Hello Stephen,

"Stephen Harris" <stephen.p.harris@sbcglobal.net> wrote in message
news:<bNBSb.18121$SK3.10273@newssvr27.news.prodigy.com>...
SH: Number theory as a formal system is not constructed
only by logic. It requires axioms (unproven assumptions).
Peano Arithmetic attempts, I think, to have the human
experience with numbers guide the selection of axioms.
Godel's Inc. Theorem is a result about a formal system, not reality.

Natural language also existed before any attempt was made
to formalize it. Cyc is a product of human ontolgists using their
intuition in an attempt to approximate the unknown rules which
generate natural language. The million common-sense rules that
Cyc uses to describe/simulate the function of language all act
as axioms, none are proven. There is no algorithmic method
to generate the actual rules (supposing there is a set of actual rules)
which compose the interaction of natural language. It is backwards
to claim that formal Incompleteness results back-propagate and cause
our incomplete knowlege of reality. The very act of representing
reality into a formal system creates self-referential artifacts.
Substituting equivalneces for Incompleteness such as lambda calculus
doesn't make a formal system any more authentic or of original import.


I agree. These are all great observations, indeed.

I think Incompleteness is not a synonym for physical uncertainty,
except for some formal system which postulates this relationship.

Do you mean Heisenberg uncertainty principle? I tend to agree, however
uncertainy seems to be the result of a more specific complexity law in
action.

Regards,

--
Eray Ozkural

Hello Stephen,

"Stephen Harris" <stephen.p.harris@sbcglobal.net> wrote in message
news:<bNBSb.18121$SK3.10273@newssvr27.news.prodigy.com>...
SH: Number theory as a formal system is not constructed
only by logic. It requires axioms (unproven assumptions).
Peano Arithmetic attempts, I think, to have the human
experience with numbers guide the selection of axioms.
Godel's Inc. Theorem is a result about a formal system, not reality.

Natural language also existed before any attempt was made
to formalize it. Cyc is a product of human ontolgists using their
intuition in an attempt to approximate the unknown rules which
generate natural language. The million common-sense rules that
Cyc uses to describe/simulate the function of language all act
as axioms, none are proven. There is no algorithmic method
to generate the actual rules (supposing there is a set of actual rules)
which compose the interaction of natural language. It is backwards
to claim that formal Incompleteness results back-propagate and cause
our incomplete knowlege of reality. The very act of representing
reality into a formal system creates self-referential artifacts.
Substituting equivalneces for Incompleteness such as lambda calculus
doesn't make a formal system any more authentic or of original import.


I agree. These are all great observations, indeed.

I think Incompleteness is not a synonym for physical uncertainty,
except for some formal system which postulates this relationship.

Do you mean Heisenberg uncertainty principle? I tend to agree, however
uncertainy seems to be the result of a more specific complexity law in
action.

Regards,

"Tristan Lear" <tristanlear3309@yahoo.com> wrote in message
news:f010abdf.0401292338.2b822144@posting.google.com...
"Stephen Harris" <stephen.p.harris@sbcglobal.net> wrote in message
news:<OphSb.7584$Fp5.1812@newssvr29.news.prodigy.com>...
"Wolf Kirchmeir" <wwolfkir@sympatico.can> wrote in message
news:jbysxveflzcngvpbpna.hs8e843.pminews@news1.sympatico.ca...
On 27 Jan 2004 21:28:01 -0800, Ron Peterson wrote:

"Wolf Kirchmeir" <wwolfkir@sympatico.can> wrote in message
news:<jbysxveflzcngvpbpna.hrwqx04.pminews@news1.sympatico.ca>...
On Thu, 22 Jan 2004 19:30:41 GMT, Lester Zick wrote:

Well I don't see any obvious reason why the language we use is
necessarily inadequate to explaining the problems we phrase in the
language.

Well, it's _human_ language, isn't it? That's an obvious enough
reason
for
me.

Human languages are extensible, so I think that any problem that can
be posed can be explained. Does someone have an example of a problem
that can't be explained?

