A disproof of propositional calculus.
ArcticBonfire
Suppose I have a ball called Albert that is exactly half
white and half black. Now, take the following statement:
"Albert is white." Such a statement can never be just
true or false.
Therion Ware
wrote in alt.atheism:
Betcha they say "Albert is white" isn't true or false, but
meaningless.
--
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DarkAngel
That's because your statement is ill-defined. It is ambiguous. "Albert
is white" can mean both "Albert is entirely white", which is false, or
"Albert has some part of it that is white", which is true. Once you
define your statement correctly, without ambiguities, then there is no
problem at all.
--
a.a atheist #1172 Anarchy & Peace
"We can break these chains, we make them up ourselves"
- False Prophets, "Baghdad Stomp"
The Anarchism FAQ
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Matthias Weiss
Define the set of white objects, and I'll tell you whether Albert is in
it. That's all what a first-order logic claims to do -- and does.
Matthias Weiss.
Mark Richardson
Some things are neither true nor false but mearly meaningless.
What is the sound of one hand clapping?
Mark
--------------------------------------------
Mark Richardson. m.rich...@utas.edu.au
Member of SMASH
(Sarcastic Middle-aged Atheist with a Sense of Humor)
--------------------------------------------------
coffee
Um, given your statements, Albert *is* white. Thus, it's true.
"Albert is *all* white" would be false. "Albert is black" is true also.
Also, "Albert is a ball" is true, and if "A ball is a sphere" is
true, then "Albert is a sphere" is also true.
Whoa, coffee, do you mean to say that more than one word
can be used to described some things?! no wonder all my
novels were returned...
And while this might sound a bit Clintonesque, it would get down
to what you consider "is" to be, thus the vaguery in whether
"Albert is white" is true or false. If one desides to define
that a named object can be defined to be color X only if a said
object is mostly colored X" then "Albert is white" would
clearly be false, with no ambiguity.
Given your previous posts, I suspect that your vague terms
were intended to be misleading. If you're going to try and
call something a "disproof" please at least make an *attempt*
at formality (and no, I don't mean "call me sir").
Sigh, you've been funnier than this arcty, why are you holding
yourself back?
-coffee (do not taunt the happy fun arcty?)
Sent via Deja.com
http://www.deja.com/
Lars Eighner
the lovely and talented ArcticBonfire
broadcast on alt.atheism:
A> According to pc every statement is either true or false.
Yes, because unless it is either true or false, it is not a statement.
It is, in other words, the definition of a statement. It does not
follow that every declarative English sentence is a pc statement.
A> Suppose I
A> have a ball called Albert that is exactly half white and half
A> black. Now, take the following statement: "Albert is white." Such
A> a statement can never be just true or false.
Because it is not a statement. Neither is "Albert is honest" if Albert
is a marble. Come back when you have got a little bit of education.
--
Lars Eighner eig...@io.com http://www.io.com/~eighner/
OLE users: My reader discards html and all multipart news and email unread
"Of religion I know nothing -- at least, in its favor." --Lord Byron
Dave Holloway
wrote:
>According to pc every statement is either true or false.
Oh wow. Centuries of work by hundreds of thousands of mathematicians,
logicians, scientists and philosophers, thrown out the window because
an AOLer wrote a single paragraph. :op
There is indeed a problem here, but it is a linguistic problem, not a
logical problem. Statements are not either true or false. Propositions
are either true or false.
Dave
--
From the warped mind of Dave Holloway, #1184
Quotemeister; DDS, EAC Mars Division; Disgruntled Merkin
Finally updated: http://thinking.welcome.to
ArcticBonfire
> Betcha they say "Albert is white" isn't true or false, but
> meaningless.
Betcha, they don't. Clearly, "Albert is white" is not a
meaningless statement.
ArcticBonfire
> That's because your statement is ill-defined.
My statement is not ill-defined.
> It is ambiguous.
My statement is not ambiguous.
> "Albert is white" can mean both "Albert is entirely white",
> which is false, or "Albert has some part of it that is white",
> which is true. Once you define your statement correctly,
> without ambiguities, then there is no problem at all.
You can say this about every contradiction.
ArcticBonfire
> Define the set of white objects, and I'll tell you whether Albert is in
> it. That's all what a first-order logic claims to do -- and does.
Define "white" anyway you want, and my statement will lead
to a contradiction. Just reember any definition you make for
"white" must imply an analgous definition for "black" in order
for your language to be consistent.
ArcticBonfire
> Some things are neither true nor false but mearly meaningless.
My statement is not meaningless. There is no reason why my
statement should be meaningless. If you choose, you can
claim any contradiction is meaningless.
Fred Stone
The difficulty here is one that many students of elementary
logic have: you have not properly defined the predicate "is"
which in this instance could be stated as "is_colored".
If we define is_colored(A,color) as "A contains color and only color"
then
is_colored(albert,white) is false as is is_colored(albert,black)
If, however, we define is_colored(A,color) as "A contains color"
then is_colored(albert,white) is true.
--
Fred Stone
aa # 1369
Since when is ignorance a viewpoint?
ArcticBonfire
> A> According to pc every statement is either true or false.
>
> Yes, because unless it is either true or false, it is not a statement.
> It is, in other words, the definition of a statement. It does not
> Because it is not a statement. Neither is "Albert is honest" if Albert
> is a marble. Come back when you have got a little bit of education.
"Albert is white" is a statement. Clearly, if Albert was 100% white,
the statement would be true. Why should a statement not
become a statement simply because of different facts? Either
a certain group of words defined a certain way do form a statement
or a certain group of words defined a certain way do not form a
statement. A statement does not cease being a statement simply
because a different set of facts are present.. There is no logician who
will say that "Albert is white" is not a statement or is meaningless.
