Charles,
It might be off-track here, but it would be perfectly on-track in the
agi-philosophy list that Ben might eventually split off of this one.
But, thanks, that clarifies what you were saying greatly.
--Abram
On Mon, Nov 3, 2008 at 10:50 PM, Charles Hixson
[EMAIL PROTECTED] wrote:
That's
That's a lot stronger and more interesting that the theories that I was
referring to. Also a lot more complex.
**This is getting way off topic, so the rest should probably be ignored.**
One of the theories that I was referring to contained only 0 and a rule
that given a number allowed you
It all depends on what definition of number you are using. If it's
constructive, then it must be a finite set of numbers. If it's based on
full Number Theory, then it's either incomplete or inconsistent. If
it's based on any of several subsets of Number Theory that don't allow
If you were talking about something actual, then you would have a valid
point. Numbers, though, only exist in so far as they exist in the
theory that you are using to define them. E.g., if I were to claim that
no number larger than the power-set of energy states within the universe
were
Charles,
OK, but if you argue in that manner, then your original point is a
little strange, doesn't it? Why worry about Godelian incompleteness if
you think incompleteness is just fine?
Therefore, I would assert that it isn't that it leaves *even more*
about numbers left undefined, but that
Sent: Tuesday, October 28, 2008 5:55 PM
Subject: Re: [agi] constructivist issues
Any formal system that contains some basic arithmetic apparatus
equivalent to http://en.wikipedia.org/wiki/Peano_axioms is doomed to be
incomplete with respect to statements about numbers... that is what
paper because I didn't
get that out of it at all.
- Original Message -
*From:* Ben Goertzel [EMAIL PROTECTED]
*To:* agi@v2.listbox.com
*Sent:* Tuesday, October 28, 2008 6:41 PM
*Subject:* Re: [agi] constructivist issues
well-defined is not well-defined in my view...
However
Ben,
Thanks, that writeup did help me understand your viewpoint. However, I
don't completely unserstand/agree with the argument (one of the two,
not both!). My comments to that effect are posted on your blog.
About the earlier question...
(Mark) So Ben, how would you answer Abram's question So
To rephrase. Do you think there is a truth of the matter concerning
formally undecidable statements about numbers?
--Abram
That all depends on what the meaning of is, is ... ;-)
---
agi
Archives: https://www.listbox.com/member/archive/303/=now
RSS
that
integer to describe the size of the universe.
;-) Nice try, but . . . . :-p
- Original Message -
From: Ben Goertzel
To: agi@v2.listbox.com
Sent: Wednesday, October 29, 2008 9:48 AM
Subject: Re: [agi] constructivist issues
but we never need arbitrarily large integers in any
Message -
*From:* Ben Goertzel [EMAIL PROTECTED]
*To:* agi@v2.listbox.com
*Sent:* Wednesday, October 29, 2008 9:48 AM
*Subject:* Re: [agi] constructivist issues
but we never need arbitrarily large integers in any particular case, we
only need integers going up to the size of the universe
/contexts but many others are just/simply context-dependent.
- Original Message -
From: Abram Demski [EMAIL PROTECTED]
To: agi@v2.listbox.com
Sent: Wednesday, October 29, 2008 10:08 AM
Subject: Re: [agi] constructivist issues
Ben,
Thanks, that writeup did help me understand your
to show that all integers are necessary as a safety margin
is pretty obvious . . . .
- Original Message -
From: Ben Goertzel
To: agi@v2.listbox.com
Sent: Wednesday, October 29, 2008 10:38 AM
Subject: Re: [agi] constructivist issues
sorry, I should have been more precise
Ben,
So, for example, if I describe a Turing machine whose halting I prove
formally undecidable by the axioms of peano arithmetic (translating
the Turing machine's operation into numerical terms, of course), and
then I ask you, is this Turing machine non-halting, then would you
answer, That
On Wed, Oct 29, 2008 at 11:19 AM, Abram Demski [EMAIL PROTECTED]wrote:
Ben,
So, for example, if I describe a Turing machine whose halting I prove
formally undecidable by the axioms of peano arithmetic (translating
the Turing machine's operation into numerical terms, of course), and
then I
Ben,
OK, that is a pretty good answer. I don't think I have any questions
left about your philosophy :).