--
Ron

Nice question. I'm not sure what you mean by "explaining" a problem.
It
seems
to me that posing a problem is equivalent to explaining it. So I'll
shift
the
ground, perhaps unfairly, to solving problems rather than explaining
them.
Granting this shift, we see that posing a problem is not the same as
solving
it. Mathematics is full of examples of problems that can be clearly
stated
but whose solution is by no means clear. You may object that
mathematics
isn't what you mean by an extension of language. But I would argue
that
mathematics is an extension of language, and then some. I suppose we
can
dismiss those problems of which we know that there is no solution,
since
showing that no solution is possible is a type of solution.

Here follow a few examples that I know of, and to some extent
understand:
There are problems that cannot be solved because the universe will not
last
long enough to arrive at a solution. There are problems that cannot
solved
because we cannot determine whether the algorithm that could solve
them
will
ever arrive at a solution. (This is "the halting problem.") There are
others
of which one cannot say whether they have a solution. (This is the
decidability problem.) If one may paraphrase Goedel's theorem in terms
of
solving problems, one may say that there are problems that cannot be
solved
within the system in which they are posed. (But I'm not sure that this
paraphrase of Goedel is permissible, which in itself shows that not
all
problems that can be posed can be solved.) There are problems of which
one
cannot say that they are solvable, or if solvable, whether the
solution is
optimal. There are problems of which one can say that a solution
exists,
but
one cannot say what that solution is (this is sometimes enough to
inspire
work that produces a solution, so some of these problems don't answer
your
question.)

HTH


The issue under discussion is whether language is adequate. Language is
composed of words representing concepts. Concepts can include terms
which do not have an explanation. The word "electricity" represents a
concept but the question "What is electricity" has not been rigorously
answered because the answer resides in _theories_ of Physics which
does not have a "Theory of Everything". It seems to me that "adequacy"
has the word "incompleteness" substituted for it when the limits of
formal
axiomatic systems such as Goedel's Incompleteness theorem is mentionded.

Natural language is not a formal axiomatic system. Goedlian
Incompleteness
cannot be utilized to "explain" why AI can only be realized by humans
and
not by machines, even if the assertion is true independent of that
surmise.

Wolf Kirchmeir writes:
"You may object that mathematics isn't what you mean by an extension of
language. But I would argue that mathematics is an extension of
language,
and then some."

SH: Then you would certainly be in the minority. The "unreasonable
effectiveness of mathematics" is often commented upon but that is
due to its attempts to map to our consensus reality. That is not what
formal languages and formal mathematical axiomatics systems prioritize.

So our natural language is a collection of words and their usage and the
words are based upon expressing concepts. Creating a hypothetical
concept which cannot be conceived, thus no example can be given
thus the concept cannot be named, is a logical paradox not an example
of the inadequacy of language.

What happens when an irresistable force encounters an immovable object?
How can the significance of counterfactual mathematical theorems be
mapped to the underlying reality of our existence? Do heros in our
fictional
books actually suffer fates? I've read the clever sounding: 'the
solution to
a
problem is found in the question' which is so general as to become
trivial.

Regards,
Stephen


Have any of you guys heard of "E-Prime?" (English minus the verb "to
be" as an attempt to reduce aristotlean logic and replace it with a
more probablistic, concrete, accountable mode of evaluating?? it
relies on the sapir-whorf-korzybyski hypothesis in that if we alter
our language we can alter our perceptions (they argue for the better
by eliminating "to be") i've written three papers in the modified
language so far and I've found it helps me write more vividly and
pulls my head out of the clouds (no vague abstractions).. robert anton
wilson talks about it alot in his book quantum psychology ..

the international society for general semantics
http://www.generalsemantics.org and the institute for general
semantics http://www.general-semantics.org have some literature on it


I once heard of this but have not tried it. I think such solutions contain
an inherent shortcoming. I think it is a theorem that any two languages
which do not contain the exact same symbols will contain descriptions
which cannot be identically translated from one language to the other.
So I think there are areas of a language which dispenses with "to be"
which will not have identical meaning substitutions in our natural language.