It is a perfectly legitimate statement.
I beat college students at Wff n' Proof when I was nine. I read Principia
Mathematica when I was twelve. I took several formal, undergraduate
logic courses at University of Michigan when I was thirteen. I read just
about every book that Copi ever wrote. I took several more logic courses,
when I was fully matriculated. I sincerely doubt you have the formal
educational background in logic that I have or the fundamental grasp.
John Hattan
>I beat college students at Wff n' Proof when I was nine. I read Principia
>Mathematica when I was twelve. I took several formal, undergraduate
>logic courses at University of Michigan when I was thirteen. I read just
>about every book that Copi ever wrote. I took several more logic courses,
>when I was fully matriculated. I sincerely doubt you have the formal
>educational background in logic that I have or the fundamental grasp.
Check out the big brain on bonfire!
---
John Hattan Grand High UberPope - First Church of Shatnerology
jo...@thecodezone.com http://www.freespeech.org/shatner
Martin Thomas
> According to pc every statement is either true or false.
All that proves is that life is far bigger than propositional
calculus. Are there a few idiots around who have never noticed that?
Propositional calculus is still a valid and useful tool in its
proper domain. Mathematics and computer science would be poorer
without it.
BTW, propositional calculus allows for statements to be
indeterminate.
** Martin Thomas **
What does not kill me makes me stronger - Nietzsche
http://www.thehungersite.com/cgi-bin/WebObjects/HungerSite
To reply, turn off the light.
Mike Smith
=According to pc every statement is either true or false.
=Suppose I have a ball called Albert that is exactly half
=white and half black. Now, take the following statement:
="Albert is white." Such a statement can never be just
=true or false.
It's false. It's half black.
__________________________________________
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Mike Smith | aa #1164 | Founder of SMASH
(Sarcastic Middle-aged Atheist with a Sense of Humor)
__________________________________________
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
"Eat thou not the bread of him that hath an evil eye,
neither desire thou his dainty meats." - Pr.23:6
Blackadder
"ArcticBonfire" <arctic...@aol.com> wrote in message
news:20010208213620...@ng-bj1.aol.com...
> DarkAngel drkan...@hotmail.com wrote:
> > That's because your statement is ill-defined.
>
> My statement is not ill-defined.
Yes it is.
> > It is ambiguous.
>
> My statement is not ambiguous.
Yes it is.
> > "Albert is white" can mean both "Albert is entirely white",
> > which is false
Ill defined.
>> "Albert has some part of it that is white",
> > which is true. Once you define your statement correctly,
> > without ambiguities, then there is no problem at all.
Ambiguous.
Do you see it now?
> You can say this about every contradiction.
No, you can only say it about contradictions which seem to exist because the
person claiming to have discovered the contradiction has intentionally used
an ill defined and ambiguous statement to manufacture one.
=)
-Adder.
Mark Richardson
wrote:
Hell, thats the last time I agree with you!
8-)
Mark.
Mark Richardson
wrote:
>arctic...@aol.com (ArcticBonfire) wrote:
>
>>I beat college students at Wff n' Proof when I was nine. I read Principia
>>Mathematica when I was twelve. I took several formal, undergraduate
>>logic courses at University of Michigan when I was thirteen. I read just
>>about every book that Copi ever wrote. I took several more logic courses,
>>when I was fully matriculated. I sincerely doubt you have the formal
>>educational background in logic that I have or the fundamental grasp.
>
>Check out the big brain on bonfire!
>
Woo Hoo!
It's a beauty!
The Owen
The statement is false.
Albert is black AND white.
A = B ^ W
--
"The" Owen
The Owen
>
> ArcticBonfire wrote:
> >
> > According to pc every statement is either true or false.
> > Suppose I have a ball called Albert that is exactly half
> > white and half black. Now, take the following statement:
> > "Albert is white." Such a statement can never be just
> > true or false.
>
> The statement is false.
True I mean.
Your statement is false.
> Albert is black AND white.
>
> A = (B ^ W)
Or something.
>
> --
> "The" Owen
Noah Simoneaux
>arctic...@aol.com (ArcticBonfire) wrote:
>
>>I beat college students at Wff n' Proof when I was nine. I read Principia
>>Mathematica when I was twelve. I took several formal, undergraduate
>>logic courses at University of Michigan when I was thirteen. I read just
>>about every book that Copi ever wrote. I took several more logic courses,
>>when I was fully matriculated. I sincerely doubt you have the formal
>>educational background in logic that I have or the fundamental grasp.
>
>Check out the big brain on bonfire!
Yep, he's a regular legend in his own mind. :/
Noah Simoneaux
Education is the process of moving from cocksure ignorance to thoughtful uncertainty.- Utvich's Observation
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Kevin Gassaway
<silen...@peoplepc.com> wrote:
>On 08 Feb 2001 21:47:25 GMT, arctic...@aol.com (ArcticBonfire)
>wrote:
>
>>According to pc every statement is either true or false.
>>Suppose I have a ball called Albert that is exactly half
>>white and half black. Now, take the following statement:
>>"Albert is white." Such a statement can never be just
>>true or false.
>
>Oh wow. Centuries of work by hundreds of thousands of mathematicians,
>logicians, scientists and philosophers, thrown out the window because
>an AOLer wrote a single paragraph. :op
Perhaps he'll post a 'disproof' of Quantum Mechanics for us later. :-)
-snip an explanation that'll go right over Arcty's head-
--
Kevin Gassaway (Remove NO SPAM to e-mail me.)
