Re: All languages are equally fit

On Wed, 04 Nov 2009 10:41:43 +0800, LEE Sau Dan
<danlee@xxxxxxxxxxxxxxxxxxxxxxxxxx> wrote in
<news:87hbtb2eqg.fsf@xxxxxxxxxxxxxxxxxxxxxxxxxx> in
sci.lang:

"Nathan" == Nathan Sanders <nsanders@xxxxxxxxxxxx> writes:

[...]

Nathan> True linguistic ambiguity is completely different, and
Nathan> occurs within any given language. This kind of linguistic
Nathan> ambiguity could be lexical (1), structural (2), referential
Nathan> (3), or scopal (4):

Take "1 + 1 = 1" as an example. It is a formula in boolean algebra.

1) Lexically, the "1" doesn't refer to "one", but "true".
Also, the "+" doesn't mean "addition", but "logical or".

I agree that this is analogous to lexical ambiguity.

2) Structurally, I'm using infix notation. One could have
equivalently used prefix or postfix notations.

Irrelevant: none of them is structurally ambiguous.

[...]

4) Scopal? This problem occurs frequently in
formulas with free variables. e.g. "E = m c^2". What
is "c"? What is "m"? What is "E"? Why? Which
context?

This has nothing to do with scope. Linguistic scope is
analogous to the scope of a quantifier in predicate logic.

Also, The set "N", the set of natural numbers, can
include "0" or exclude it, depending on context.

No, it's not a matter of context; there are simply two
competing definitions. (And only those who don't know
better use the one that excludes 0.)

And if you see "x^y" in a formula, where both "x" and
"y" could be zero, it is up to the context to determine
whether you should take "x^y" to be zero or one.

No, it isn't. It's up to the writer to define 0^0 or
declare it to be undefined. (And while there are contexts
in which it's useful to declare it to be undefined, only an
idiot would define it to be anything other than 1.)

In the open question "P = NP?", what are P and N?

Standard names for complexity classes. So what?

[...]

Nathan> The lack of these kinds of linguistic ambiguity is one of
Nathan> the ways that mathematical notation is completely unlike
Nathan> natural language.

You're too simplistic.

You're mostly talking through your hat. It's clear that
with the possible exception of 'lexical ambiguity', you
don't understand the meaning of linguistic ambiguity.

Study more maths and you'll find this the above is a very
naive assumption about mathematical notations.

As I recall, Nathan started out in mathematics. And I'm a
mathematician.

[...]

Brian
.

Relevant Pages

  • Re: All languages are equally fit
    ... Mathematical notation, unlike language, was ... Nathan> consciously and intentionally designed. ... and what you think is ambiguity is really just ... Are you suggesting that after we design a system, ...
    (sci.lang)
  • Re: All languages are equally fit
    ... Nathan> That isn't ambiguity in the linguistic sense. ... Nathan> uncertainty over which formal notation system is being used. ... The interpretation of mathematical notation does not depend on culture ...
    (sci.lang)
  • Re: All languages are equally fit
    ... Nathan> occurs within any given language. ... I agree that this is analogous to lexical ambiguity. ... depending on context. ... Nathan> the ways that mathematical notation is completely unlike ...
    (sci.lang)
  • Re: All languages are equally fit
    ... Nathan> In what single mathematical notational system is operator ... random string of symbols. ... True ambiguity occurs ... mathematical notation counts as a single system. ...
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  • Re: All languages are equally fit
    ... Nathan> That isn't ambiguity in the linguistic sense. ... Nathan> uncertainty over which formal notation system is being used. ... common among linguists who define "ideographic" that way? ...
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