2009 10:35 pm |
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[quote]"Nathan" == Nathan Sanders <nsanders at (no spam) williams.edu> writes:
No. You seem to consider mathematical notation as a
prescriptivist considers English.
[/quote]
Nathan> Of course. Mathematical notation, unlike language, was
Nathan> consciously and intentionally designed.
Designed by whom? God?
If you realized that it is designed by human beings, would you still
suppose that it is flawless?
Nathan> Both systems have governing rules, but for language, we
Nathan> don't know what they are, so we can only describe the system
Nathan> through descriptive observation.
You don't know the *precise and complete* rules for mathematical
notations, either. And there is NO SINGLE system.
Nathan> In the case of mathematical notation however, we know the
Nathan> rules, because we designed them!
No. Even if we designed them, there could be flaws to leave in holes
for ambiguities. Sometimes, the designers DELIBERATLY allow ambiguities
for flexibility. These are not bugs, but features! Just revisit the
SQL example.
[quote]Strange attitude for a linguist.
[/quote]
Nathan> Hardly strange at all! Linguists don't describe English by
Nathan> how French speakers interpret it.
What does this have to do with how *human programmers* interpret program
code written by another *human programmer*?
What does this have anything to do with how *mathematicians* read
mathematical formulae written by another *mathematician*?
--
Lee Sau Dan §õ¦u´° ~{ at (no spam) nJX6X~}
E-mail: danlee at (no spam) informatik.uni-freiburg.de
Home page: http://www.informatik.uni-freiburg.de/~danlee |
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| LEE Sau Dan... |
| Posted: Fri Nov 06, 2009 10:35 pm |
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[quote]"Nathan" == Nathan Sanders <nsanders at (no spam) williams.edu> writes:
So you think that someone wrote a handbook of mathematical
notation that formally defines it and mathematicians are supposed
to stick to those rules. That somehow must have evaded my
attention.
[/quote]
Nathan> "A" handbook? No.
Then, are there any "language academy" for mathematical notations?
[quote]In the case of mathematical notation however, we know the
rules, because we designed them!
But not in an organized plan, but as ad-hoc-addictions and
changes piling up, and governed by taste.
[/quote]
Nathan> How does that contradict what I said?
A patchy system usually has may flaws, due to the gaps and overlaps
between the different patches.
Nathan> The rules were designed, we know what they are,
That doesn't mean the rules are complete, or not self-conflicting.
Esperanto was also designed. So, is it flawless and free of ambiguities?
Nathan> so it's reasonably to approach mathematical notation from a
Nathan> prescriptive standpoint.
Do linguists approach Esperanto from a prescriptive standpoint? Do
Esperanto speakers really use the language that way?
--
Lee Sau Dan §õ¦u´° ~{ at (no spam) nJX6X~}
E-mail: danlee at (no spam) informatik.uni-freiburg.de
Home page: http://www.informatik.uni-freiburg.de/~danlee |
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| LEE Sau Dan... |
| Posted: Fri Nov 06, 2009 10:35 pm |
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[quote]"Nathan" == Nathan Sanders <nsanders at (no spam) williams.edu> writes:
I don't believe that the formal notation systems you are talking
about really exist except as idealisations.
[/quote]
Nathan> Isn't that precisely what mathematical notation is for?
That's the goal, but we are far far from that goal.
That you *want* to become rich, doesn't mean you _will* be rich.
Nathan> It'd be a shame if it couldn't do it's job!
It'd be a shame if you don't realize that:
In theory, theory and practice coincide;
in practice, they don't.
--
Lee Sau Dan §õ¦u´° ~{ at (no spam) nJX6X~}
E-mail: danlee at (no spam) informatik.uni-freiburg.de
Home page: http://www.informatik.uni-freiburg.de/~danlee |
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