"If you have seen me cross myself, it was to Science, Art and Nature."
- Bela Bartok
Bob Dog
>
>According to pc every statement is either true or false.
According to common sense, every statement is true,
false, or unknown if it is either. Statements are
ideas posited on fact or observation; they are not
indicative of the facts' existence.
Some people wonder why they fall on their face yet
don't try to find out if they are starting out on
the right foot.
Bob Dog
bg12345.apexmail@com
Atheist #153
----------
"From the least to the greatest, all are greedy for gain;
prophets and priests alike, all practice deceit."
- Jeremiah 6:13
eyele...@my-deja.com
arctic...@aol.com (ArcticBonfire) wrote:
> I beat college students at Wff n' Proof when I was nine. I read
> Principia Mathematica when I was twelve.
"Apes don't read philosophy!"
"Yes they do, Otto, they just don't understand it!"
> I took several formal, undergraduate logic courses at University of
> Michigan when I was thirteen. I read just about every book that Copi
> ever wrote. I took several more logic courses, when I was fully
> matriculated.
And in every class you somehow missed the day where they said 'in order
to do formal logic you must define your terms'? And you missed where
they talked about how imprecise definitions lead to ambiguity? And where
defining something in English is insufficient, it has to be defined
*within the context of the propositional calculus* for it to be *used*
within propositional calculus?
Definitions in everyday language are slippery -- like when you say that
something 'is white'; what do you mean to say? That it is entirely
white? That it has portions that are white?
> I sincerely doubt you have the formal
> educational background in logic that I have or the fundamental grasp.
Show your work. Using only the symbols of propositional calculus, write
out the statements 'Albert is half white', 'Albert is half black', and
'Albert is white', and show your disproof. I dare you. Clearly you've
taken plenty of propositional calculus, and converting these statements
(which you claim are not ill-defined) into statements of propositional
calculus should be a trivial job. Let's see it.
(Caltech '92)
coffee
> > A> According to pc every statement is either true or false.
> >
> > Yes, because unless it is either true or false, it is not a statement.
> > It is, in other words, the definition of a statement. It does not
> > follow that every declarative English sentence is a pc statement. . . .
> > Because it is not a statement. Neither is "Albert is honest" if Albert
> > is a marble. Come back when you have got a little bit of education.
>
> "Albert is white" is a statement. Clearly, if Albert was 100% white,
> the statement would be true.
And that helps show why your wording is vague. What do you mean by
"Albert is white" do you mean "Albert is >= 50% white"
"Albert is >= 10% white" "Albert is >= 90% white"
"Albert is 100% white" ? I have heard people mean all of the
above statements (and more) by saying that something "is white"
or is blue.
English is vague, and context helps shape the
language. Context allows one to tell the bow of a ship from
a bow that one uses to shoot an arrow. The context of Albert
being 100% white allows one to know that "Albert is white" is
'safe.'
> Why should a statement not
> become a statement simply because of different facts?
It is because with the additional information of Albert
being 100% white that the vagueness of your statement becomes
moot. To be fully honest, it seems to be just intellectual
sloppiness to say that "Albert is white" becomes a statement
with the additional information.
> There is no logician who will say that "Albert is white"
> is not a statement or is meaningless.
> It is a perfectly legitimate statement.
It is a perfectly legitimate statement when one defines what it
means to declare that an object is of a certain color. However
once one clearly defines what it means, suddenly the doubt of
whether "Albert is white" is true of false collapses to either
true or false.
-coffee
coffee
eyele...@my-deja.com wrote:
> (Caltech '92)
out of curiosity, what house? A fellow Skurve?
-coffee (Caltech '99)
coffee
m.rich...@utas.edu.au (Mark Richardson) wrote:
> On Thu, 08 Feb 2001 21:19:37 -0600, John Hattan <jo...@thecodezone.com>
> wrote:
>
> >arctic...@aol.com (ArcticBonfire) wrote:
> >
> >>I beat college students at Wff n' Proof when I was nine. I read Principia
> >>Mathematica when I was twelve. I took several formal, undergraduate
> >>logic courses at University of Michigan when I was thirteen. I read just
> >>about every book that Copi ever wrote. I took several more logic courses,
> >>when I was fully matriculated. I sincerely doubt you have the formal
> >>educational background in logic that I have or the fundamental grasp.
> >
> >Check out the big brain on bonfire!
> >
>
> Woo Hoo!
> It's a beauty!
Yes, truely amazing. He must be smart to be able to post to
a mensa newsgroup (/me grins). Just imagine what price Arcty's
brain would catch on http://www.brains4zombies.com/
-coffee
Mike Dowling
>I beat college students at Wff n' Proof when I was nine. I read
>Principia Mathematica when I was twelve. I took several formal,
>undergraduate logic courses at University of Michigan when I was
>thirteen. I read just about every book that Copi ever wrote. I took
>several more logic courses, when I was fully matriculated. I sincerely
>doubt you have the formal educational background in logic that I have
>or the fundamental grasp.
It's just a pity that you obviously did not understand much of all this.
For a start, propositional calculus is about propositions, not
statements. And a proposition in most treatises is _defined_ as a
statement that is either true or false.
And you really should have read Wittgenstein. Statements can be true,
false, or meaningless. It is so very easy to mistake a meaningless
statement for a proposition; that, in essence, is what lies behind
Russel's paradox; Wittgenstein cleared that up.
Your example was a silly one precisely because it was left unclear what
you meant. Did you mean that the ball was entirely white, or partially
white. (I would have interpreted it as "entirely white", and so said
that it is false.) A better example of a meaningless statement is
"Yesterday was yellow." Clearly, something temporal cannot have colour
attributes.