Some comments, though.
hmmm... you're saying the halting is provable in some more powerful
axiom system but not in Peano arithmetic?
Yea, it would be provable in whatever formal system I
But the question is what does this mean about any actual computer,
or any actual physical object -- which we can only communicate about
clearly
insofar as it can be boiled down to a finite dataset.
What it means to me is that Any actual computer will not halt (with a
correct output)
Ben,
The difference can I think be best illustrated with two hypothetical
AGIs. Both are supposed to be learning that computers are
approximately Turing machines. The first, made by you, interprets
this constructively (let's say relative to PA). The second, made by
me, interprets this classically
Ben,
No, I wasn't intending any weird chips.
For me, the most important way in which you are a constructivist is
that you think AIXI is the ideal that finite intelligence should
approach.
--Abram
On Wed, Oct 29, 2008 at 2:33 PM, Ben Goertzel [EMAIL PROTECTED] wrote:
OK ... but are both of
On Wed, Oct 29, 2008 at 4:47 PM, Abram Demski [EMAIL PROTECTED] wrote:
Ben,
No, I wasn't intending any weird chips.
For me, the most important way in which you are a constructivist is
that you think AIXI is the ideal that finite intelligence should
approach.
Hmmm... I'm not sure I
those systems contained by them.
- Original Message -
From: Abram Demski [EMAIL PROTECTED]
To: agi@v2.listbox.com
Sent: Monday, October 27, 2008 5:43 PM
Subject: Re: [agi] constructivist issues
Mark,
Sorry, I accidentally called you Mike in the previous email!
Anyway, you said:
Also
Mark,
You assert that the extensions are judged on how well they reflect the world.
The extension currently under discussion is one that allows us to
prove the consistency of Arithmetic. So, it seems, you count that as
something observable in the world-- no mathematician has ever proved a
Abram,
I could agree with the statement that there are uncountably many *potential*
numbers but I'm going to argue that any number that actually exists is
eminently describable.
Take the set of all numbers that are defined far enough after the decimal point
that they never accurately describe
PROTECTED]
To: agi@v2.listbox.com
Sent: Tuesday, October 28, 2008 9:32 AM
Subject: Re: [agi] constructivist issues
Mark,
You assert that the extensions are judged on how well they reflect the
world.
The extension currently under discussion is one that allows us to
prove the consistency of Arithmetic
Mark,
The question that is puzzling, though, is: how can it be that these
uncomputable, inexpressible entities are so bloody useful ;-) ... for
instance in differential calculus ...
Also, to say that uncomputable entities don't exist because they can't be
finitely described, is basically just
MW:Pi is a normal number is decidable by arithmetic
because each of the terms has meaning in arithmetic
Can it be expressed in purely mathematical terms/signs without using
language?
---
agi
Archives: https://www.listbox.com/member/archive/303/=now
yes
On Tue, Oct 28, 2008 at 8:46 AM, Mike Tintner [EMAIL PROTECTED]wrote:
MW:Pi is a normal number is decidable by arithmetic
because each of the terms has meaning in arithmetic
Can it be expressed in purely mathematical terms/signs without using
language?
if it is not
deducible. If the meaning is beyond the system, then it is not decidable
because you can't even express what you're deciding.
Mark
- Original Message - From: Abram Demski [EMAIL PROTECTED]
To: agi@v2.listbox.com
Sent: Tuesday, October 28, 2008 9:32 AM
Subject: Re: [agi
, October 28, 2008 11:44 AM
Subject: Re: [agi] constructivist issues
Mark,
The question that is puzzling, though, is: how can it be that these
uncomputable, inexpressible entities are so bloody useful ;-) ... for instance
in differential calculus ...
Also, to say that uncomputable
systems.