Google:
"I would advise that Mr. Post be very careful about extending what he
knows about the terminology of morphology-syntax-semantics in
NATURAL LANGUAGE/LINGUISTICS to morphology-syntax-semantics in MATHEMATICAL
LOGIC. Terms like implication are
used in very different ways in these different fields. We can show a very
clear parallel between syntax and semantics for the predicate and
propositional calculi which is not present for natural languages.
Presumably (cf. my remarks about implication and entailment above)
this intimate relation between language and meta-language has
confused Mr. Post."

Machine translation of poetry from one language to another
is reported to fail rather miserably.

From the "Phoenix Exultant" page 151. "But the universe, by definition,
must always be more complex than the information-parts or thoughts
one uses to encode that complexity."

I think this quote addresses the inability of the human mind to completely
understand the universe; not the inadequacy of language to clothe those
concepts which do have meaning with words within the tapestry of language.
I'm not at all sure that this situation of incomplete knowledge of the
universe due to limited perception of the human mind is the same as Godelian
Incompleteness in another guise failing to correlate universal knowledge.

To be or not to be,
Stephen

"Stephen Harris" <stephen.p.harris@sbcglobal.net> wrote in message
news:<bcqSb.19633$zL.14153@newssvr25.news.prodigy.com>...
"Tristan Lear" <tristanlear3309@yahoo.com> wrote in message
news:f010abdf.0401292338.2b822144@posting.google.com...
"Stephen Harris" <stephen.p.harris@sbcglobal.net> wrote in message
news:<OphSb.7584$Fp5.1812@newssvr29.news.prodigy.com>...
"Wolf Kirchmeir" <wwolfkir@sympatico.can> wrote in message
news:jbysxveflzcngvpbpna.hs8e843.pminews@news1.sympatico.ca...
On 27 Jan 2004 21:28:01 -0800, Ron Peterson wrote:

"Wolf Kirchmeir" <wwolfkir@sympatico.can> wrote in message
news:<jbysxveflzcngvpbpna.hrwqx04.pminews@news1.sympatico.ca>...
On Thu, 22 Jan 2004 19:30:41 GMT, Lester Zick wrote:

Well I don't see any obvious reason why the language we use is
necessarily inadequate to explaining the problems we phrase in the
language.

Well, it's _human_ language, isn't it? That's an obvious enough
reason
for
me.

Human languages are extensible, so I think that any problem that can
be posed can be explained. Does someone have an example of a problem
that can't be explained?

--
Ron

Nice question. I'm not sure what you mean by "explaining" a problem.
It
seems
to me that posing a problem is equivalent to explaining it. So I'll
shift
the
ground, perhaps unfairly, to solving problems rather than explaining
them.
Granting this shift, we see that posing a problem is not the same as
solving
it. Mathematics is full of examples of problems that can be clearly
stated
but whose solution is by no means clear. You may object that
mathematics
isn't what you mean by an extension of language. But I would argue
that
mathematics is an extension of language, and then some. I suppose we
can
dismiss those problems of which we know that there is no solution,
since
showing that no solution is possible is a type of solution.

Here follow a few examples that I know of, and to some extent
understand:
There are problems that cannot be solved because the universe will not
last
long enough to arrive at a solution. There are problems that cannot
solved
because we cannot determine whether the algorithm that could solve
them
will
ever arrive at a solution. (This is "the halting problem.") There are
others
of which one cannot say whether they have a solution. (This is the
decidability problem.) If one may paraphrase Goedel's theorem in terms
of
solving problems, one may say that there are problems that cannot be
solved
within the system in which they are posed. (But I'm not sure that this
paraphrase of Goedel is permissible, which in itself shows that not
all
problems that can be posed can be solved.) There are problems of which
one
cannot say that they are solvable, or if solvable, whether the
solution is
optimal. There are problems of which one can say that a solution
exists,
but
one cannot say what that solution is (this is sometimes enough to
inspire
work that produces a solution, so some of these problems don't answer
your
question.)