You read Principia Mathematica when you were twelve? Are you aware that
what Russel and Whitehead were attempting to prove with this work was
proved false before they finished it, which is why they left their work
unfinished? Did you even realise that it was unfinished?
I sincerely doubt that you have understood anything that you claim to
have read.
I'm not normally this forthright, but you sounded very arrogant, and you
elected to "pull rank" rather than adopt rational argument. It's no sin
not to have understood something, but to parade ignorance so arrogantly
is.
Cheers,
Mike
--
My email address mi...@moocow.math.tu-bs.de above is a valid email
address. It is a mail alias. Once spammed, the alias is deleted, and
the integer 'N' incremented. Currently, mike[47,48] are valid. If
email to mikeN bounces, try mikeN+1.
Lars Eighner
the lovely and talented ArcticBonfire
broadcast on alt.atheism:
A> Lars Eighner eig...@io.com wrote:
>> Come back when you have
>> got a little bit of education.
A> I beat college students at Wff n' Proof when I was nine. I read
A> Principia Mathematica when I was twelve. I took several formal,
A> undergraduate logic courses at University of Michigan when I was
A> thirteen. I read just about every book that Copi ever wrote. I
A> took several more logic courses, when I was fully matriculated. I
A> sincerely doubt you have the formal educational background in logic
A> that I have or the fundamental grasp.
You're a funny little man.
--
Lars Eighner eig...@io.com http://www.io.com/~eighner/
OLE users: My reader discards html and all multipart news and email unread
"Not only is God dead, but just try to find a plumber on weekends."
--Woody Allen
Arturo Magidin
This is what I get for peeking behind my killfile. Sigh...
In article <20010208220427...@ng-bj1.aol.com>,
ArcticBonfire <arctic...@aol.com> wrote:
[.snip.]
>I beat college students at Wff n' Proof when I was nine. I read Principia
>Mathematica when I was twelve. I took several formal, undergraduate
>logic courses at University of Michigan when I was thirteen. I read just
>about every book that Copi ever wrote. I took several more logic courses,
>when I was fully matriculated. I sincerely doubt you have the formal
>educational background in logic that I have or the fundamental grasp.
This from the man who complains when others mention their
credentials...
The description he gave of propositional calculus is the problem. It's
imprecise.
For example, from Stephen Kleene's _Mathematical Logic_, part I,
chapter I, secion I, "The Propositional Calculus; Linguistic
considerations: Formulas":
"[W]e are dealing with one or another object language in which there
is a class of (declarative) sentences, consisting of certain sentences
(the aforementioned building blocks) and all further sentences that
can be built from them by certain operations, as we describe
next. These sentences we call <i>formulas</i>, in deference to the use
of mathematical symbolism in them or at least in our names for them."
[emphasis in the original]
" First, in this language there are to be some unambiguously
constituted sentences, whose internal structure we shall ignore (for
our study of propositional calculus) except for the purpose of
identifying the sentences. We call <i>these</i> sentences <i>prime
formulas</i> or <i>atoms</i>[.] [emphasis in the original."
"Second, the language is to provide five particular constructions or
operations for building new sentences from given sentences. Starting
with the prime formulas or atoms, we can use these operations over and
over again, to build other sentences, called <i>composite formulas</i>
or <i>molecules</i>, as follows.[...] If each of A and B is a given
<i>formula</i> (i.e. either a prime formula, or a composite formula
already constructed), then A<->B, A->B, A&B, A|B are <i>(composite)
formulas</i>. If A is a given <i>formula</i>, then ~A is a
<i>(composite) forumal</i>. [emphasis in the original]"
The key here is that Propositional Calculus starts out by considering
only ->certain sentences<- among an already possibly restricted class
of declarative sentences. It then proceeds to study how the truth
value of composite formulas may be derived from the truth value of the
prime formulas they are built out of. Nothing in Propositional
Calculus asserts that ->every<- declarative sentence in the object
language be a prime or atomic formula, as was asserted to begin with.
It should also be added the caveat Kleene adds in page 5 (third page
of Chapter 1, Section 1):
"Here we must mention the fact that the natural word languages, such
as English, suffer from ambiguities. (Of this, more will be said
later.) Logicians are therefore prone to build special symbolic
languages."
Much later, in Section 14, "Applications to ordinary language:
analysis of arguments", we have:
"In this section we shall treat some points concerning the application
of the classical propositional calculus to reasoning in ordinary
language (English).
"A <i>full</i> procedure for solving logical problems arising in
verbal form would be first to translate the sentences concerned into
the symbolism of the propositional calculus[*footnte: or to construe
them as formulas in our symbolism, if the object language is verbal],
and second to apply the theory and techniques of the calculus (as
developed above) to the resulting formula." [emphasis in the original]
Again, we have the notion that natural language must be formalized
before Propositional Calculus can be applied.
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
mag...@math.berkeley.edu
Noah Simoneaux
(snip)
>Yes, truely amazing. He must be smart to be able to post to
>a mensa newsgroup (/me grins). Just imagine what price Arcty's
>brain would catch on http://www.brains4zombies.com/
Hey, I think ArcticBonehead's brain should bring a premium price there. It's in
mint condition, hardly used, and never strained. ;)
DarkAngel
> DarkAngel drkan...@hotmail.com wrote:
> > That's because your statement is ill-defined.
>
> My statement is not ill-defined.
>
> > It is ambiguous.
>
> My statement is not ambiguous.
Yes it is. It has two different meanings.
> > "Albert is white" can mean both "Albert is entirely white",
> > which is false, or "Albert has some part of it that is white",
> > which is true. Once you define your statement correctly,
> > without ambiguities, then there is no problem at all.