- Original Message -
From: Abram Demski [EMAIL PROTECTED]
To: agi@v2.listbox.com
Sent: Tuesday, October 28, 2008 12:06 PM
Subject: Re: [agi] constructivist issues
Mark,
Yes, I do keep dropping the context. This is because I am concerned
only with mathematical knowledge
)?
Saying that Gödel is about mathematical systems is not saying that it's not
about cat-including systems.
- Original Message - From: Abram Demski [EMAIL PROTECTED]
To: agi@v2.listbox.com
Sent: Tuesday, October 28, 2008 12:06 PM
Subject: Re: [agi] constructivist issues
, 2008 3:47 PM
Subject: Re: [agi] constructivist issues
Mark,
Thank you, that clarifies somewhat.
But, *my* answer to *your* question would seem to depend on what you
mean when you say fully defined. Under the classical interpretation,
yes: the question is fully defined, so it is a pi question
Mark,
That is thanks to Godel's incompleteness theorem. Any formal system
that describes numbers is doomed to be incomplete, meaning there will
be statements that can be constructed purely by reference to numbers
(no red cats!) that the system will fail to prove either true or
false.
So my
--- On Tue, 10/28/08, Mike Tintner [EMAIL PROTECTED] wrote:
MW:Pi is a normal number is decidable by arithmetic
because each of the terms has meaning in arithmetic
Can it be expressed in purely mathematical terms/signs
without using language?
No, because mathematics is a language.
--
Ben,
What are the mathematical or logical signs for normal number/ rational
number? My assumption would be that neither logic nor maths can be done
without some language attached - such as the term rational number - but I'm
asking from extensive ignorance.
Ben:yes
MT:MW:Pi is a normal
All of math can be done without any words ... it just gets annoying to read
for instance, all math can be formalized in this sort of manner
http://www.cs.miami.edu/~tptp/MizarTPTP/TPTPProofs/arithm/arithm__t1_arithm
and the words in there like
v1_ordinal1(B)
could be replaced with
v1_1234(B)
Hi guys,
I took a couple hours on a red-eye flight last night to write up in more
detail my
argument as to why uncomputable entities are useless for science:
http://multiverseaccordingtoben.blogspot.com/2008/10/are-uncomputable-entities-useless-for.html
Of course, I had to assume a specific
Message - From: Abram Demski [EMAIL PROTECTED]
To: agi@v2.listbox.com
Sent: Tuesday, October 28, 2008 5:02 PM
Subject: Re: [agi] constructivist issues
Mark,
That is thanks to Godel's incompleteness theorem. Any formal system
that describes numbers is doomed to be incomplete, meaning
as
to why uncomputable entities are useless for science. I'm going to need to go
back over it a few more times though.:-)
- Original Message -
From: Ben Goertzel
To: agi@v2.listbox.com
Sent: Tuesday, October 28, 2008 5:55 PM
Subject: Re: [agi] constructivist issues
Any
Goertzel [EMAIL PROTECTED]
*To:* agi@v2.listbox.com
*Sent:* Tuesday, October 28, 2008 5:55 PM
*Subject:* Re: [agi] constructivist issues
Any formal system that contains some basic arithmetic apparatus equivalent
to http://en.wikipedia.org/wiki/Peano_axioms is doomed to be incomplete
with respect
Matt,
Interesting question re the differences between mathematics - i.e.
arithmetic, algebra - and logic vs language.
I haven't really thought about this, but I wouldn't call maths a language.
Maths consists of symbolic systems of quantification and schematic patterns
(geometry) which can
Excuse me, but I thought there were subsets of Number theory which were
strong enough to contain all the integers, and perhaps all the rational,
but which weren't strong enough to prove Gödel's incompleteness theorem
in. I seem to remember, though, that you can't get more than a finite
number
Charles,
Interesting point-- but, all of these theories would be weaker then
the standard axioms, and so there would be *even more* about numbers
left undefined in them.