HTH


The issue under discussion is whether language is adequate. Language is
composed of words representing concepts. Concepts can include terms
which do not have an explanation. The word "electricity" represents a
concept but the question "What is electricity" has not been rigorously
answered because the answer resides in _theories_ of Physics which
does not have a "Theory of Everything". It seems to me that "adequacy"
has the word "incompleteness" substituted for it when the limits of
formal
axiomatic systems such as Goedel's Incompleteness theorem is mentionded.

Natural language is not a formal axiomatic system. Goedlian
Incompleteness
cannot be utilized to "explain" why AI can only be realized by humans
and
not by machines, even if the assertion is true independent of that
surmise.

Wolf Kirchmeir writes:
"You may object that mathematics isn't what you mean by an extension of
language. But I would argue that mathematics is an extension of
language,
and then some."

SH: Then you would certainly be in the minority. The "unreasonable
effectiveness of mathematics" is often commented upon but that is
due to its attempts to map to our consensus reality. That is not what
formal languages and formal mathematical axiomatics systems prioritize.

So our natural language is a collection of words and their usage and the
words are based upon expressing concepts. Creating a hypothetical
concept which cannot be conceived, thus no example can be given
thus the concept cannot be named, is a logical paradox not an example
of the inadequacy of language.

What happens when an irresistable force encounters an immovable object?
How can the significance of counterfactual mathematical theorems be
mapped to the underlying reality of our existence? Do heros in our
fictional
books actually suffer fates? I've read the clever sounding: 'the
solution to
a
problem is found in the question' which is so general as to become
trivial.

Regards,
Stephen


Have any of you guys heard of "E-Prime?" (English minus the verb "to
be" as an attempt to reduce aristotlean logic and replace it with a
more probablistic, concrete, accountable mode of evaluating?? it
relies on the sapir-whorf-korzybyski hypothesis in that if we alter
our language we can alter our perceptions (they argue for the better
by eliminating "to be") i've written three papers in the modified
language so far and I've found it helps me write more vividly and
pulls my head out of the clouds (no vague abstractions).. robert anton
wilson talks about it alot in his book quantum psychology ..

the international society for general semantics
http://www.generalsemantics.org and the institute for general
semantics http://www.general-semantics.org have some literature on it


I once heard of this but have not tried it. I think such solutions contain
an inherent shortcoming. I think it is a theorem that any two languages
which do not contain the exact same symbols will contain descriptions
which cannot be identically translated from one language to the other.
So I think there are areas of a language which dispenses with "to be"
which will not have identical meaning substitutions in our natural language.

Google:
"I would advise that Mr. Post be very careful about extending what he
knows about the terminology of morphology-syntax-semantics in
NATURAL LANGUAGE/LINGUISTICS to morphology-syntax-semantics in MATHEMATICAL
LOGIC. Terms like implication are
used in very different ways in these different fields. We can show a very
clear parallel between syntax and semantics for the predicate and
propositional calculi which is not present for natural languages.
Presumably (cf. my remarks about implication and entailment above)
this intimate relation between language and meta-language has
confused Mr. Post."

Machine translation of poetry from one language to another
is reported to fail rather miserably.

From the "Phoenix Exultant" page 151. "But the universe, by definition,
must always be more complex than the information-parts or thoughts
one uses to encode that complexity."

I think this quote addresses the inability of the human mind to completely
understand the universe; not the inadequacy of language to clothe those
concepts which do have meaning with words within the tapestry of language.
I'm not at all sure that this situation of incomplete knowledge of the
universe due to limited perception of the human mind is the same as Godelian
Incompleteness in another guise failing to correlate universal knowledge.