>
> You can say this about every contradiction.
It is not a contradiction. A contradiction would be "Albert is entirely
white and entirely black".
What you have done basically is claim that "Albert is white" is one
proposition, when in fact it is not. It is ambiguous and can be one of
two different propositions, one of which would be false in this context
and the other one would be true. You claim that "Albert is white" is
both true and false, when in fact it isn't. One of the propositions
referenced by "Albert is white" is true, and the other is false, but
they are not the same proposition. In this case, it is not logic which
is inappropriate, but language which is ambiguous.
--
a.a atheist #1172 Anarchy & Peace
"We can break these chains, we make them up ourselves"
- False Prophets, "Baghdad Stomp"
The Anarchism FAQ
http://www.infoshop.org/faq/
Brian E. Clark
> My statement is not meaningless.
The statement is ambiguous, however. You made it ambiguous by
relying on an equivocal "is". ;-)
If you clarify what you mean by "Albert is white," the problem
disappears. What your example points out, in fact, is a the
danger of imprecise phrasing.
--
--------------
Brian E. Clark
brian -at- telerama -dot- com
Cats do stumble, yes, but no cat has yet
acknowledged it.
ArcticBonfire
> And in every class you somehow missed the day
> where they said 'in order to do formal logic you
All the terms, I used were defined. What term did
I use, do you alledge is undefined?
> And you missed where they talked about how imprecise
> definitions lead to ambiguity?
The definitions for white, black and half are precise. Certainly,
they can be made as precise as any English word. Are
you claiming that no language statement about the real
world can be substituted for "p" and "q." The words I used
are words that are used in science all the time.
> And where defining something in English is insufficient, it has
> to be defined *within the context of the propositional calculus*
> for it to be *used* within propositional calculus?
You should mind your Ps and Qs.
White, black and half are defined in English as precise
as any non-mathematical English word or for that matter
as precise as any non-mathematical word in any non-
mathematical language.
Basically, what you are saying is that you can insert no
English statement for "p" and "q." If so, then propositional
calculus is utterly meaningless, as you can never substitute
statements about the real world for p and q. If you claim
this then you are agreeing with me, that propositional
calculus is only valid for mathematical statements which
in fact only have true or false values, and is useless for
analyzing English statements about the real world.
I have a system of logic that CLAIMS that every statement
is either true, false or meaningless. I define meaningless
as any statement that is not true or false. This is ciruclar
reasoning. All of propositional calculus is circular
reasoning. You start out with a definition that says every
statement is either true or false. Any statement that
agrees with your definition is true and any statement
that disagrees with your definition is false. And then you
"prove" every statement is either true or false. Clearly, the
result of every proof in propositional calculus is merely a
reiteration of its definition of a statement. So everything
is either true or false by definition. If this is all what
propositional calculus has to say, then it is pretty silly,
and just a manipulation of abstract symbols that have
no bearing on the real world and real truth.
My claim is that statements about the real world are
often partly true and partly false. But propositional
calculus only recognizes two possible truth values for
a statement, T or F. According to propositional
calculus no statement is 50% True and 50% percent
False. As such, by definition propositional calculus
dictates that everything in the real world is either 0
or 1, digital, and binary. Propositional calculus is
false for anything in the real world that is not 0 or 1.
Or put another way, propositional calculus would be
true of the real world, if all balls were 100% black or
if all balls were 100% white, but in a world that is
partly black, partly white and partly grey, propositional
calculus will always deliver a false answer.
> Definitions in everyday language are slippery
When you say, "everday language," you don't say
what you really mean. You mean any language that
pertains to the real world which contains things that
are not pure, that are not 0-1, that are partly black
and partly white, that are shades grey. Say what
you really mean. Don't decieve!
> Using only the symbols of propositional calculus, write
> out the statements 'Albert is half white', 'Albert is half black', and
> 'Albert is white', and show your disproof. I dare you. Clearly
> you've taken plenty of propositional calculus, and converting
> these statements (which you claim are not ill-defined) into
> statements of propositional calculus should be a trivial job.
> Let's see it.
So what you are saying is that you can only substitute
symbolic propositional calculus statements for "p" and "q,"
you can't insert statements about the real world for "p"
and "q." Then I quite agree. But this proves my point
that you can only substitute for "p" and "q" statements
from Boolean logic and such, but not any statement that
applies to the real world. As such, propositional calculus
would be quite useless. Actually, I don't have as dim a
view of propositional calculus as you. I maintain that
English statements can be substituted for "p" and "q"
so long as all the underlying reality is binary, discrete,
and digital. Propositional calculus can be used
effectively for describing the position of billard balls,
because every billard ball is either at a certain position
or its not.
Matthias Weiss
>
> Matthias Weiss mm...@po.cwru.edu wrote:
> > Define the set of white objects, and I'll tell you whether Albert is in
> > it. That's all what a first-order logic claims to do -- and does.
>
> Define "white" anyway you want, and my statement will lead
> to a contradiction. Just reember any definition you make for
> "white" must imply an analgous definition for "black" in order
> for your language to be consistent.
That's not what I said. I said "Define the set of white OBJECTS!".
Moreover, I do not need to say anything about "black" if I want to talk
about "white". I don't have to talk about negative integers if I want to
discuss natural numbers. I can talk consistently about "water" without
any reference to "steam" or "ice".
Propositional calculus is not about natural languages with their fuzzy
definitions either. It defines a relation R as a subset of the cross
product of two sets, X and Y. If x is in X and y is in Y, then "xRy" is
a true statement if and only if (x,y) is an element of R. Thus "is
element of X" is just a special case of this with R=X and Y the empty
set. Once you've described the set X, you can do propositional calculus
with it.