--Abram
On Tue, Oct 28, 2008 at 10:46 PM, Charles Hixson
[EMAIL PROTECTED] wrote:
Excuse me, but I thought there were
PROTECTED]
To: agi@v2.listbox.com
Sent: Sunday, October 26, 2008 10:00 PM
Subject: Re: [agi] constructivist issues
Mark,
After some thought...
A constructivist would be justified in asserting the equivalence of
Godel's incompleteness theorem and Tarski's undefinability theorem,
based on the idea
is seriously split . . . .
Where do you fall on the constructivism of meaning?
- Original Message - From: Abram Demski [EMAIL PROTECTED]
To: agi@v2.listbox.com
Sent: Sunday, October 26, 2008 10:00 PM
Subject: Re: [agi] constructivist issues
Mark,
After some thought...
A constructivist
. . . . I agree with all that
you're saying but can't see where/how it's supposed to address/go back into
my domain model ;-)
- Original Message -
From: Abram Demski [EMAIL PROTECTED]
To: agi@v2.listbox.com
Sent: Monday, October 27, 2008 11:05 AM
Subject: Re: [agi] constructivist issues
to address/go back into
my domain model ;-)
- Original Message - From: Abram Demski [EMAIL PROTECTED]
To: agi@v2.listbox.com
Sent: Monday, October 27, 2008 11:05 AM
Subject: Re: [agi] constructivist issues
Mark,
I'm a classicalist in the sense that I think classical mathematics
needs
, October 27, 2008 12:29 PM
Subject: Re: [agi] constructivist issues
Mark,
An example of people who would argue with the meaningfulness of
classical mathematics: there are some people who contest the concept
of real numbers. The cite things like that the vast majority of real
numbers cannot even
)
which is what you are doing.
- Original Message - From: Abram Demski [EMAIL PROTECTED]
To: agi@v2.listbox.com
Sent: Monday, October 27, 2008 12:29 PM
Subject: Re: [agi] constructivist issues
Mark,
An example of people who would argue with the meaningfulness of
classical
to be ascribing arbitrariness to constructivism which is
emphatically not the case.
- Original Message - From: Abram Demski [EMAIL PROTECTED]
To: agi@v2.listbox.com
Sent: Monday, October 27, 2008 2:53 PM
Subject: Re: [agi] constructivist issues
Mark,
The number of possible
I don't think this is reasonable. For the experiment, we would isolate
you with various shielding. It is a question of the design of an
experiment, like any other physics experiment. At some point,
Occam's Razor tells you that the best theory is a non-computational
system.
And, I hate to be
It's not solved by shielding, because the hypothetical computable source
whose algorithmic information is too high for me to grok it could be within
the molecules of the brain, just where the hypothetical uncomputable
source is hypothesized to be by Penrose and Hammeroff and so forth.
You can
Algorithmic information has nothing to do with my argument.
I'm talking about time complexity.
There are limits to how fast a computer can
run its clock, for example because delta E times Delta T must
be greater than hbar, so if you try to make delta T too
small you explode.
Ben It's not
: Re: [agi] constructivist issues
Mark,
Yes.
I wouldn't normally be so picky, but Godel's theorem *really* gets
misused.
Using Godel's theorem to say made it sound (to me) as if you have a
very fundamental confusion. You were using a theorem about the
incompleteness of proof to talk about
Eric,
Nobody here is actually arguing that the brain is non-computational,
though. (The quote you refer to was a misunderstanding).
I was arguing that we have an understanding of noncomputational
entities, and Ben was arguing (approximately) that any actual behavior
could be explained equally
The limitations of Godelian completeness/incompleteness are a subset of
the much stronger limitations of finite automata.
Can we get a listing of what you believe these limitations are and whether
or not you believe that they apply to humans?
I believe that humans are constrained by *all*
Forget consensus! I don't even see a discussion forming. This is all
quite long and impenetrable. What have we learned here? If possible I
want to catch up.