To be or not to be,
Stephen


the descriptions, for that matter, probably aren't translateable from
one person to the next -- behind each word it is probable that we
recall a magnificant gestalt of previous uses of that word according
to our own experience .. rather than a merriam-webster definition ..

that at least applies to nouns and adjectives.. the e-prime advocates
say that we're not really changing the lexicon that much by removing
to be... rather we're forcing a certain type of sentance structure ..
its more behind the assembley of the sentences than it is beind the
words themselves..

the french "what are you called" is closer to "reality" than the
english "what is your name?" while neither are in e-prime .. the
second one gets closer to the first one when e-prime is used ..

"what do people call you?" -- e-prime

It seems to me that this usage of "incompleteness" does not connote
the same level of categorical meaning since the generating method diifers.
I think for the meanings to be quite analogous would require some type
of self-evident assumption that the cosmos deploys incompleteness in
the same sense that it is encountered within a formal system, perhaps
by regarding the universe as an algorithmic operation, computer or CA.
A similar premise arises for computationalism and the human mind.. But
failing this assumption(s) then "incompleteness" does not share the same
shade of meaning lurking in the shadowy, shallow pools of interpretation.

Regards,
Stephen


From the "Phoenix Exultant" page 151. by John C. Wright
"But the universe, by definition, must always be more complex than
the information-parts or thoughts one uses to encode that complexity."

"Stephen Harris" <stephen.p.harris@sbcglobal.net> wrote in message
news:<8zUSb.8391$Wi.5824@newssvr29.news.prodigy.com>...
[snip]
It seems to me that this usage of "incompleteness" does not connote
the same level of categorical meaning since the generating method
diifers.
I think for the meanings to be quite analogous would require some type
of self-evident assumption that the cosmos deploys incompleteness in
the same sense that it is encountered within a formal system, perhaps
by regarding the universe as an algorithmic operation, computer or CA.
A similar premise arises for computationalism and the human mind.. But
failing this assumption(s) then "incompleteness" does not share the same
shade of meaning lurking in the shadowy, shallow pools of
interpretation.


It took a while to understand the discussion among you but, I think my
answer is: Yes!

Regards,
Stephen


From the "Phoenix Exultant" page 151. by John C. Wright
"But the universe, by definition, must always be more complex than
the information-parts or thoughts one uses to encode that complexity."

Oh, algorithmic incompleteness can at least be expressed in purely
natural language!

Regards,

--
Eray Ozkural

...It's not just the size of the vocabulary, but it's the
way the vocabulary is used. I.e., where the verbs, nouns, and modifiers
are placed and how some modifiers change the meaning of some words
differently than other words, etc.

The issue under discussion is whether language is adequate. Language is
composed of words representing concepts.

Concepts can include terms
which do not have an explanation. The word "electricity" represents a
concept but the question "What is electricity" has not been rigorously
answered because the answer resides in _theories_ of Physics which
does not have a "Theory of Everything". It seems to me that "adequacy"
has the word "incompleteness" substituted for it when the limits of formal
axiomatic systems such as Goedel's Incompleteness theorem is mentionded.

Natural language is not a formal axiomatic system.

Goedlian Incompleteness
cannot be utilized to "explain" why AI can only be realized by humans and
not by machines, even if the assertion is true independent of that surmise.

Wolf Kirchmeir writes:
"You may object that mathematics isn't what you mean by an extension of
language. But I would argue that mathematics is an extension of language,
and then some."

SH: Then you would certainly be in the minority. The "unreasonable
effectiveness of mathematics" is often commented upon but that is
due to its attempts to map to our consensus reality. That is not what
formal languages and formal mathematical axiomatics systems prioritize.

So our natural language is a collection of words and their usage and the
words are based upon expressing concepts. Creating a hypothetical
concept which cannot be conceived, thus no example can be given
thus the concept cannot be named, is a logical paradox not an example
of the inadequacy of language.

What happens when an irresistable force encounters an immovable object?

How can the significance of counterfactual mathematical theorems be
mapped to the underlying reality of our existence? Do heros in our fictional
books actually suffer fates? I've read the clever sounding: 'the solution to a
problem is found in the question' which is so general as to become trivial.