Complete the following statement: "An object 'A' is called white if and
only if..." Mathematics is not concerned about objects that are not
well-defined. Your problem is linguistic in nature, not mathematical.
You're attempting to discredit the theory by claming that it cannot do
what it never intented to do in the first place. It must be Strawman
festival in town (c.f. the "Nihilism" post).
Matthias Weiss.
Geoff Sheffield
arctic...@aol.com (ArcticBonfire) wrote:
> According to pc every statement is either true or false.
> Suppose I have a ball called Albert that is exactly half
> white and half black. Now, take the following statement:
> "Albert is white." Such a statement can never be just
> true or false.
>
Did you post this to sci.math? That seems to be the
proper place to post a great discovery such as this.
You don't want somebody else to come along and take
credit for it, do you?
--
Geoff Sheffield
ArcticBonfire
> This from the man who complains when others mention
> their credentials...
I only complain when others supply their credentials to
bolster their position. I did not supply my credentials
to bolster my position, but to refute the insult and
ad hominem attack that I was uneducated. If I had
accused you of being uneducated in the field of math,
then I would have found nothing wrong with your
supplying math credentials. But as I recall, you supplied
your math credentials to bolster your argument.
mag...@math.berkeley.edu (Arturo Magidin) wrote:
> The key here is that Propositional Calculus starts out by
> considering only ->certain sentences<- among an already
> possibly restricted class of declarative sentences. It then
> proceeds to study how the truth value of composite formulas
> may be derived from the truth value of the prime formulas they
> are built out of. Nothing in Propositional Calculus asserts that
> ->every<- declarative sentence in the object language be a
> prime or atomic formula, as was asserted to begin with.
As far as I'm concerned, this is just a bunch of crap. Give me
a reality that is digital, discrete, quantum and non-fractional where
every statement is either true or false, and propositional
calculus (PC) will be valid for all statements about such a reality.
Give me a reality that is analog, fractional, continuum, fractal
and propositional calculus will stumble.
You can't prove what you assume by definition. And PC
assumes by definition that every statement is either true
or false. In every PC proof there is a hidden premise.
That premise is hidden in the number of truth values
assigned to every proposition, it is hidden in the definition
of "statement" and "meaningless." Every proof in PC is
simply a reiteration of these hidden premises. Every
proof in PC should really contain the following line in its
list of premises: "p v -p."
> "Here we must mention the fact that the natural word
> languages, such as English, suffer from ambiguities. (Of
> this, more will be said later.) Logicians are therefore prone
> to build special symbolic languages."
As I have stated again and again, as long as you can
limit pc to mathematical statements or logical statements
that do not apply to the real world, but are merely symbolic
restatements of the hidden premise "p v -p", then this dirty
hidden premise of PC is not violated, and the conclusion
of any PC proof will be true. But as soon as you try
applying PC to the real world which contains shades of
grey, object that are not discrete, scales that are continuum
and not quantum, PC stumbles.
> Again, we have the notion that natural language must be
> formalized before Propositional Calculus can be applied.
The use of the word "natural language" is dishonest. What
logicians really mean by "natural language" is any language
where real world objects or properties can be substituted for
symbols.
ArcticBonfire
>You're a funny little man.
And you are an unfunny, fat slob.
Arturo Magidin
ArcticBonfire <arctic...@aol.com> wrote:
>mag...@math.berkeley.edu (Arturo Magidin) wrote:
[.snip.]
>mag...@math.berkeley.edu (Arturo Magidin) wrote:
>> The key here is that Propositional Calculus starts out by
>> considering only ->certain sentences<- among an already
>> possibly restricted class of declarative sentences. It then
>> proceeds to study how the truth value of composite formulas
>> may be derived from the truth value of the prime formulas they
>> are built out of. Nothing in Propositional Calculus asserts that
>> ->every<- declarative sentence in the object language be a
>> prime or atomic formula, as was asserted to begin with.
>
Please note that the respondent has removed, without marking the
deletion, direct quotes from the textbook by Stephen Kleene which I
have provided.
>As far as I'm concerned, this is just a bunch of crap.
Good for you. The mathematical community disagrees, but what the
hey. You're a genius anyway.
[.snip.]
>You can't prove what you assume by definition. And PC
>assumes by definition that every statement is either true
>or false. In every PC proof there is a hidden premise.
>That premise is hidden in the number of truth values
>assigned to every proposition, it is hidden in the definition
>of "statement" and "meaningless."
You are confusing the theory with its model. You have provided an
attempted model which does not meet the axiomatic requirements of
PC. Big surprise when it turns out not to apply.
> Every proof in PC is
>simply a reiteration of these hidden premises. Every
>proof in PC should really contain the following line in its
>list of premises: "p v -p."
Every theorem in mathematics (at least, the math which is done using
the axiomatic method) is nothing but "simply a reiteration of these
[...] premises". There is nothing "hidden" about the premises, since
they are always put forth front and center at the beginning. Common
practice, of course, is to state theorems not in the clumsy "If all
the axioms hold and all the premises hold, then this thing happens",
but rather to leave the "all axioms hold" as an understood
requirement, since we are working within the theory. Surely you
noticed this practice in the _Principia_?
For example, in Propositional Calculus, the fact that not all
declarative sentences of the object language are necessarily
considered, and that certain conditions must apply to all the
sentences which ->are<- considered, is also front and center, and
there is nothing hidden about it. For example, in the quote I
provided, which you removed, it is clear that they appear in the
second page of the textbook in Mathematical Logic which I refered
to. The axioms and the hypothesis are the very first thing which is
stated.