Eric B
---
agi
Archives: https://www.listbox.com/member/archive/303/=now
RSS Feed:
Matthias,
OK, that seems fair. Perhaps you will let me get away with a weaker statement:
Since it is convenient to *pretend* that computers are Turing machines
rather than finite-state machines when doing theoretical work, it is
*also* convenient to pretend that Godelian limitations are all that
I know I've expressed frustration with this thread in the past. But I
don't want to discourage its development. If someone wants to hit me
with a summary off-list maybe I can contribute something _
---
agi
Archives:
Mark,
It makes sense but I'm arguing that you're making my point for me . . . .
I'm making the point natural language is incompletely defined for
you, but *not* the point natural language suffers from Godelian
incompleteness, unless you specify what concept of proof applies to
natural language.
But I do not agree that most humans can be scientists. If this is
necessary
for general intelligence then most humans are not general intelligences.
Soften be scientists to generally use the scientific method. Does this
change your opinion?
- Original Message -
From: Dr. Matthias
]
To: agi@v2.listbox.com
Sent: Friday, October 24, 2008 11:31 AM
Subject: Re: [agi] constructivist issues
Mark,
It makes sense but I'm arguing that you're making my point for me . . .
.
I'm making the point natural language is incompletely defined for
you, but *not* the point natural language
Message - From: Abram Demski [EMAIL PROTECTED]
To: agi@v2.listbox.com
Sent: Friday, October 24, 2008 11:31 AM
Subject: Re: [agi] constructivist issues
Mark,
It makes sense but I'm arguing that you're making my point for me . . .
.
I'm making the point natural language is incompletely
On Sat, Oct 25, 2008 at 3:01 AM, Eric Baum [EMAIL PROTECTED] wrote:
For example, to make this concrete and airtight, I can add a time element.
Say I compute offline the answers to a large number of
problems that, if one were to solve them with a computation,
provably could only be solved by
Eric,
According to your argument, there are some cases in which you could
demonstrate that I was producing outputs that could not be generated by the
specific computer that is **my brain** according to our current
understanding of my brain.
However, this would not demonstrate that the source is
.listbox.com
Sent: Wednesday, October 22, 2008 9:05 PM
Subject: Re: [agi] constructivist issues
Mark,
I own and have read the book-- but my first introduction to Godel's
Theorem was Douglas Hofstadter's earlier work, Godel Escher Bach.
Since I had already been guided through the details of the proof
, 2008 9:23 PM
Subject: Lojban (was Re: [agi] constructivist issues)
Why would anyone use a simplified or formalized English (with regular
grammar and no ambiguities) as a path to natural language understanding? Formal
language processing has nothing to do with natural language
--- On Thu, 10/23/08, Mark Waser [EMAIL PROTECTED] wrote:
Hi. I don't understand the following
statements. Could you explain it some more?
- Natural language can be learned from examples. Formal language
can not.
I really mean that formal languages like C++ and HTML are not designed to
: Abram Demski [EMAIL PROTECTED]
To: agi@v2.listbox.com
Sent: Thursday, October 23, 2008 11:54 AM
Subject: Re: [agi] constructivist issues
---
agi
Archives: https://www.listbox.com/member/archive/303/=now
RSS Feed: https://www.listbox.com/member/archive/rss
You may not like Therefore, we cannot understand the math needed to define
our own intelligence., but I'm rather convinced that it's correct.
Do you mean to say that there are parts that we can't understand or that the
totality is too large to fit and that it can't be cleanly and completely
It doesn't, because **I see no evidence that humans can
understand the semantics of formal system in X in any sense that
a digital computer program cannot**
I just argued that humans can't understand the totality of any formal system X
due to Godel's Incompleteness Theorem but the rest of
I don't want to diss the personal value of logically inconsistent thoughts.
But I doubt their scientific and engineering value.
I doesn't seem to make sense that something would have personal value and then
not have scientific or engineering value.
I can sort of understand science if you're
(1) We humans understand the semantics of formal system X.