I thought you might find this interesting since it is a bit obscure,

English cannot be reduced to a consistent set of rules. Many have tried.
All have failed. Perhaps you should look into Noam Chomsky's attempts at
the task; search for references to "Transformational Grammar" for a
start. He appears to have begun with the assumption that [natural]
language can be modeled with a finite set of rules, but the last I saw on
the topic looked more like a proof that Goedel's Incompleteness Theorem
(q.v.) applies.

...It's not just the size of the vocabulary, but it's the
way the vocabulary is used. I.e., where the verbs, nouns, and modifiers
are placed and how some modifiers change the meaning of some words
differently than other words, etc.

The "rules" for explaining the grammar are not completely expressible in
formal terms which are less complex than the grammar itself. Any complete
description of the rules will end up *being* the rules, and vice versa.

The idea, like most good ideas, is simple. Suppose we have an
axiomatic theory formulated in terms of the primitive concepts
"line", "point", and "number". We're convinced that there isn't any
way of defining, say, "number" in terms of "line" and "point". But
how do we prove this? Well, if "number" could in fact be defined
in terms of "line" and "point", then for any two systems of objects
and relations satisfying our axioms, if they agree on the meaning
of "line" and "point", they must also agree on the meaning of
"number". So to prove that "number" can't be defined in terms of
"line" and "point" we exhibit two different systems of objects and
relations satisfying the axioms which agree on the meaning of
"line" and "point" but disagree on the meaning of "number".

This may seem very simple of me, but to me there is some similarity

On Fri, 30 Jan 2004 00:18:54 GMT, Stephen Harris wrote:

The issue under discussion is whether language is adequate. Language is
composed of words representing concepts.

I wish it were that simple.

But by the same token, my claim that human language is inadequate also
needs
refining. I hope my comments have gone a small step or two towards that
goal.

--
Wolf Kirchmeir, Blind River ON Canada
"Nature does not deal in rewards or punishments, but only in
consequences."
(Robert Ingersoll)

On 27 Jan 2004 21:28:01 -0800, Ron Peterson wrote:

Human languages are extensible, so I think that any problem that can
be posed can be explained. Does someone have an example of a problem
that can't be explained?

Human language is adequate for posing the problem and for posing the
solution whether or not the solution is achievable.

On Fri, 30 Jan 2004 00:18:54 GMT, Stephen Harris wrote:

The issue under discussion is whether language is adequate. Language is
composed of words representing concepts.

I wish it were that simple.

But by the same token, my claim that human language is inadequate also
needs
refining. I hope my comments have gone a small step or two towards that
goal.

--
Wolf Kirchmeir, Blind River ON Canada
"Nature does not deal in rewards or punishments, but only in
consequences."
(Robert Ingersoll)

lesterDELzick@worldnet.att.net (Lester Zick) wrote in message news:<40192598.97600656@netnews.att.net>...

On 27 Jan 2004 21:28:01 -0800, Ron Peterson wrote:

Human languages are extensible, so I think that any problem that can
be posed can be explained. Does someone have an example of a problem
that can't be explained?

Human language is adequate for posing the problem and for posing the
solution whether or not the solution is achievable.

People that are color blind don't have the concept of color, but can
get the concept from those that aren't color blind. So the question is
whether there is some concept that humans don't know about that can
never be discovered.

On Fri, 30 Jan 2004 00:18:54 GMT, Stephen Harris wrote:

The issue under discussion is whether language is adequate. Language is
composed of words representing concepts.

I wish it were that simple.

"Wolf Kirchmeir" <wwolfkir@sympatico.can> wrote in message
news:jbysxveflzcngvpbpna.hsgsja1.pminews@news1.sympatico.ca...
On Fri, 30 Jan 2004 00:18:54 GMT, Stephen Harris wrote:

The issue under discussion is whether language is adequate. Language is
composed of words representing concepts.

I wish it were that simple.


I think it is that simple. I will present again the statement to which I
objected:

Wolf wrote;
"You may object that mathematics isn't what you mean by an extension
of language. But I would argue that mathematics is an extension of language,
and then some."