In an axiomatic theory, of course, every theorem is nothing more than
a direct formal consequence of the axioms. This is true of the entire
field of Group Theory, Field Theory, Ring Theory, Linear Algebra,
Module Theory, and countless others.
There is nothing surprising about it, nor is there anything that might
suggest otherwise. The axioms of Propositional Calculus are, indeed,
tautologies. A full, complete formal proof, contains nothing but
axioms, and direct formal consequences of previous lines; as such,
your statement is of course correct, well known, and hardly
interesting.
In the specific case of Propositional Calculus, it is not hard to
construct a Turing Machine that will test an arbitrary well-formed
formula and decide whether or not it is a theorem (i.e. a logical
consequence of the axioms). Which does not mean it is a trivial theory
in and of itself, of course...
>> "Here we must mention the fact that the natural word
>> languages, such as English, suffer from ambiguities. (Of
>> this, more will be said later.) Logicians are therefore prone
>> to build special symbolic languages."
>
>As I have stated again and again, as long as you can
>limit pc to mathematical statements or logical statements
>that do not apply to the real world, but are merely symbolic
>restatements of the hidden premise "p v -p", then this dirty
>hidden premise of PC is not violated, and the conclusion
>of any PC proof will be true.
There is nothing "hidden" or "dirty" in the axiomatization of
Propositional Calculus. It is right there in the open, and it is, of
course, understood by its practitioners. As someone with a deep grasp
of the subject, as you have stated, you are surely aware of how
axiomatic theories work. You are probably also aware that any use to a
model requires a very precise identification of the primitive terms
and a very careful verification of the axioms before the conclusions
derived from the axiomatic method can be said to apply to the
particular model.
> But as soon as you try
>applying PC to the real world which contains shades of
>grey, object that are not discrete, scales that are continuum
>and not quantum, PC stumbles.
Amazingly enough, given that PC is not ->intended<- to apply to such
models and situations. It's almost as surprising as the fact that my
car cannot fly, given that it was not designed for such a purpose.
>> Again, we have the notion that natural language must be
>> formalized before Propositional Calculus can be applied.
>
>The use of the word "natural language" is dishonest.
Hardly. It is a common usage in the context of mathematical logic. And
it is clearly defined in the book I am quoting before being used.
> What logicians really mean by "natural language" is any language
>where real world objects or properties can be substituted for
>symbols.
I'll add "mind-reader" to your already quasi-impressive list of
qualifications.
Again, you are confusing the theory with the model. It is a relatively
easy matter to find a model for Propositional Calculus inside of the
'real world', provided you do not insist that the collection of atomic
formulas include everything which constitutes a "declarative
sentence." Which is why, for example, Kleene immediately talks about a
->class<- of declarative sentences, consisting only of ->certain<-
sentences. These sentences can relate to the real world, provided the
axioms are satisfied. Or they can be entirely meaningless from a
grammatical point of view... provided the axioms are satisfied.
At best, your arguments show that, with English as the object
language, interpreting "prime formulas" to mean all declarative
sentences in the English language is not a model for Propositional
Calculus. A truly remarkable feat, given that it has been known for at
least as long as Propositional Calculus has existed as a formal
mathematical axiomatic theory.
If I were forced to try and find anything hidden or dishonest, I would
have to point the finger at someone claiming expertise who nonetheless
misrepresents the field to such an extent as to contradict what
appears in page 2 of a standard textbook of the field.
But that would probably just be me.
I'll look forward to your presentation at the next AMS meeting, or
else to your posting your argument in sci.math.
Until then, good bye. You are welcome to the last word.
coffee
arctic...@aol.com (ArcticBonfire) wrote:
(snip)
Sigh, I'm unsure what to think. Are you a moderately intelligent troll as
you claim? well, technically I don't think that you've claimed to be a
troll, but if any of the sticks up your ass that you mentioned earlier are
true, then you are purposefully misunderstanding things, or ... I know now
... you only alluded to being at least 12, and then mentioned "several more"
logic courses upon real enrollment. You're 13, or 14 right? Cool, a PFY to
play with. I wonder if you've entered Piaget's "formal operations" stage?
If you haven't that could explain why you can say a lot of words yet still
not comprehend them.
I'd say your potential youth makes you even more entertaining,
except that I hate kids. I don't suppose someone who does
like kids would like to take care of him? Perhaps we
could keep him/her as something like a pet? Does Arcty do
any tricks? Huh, do ya? do ya? (throws stick into
some.mensa.group) Go fetch Arcty, fetch! (whispering)Everyone
get ready to shut the door when it runs out.
-coffee
Arturo Magidin
>> This from the man who complains when others mention
>> their credentials...
>
>I only complain when others supply their credentials to
>bolster their position. I did not supply my credentials
>to bolster my position, but to refute the insult and
>ad hominem attack that I was uneducated. If I had
>accused you of being uneducated in the field of math,
>then I would have found nothing wrong with your
>supplying math credentials. But as I recall, you supplied
>your math credentials to bolster your argument.
[.rest deleted.]
Your memory, I fear, is faulty.
I mentioned my credentials in response to the following statement,
made in article <20010204155655...@ng-fk1.aol.com>:
"You wouldn't know a Schwarzschild metric from a
Euclidean-Schwarzschild metric, you wouldn't know an eigenvalue from
an eigenvector, and you wouldn't know a Calabi-Yau space from a
Lobachevskian space."
Although two of the comparisons relate to terminology used mostly in
physics, one of them relates to very basic mathematical terminology,
and in case, they all relate to mathematics (metrics are mathematical
entities, as are the spaces mentioned in the third statement). As
such, even if not intended to, your statement did inlcude an
accusation of being ignorant about at least one very basic
mathematical subject.