No. This is the root of your problem. For example, replace formal system
X with XML. Saying that We humans understand the semantics of XML
certainly doesn't work and why I would argue that natural language
understanding is
On Wed, Oct 22, 2008 at 10:51 AM, Mark Waser [EMAIL PROTECTED] wrote:
I don't want to diss the personal value of logically inconsistent
thoughts. But I doubt their scientific and engineering value.
I doesn't seem to make sense that something would have personal value and
then not have
diagnosing/fixing/debugging it -- but I can always learn them as I go . . . .
- Original Message -
From: Ben Goertzel
To: agi@v2.listbox.com
Sent: Tuesday, October 21, 2008 11:26 PM
Subject: Re: [agi] constructivist issues
Well, if you are a computable system, and if by think
I disagree, and believe that I can think X: This is a thought (T) that is
way too complex for me to ever have.
Obviously, I can't think T and then think X, but I might represent T as a
combination of myself plus a notebook or some other external media. Even if
I only observe part of T at
You have not convinced me that you can do anything a computer can't do.
And, using language or math, you never will -- because any finite set of
symbols
you can utter, could also be uttered by some computational system.
-- Ben G
Can we pin this somewhere?
(Maybe on Penrose? ;-)
The problem is to gradually improve overall causal model of
environment (and its application for control), including language and
dynamics of the world. Better model allows more detailed experience,
and so through having a better inbuilt model of an aspect of
environment, such as language,
Subject: Re: [agi] constructivist issues
Personally, rather than starting with NLP, I think that we're going to need
to start with a formal language that is a disambiguated subset of English
IMHO that is an almost hopeless approach, ambiguity is too integral to
English or any natural
(joke)
What? You don't love me any more?
/thread
- Original Message -
From: Ben Goertzel
To: agi@v2.listbox.com
Sent: Wednesday, October 22, 2008 11:11 AM
Subject: Re: [agi] constructivist issues
(joke)
On Wed, Oct 22, 2008 at 11:11 AM, Ben Goertzel [EMAIL
, if not the subsequently warped
thoughts, do have the serious value of raising your mental Boltzmann
temperature.
- Original Message -
From: Ben Goertzel
To: agi@v2.listbox.com
Sent: Wednesday, October 22, 2008 11:11 AM
Subject: Re: [agi] constructivist issues
On Wed, Oct 22, 2008
On Wed, Oct 22, 2008 at 7:47 PM, Ben Goertzel [EMAIL PROTECTED] wrote:
The problem is to gradually improve overall causal model of
environment (and its application for control), including language and
dynamics of the world. Better model allows more detailed experience,
and so through having a
Too many responses for me to comment on everything! So, sorry to those
I don't address...
Ben,
When I claim a mathematical entity exists, I'm saying loosely that
meaningful statements can be made using it. So, I think meaning is
more basic. I mentioned already what my current definition of
a preferred dictionary or resource? (Google has too many for me to
do a decent perusal quickly)
- Original Message -
*From:* Ben Goertzel [EMAIL PROTECTED]
*To:* agi@v2.listbox.com
*Sent:* Wednesday, October 22, 2008 11:11 AM
*Subject:* Re: [agi] constructivist issues
So, a statement is meaningful if it has procedural deductive meaning.
We *understand* a statement if we are capable of carrying out the
corresponding deductive procedure. A statement is *true* if carrying
out that deductive procedure only produces more true statements. We
*believe* a
Mark,
The way you invoke Godel's Theorem is strange to me... perhaps you
have explained your argument more fully elsewhere, but as it stands I
do not see your reasoning.
--Abram
On Wed, Oct 22, 2008 at 12:20 PM, Mark Waser [EMAIL PROTECTED] wrote:
It looks like all this disambiguation by
: Wednesday, October 22, 2008 12:20 PM
Subject: Re: [agi] constructivist issues
Too many responses for me to comment on everything! So, sorry to those
I don't address...
Ben,
When I claim a mathematical entity exists, I'm saying loosely that
meaningful statements can be made using it. So, I think
To: agi@v2.listbox.com
Cc: [EMAIL PROTECTED]
Sent: Wednesday, October 22, 2008 12:27 PM
Subject: [OpenCog] Re: [agi] constructivist issues
This is the standard Lojban dictionary
http://jbovlaste.lojban.org/
I am not so worried about word meanings, they can always be handled via
All theorems in the same formal system are equivalent anyways ;-)
On Wed, Oct 22, 2008 at 1:03 PM, Abram Demski [EMAIL PROTECTED] wrote:
Ben,
What, then, do you make of my definition? Do you think deductive
consequence is insufficient for meaningfulness?
I am not sure exactly where you
Also, I don't prefer to define meaning the way you do ... so clarifying
issues with your definition is your problem, not mine!!
On Wed, Oct 22, 2008 at 1:03 PM, Abram Demski [EMAIL PROTECTED] wrote:
Ben,
What, then, do you make of my definition? Do you think deductive
consequence is
[EMAIL PROTECTED]
To: agi@v2.listbox.com
Sent: Wednesday, October 22, 2008 12:38 PM
Subject: Re: [agi] constructivist issues
Mark,
The way you invoke Godel's Theorem is strange to me... perhaps you
have explained your argument more fully elsewhere, but as it stands I
do not see your reasoning
: Ben Goertzel
To: agi@v2.listbox.com
Cc: [EMAIL PROTECTED]
Sent: Wednesday, October 22, 2008 1:06 PM
Subject: Re: [OpenCog] Re: [agi] constructivist issues
Well, I am confident my approach with subscripts to handle disambiguation and
reference resolution would work, in conjunction
22, 2008 4:19 PM
Subject: Re: [agi] constructivist issues
Mark,
Chapter number please?
--Abram
On Wed, Oct 22, 2008 at 1:16 PM, Mark Waser [EMAIL PROTECTED] wrote:
Douglas Hofstadter's newest book I Am A Strange Loop (currently available
from Amazon for $7.99 -
http://www.amazon.com/Am
]* wrote:
From: Ben Goertzel [EMAIL PROTECTED]
Subject: Re: [agi] constructivist issues
To: agi@v2.listbox.com
Cc: [EMAIL PROTECTED]
Date: Wednesday, October 22, 2008, 12:27 PM
This is the standard Lojban dictionary
http://jbovlaste.lojban.org/
I am not so worried about word meanings
On Thu, Oct 23, 2008 at 11:23 AM, Matt Mahoney [EMAIL PROTECTED] wrote:
So how does yet another formal language processing system help us understand
natural language? This route has been a dead end for 50 years, in spite of
the ability to always make some initial progress before getting stuck.
Ben,
Unfortunately, this response is going to be (somewhat) long, because I
have several points that I want to make.
If I understand what you are saying, you're claiming that if I pointed
to the black box and said That's a halting oracle, I'm not
describing the box directly, but instead
But, worse, there are mathematically well-defined entities that are
not even enumerable or co-enumerable, and in no sense seem computable.
Of course, any axiomatic theory of these objects *is* enumerable and
therefore intuitively computable (but technically only computably
enumerable).
Ben,
My discussion of meaning was supposed to clarify that. The final
definition is the broadest I currently endorse, and it admits
meaningful uncomputable facts about numbers. It does not appear to get
into the realm of set theory, though.
--Abram
On Tue, Oct 21, 2008 at 12:07 PM, Ben Goertzel
On Tue, Oct 21, 2008 at 4:53 PM, Abram Demski [EMAIL PROTECTED] wrote:
As it happens, this definition of
meaning admits horribly-terribly-uncomputable-things to be described!
(Far worse than the above-mentioned super-omegas.) So, the truth or
falsehood is very much not computable.
I'm
Try Rudy Rucker's book Infinity and the Mind for a good nontechnical
treatment of related ideas
http://www.amazon.com/Infinity-Mind-Rudy-Rucker/dp/0691001723
The related wikipedia pages are a bit technical ;-p , e.g.
http://en.wikipedia.org/wiki/Inaccessible_cardinal
On Tue, Oct 21, 2008
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