In addition, the credentials were mentioned explicitly as follows:
"Yeah. I probably don't know the difference between an eigenvalue (a
scalar) and an eigenvector (a vector). After all, that's why I have a
Ph.D. in math and why I'm teaching a course in linear algebra."
They were not used to bolster an argument, but to reply to your
assertion that I wouldn't know an eigenvector from an eigenvalue.
Have a nice day.
eyele...@my-deja.com
coffee <cof...@ack.caltech.edu> wrote:
> In article <9601ao$7kb$1...@nnrp1.deja.com>,
> eyele...@my-deja.com wrote:
>
> > (Caltech '92)
>
> out of curiosity, what house? A fellow Skurve?
Almost. :) Darb.
eyele...@my-deja.com
> > And in every class you somehow missed the day
> > where they said 'in order to do formal logic you
> > must define your terms.
>
> All the terms, I used were defined. What term did
> I use, do you alledge is undefined?
"Is" -- one of the most slippery words in the language. You wish to have
a definitive answer to whether "'A is half white' implies 'A is white'"
is true. "Is" can mean 'contains', 'has the property', 'is identical
to', 'has only the property', and a number of other meanings. Which
were you intending it to mean, in your latter statement ('A is white')?
You can make all the oral sex jokes you like: the former president was
absolutely correct when he said 'it depends on what your definition of
"is" is.'
I agree with what you seemed to be saying (albeit with some lack of
coherence) at the end of your post: Propositional calculus is a tool
that is applicable in some circumstances and not in others -- like *all*
of mathematics. How does this have anything to do with your subject line
-- or was the subject line merely a troll? (If so, I fell for it, I
admit.)
Termite of Temptation
"ArcticBonfire" <arctic...@aol.com> wrote in message
news:20010208164725...@ng-bd1.aol.com...
> According to pc every statement is either true or false.
> Suppose I have a ball called Albert that is exactly half
> white and half black. Now, take the following statement:
> "Albert is white." Such a statement can never be just
> true or false.
The statement you give is not well-formed in propositional calculus. Every
WELL-FORMED statement in PC is true or false. Even in a system of
multi-valued logic like you propose, deductions WITHIN that system are true
or false. The "contradiction" is caused by the ambiguity of the English
language.
What you need is a set of objects, O, of which Albert would clearly be a
member.
Then you need a set of properties P that can apply to objects in O. These
properties don't have to be mutually exclusive, but you should be clear in
your definition which properties can coexist and which can't.
In P, you tell us whether "white" and "half black, half white" are mutually
exclusive or not. Then we'll tell you whether "Albert is white" is true or
false.
Thanks.
Duncan
--
Duncan
"I never make stupid mistakes. Only very, very clever ones."
-- Doctor Who
ArcticBonfire
> It's just a pity that you obviously did not understand much of all this.
It is a pity Mike Dowling that you still go around sodomizing little boys.
Do you find this obvious, as well?
> For a start, propositional calculus is about propositions, not
> statements. And a proposition in most treatises is _defined_
> as a statement that is either true or false.
<big yawn> That was my point, genius. Try telling me something
I don't know. Propositional calculus defines every statement as
having only two truth values. Every statement in PC which
restates this definition is true. Every statement in PC which
disputes this definition is false. Every statement in PC which
says nothing about this definition is neither true nor false. All PC
does is literially rehash its definition that every statement is
either T v F. Since in the real world, this premise is not
always true, in order for PC to remain internally consistent,
it must not accept any statements about the real world,
claiming that such statements are not valid statements.
Every true statement in PC is circular logic. Find a statement
that refutes PC by being a counter-example, and PC claims
that such a statement is not a statement by definition. So
by definition every statement is either true or false, and any
statement that defies this definition is not a statement, by
definition. And every logical proof in PC is simply a reiteration
or restatement of this definition. Totally circular.
> And you really should have read Wittgenstein. Statements
> can be true, false, or meaningless. It is so very easy to mistake
> a meaningless statement for a proposition; that, in essence, is
> what lies behind Russel's paradox; Wittgenstein cleared that up.
Betrand Russell knew very well that statements can be true,
false or meaningless. You do not seem to know what you
are talking about.
> Your example was a silly one precisely because it was left
> unclear what you meant. Did you mean that the ball was entirely
> white, or partially white. (I would have interpreted it as "entirely
> white", and so said that it is false.)
No matter how you define the terms in my sentence, you will
always be left with a contradiction in PC.
> A better example of a meaningless statement is "Yesterday was
> yellow." Clearly, something temporal cannot have colour
> attributes.
Your statement is meaningless, my statement is not meaningless.
"Yesterday was yellow" conveys no information. "The ball is white"
does convey information. If a statement conveys true information,
it cannot be meaningless.
> You read Principia Mathematica when you were twelve? Are you
> aware that what Russel and Whitehead were attempting to prove
> with this work was proved false before they finished it,
I don't believe this is true. Not only do I not believe this is true,
I don't believe anything in Principia Mathematical has ever
proven to be false. I think you have been taking too many drugs.
> Are you aware that what Russel and Whitehead were attempting
> to prove with this work was proved false before they finished it,
> which is why they left their work unfinished? Did you even realise
> that it was unfinished?
If you can provide some evidence for this, I will admit you know
more about logic than I do. And I will offer you my sincere
apologies. Until you do, it is my guess that you are some druggie
or psychotic who has experienced a complete break with reality.
I don't think you have ever read Principia, nor do I believe you
know the first thing about it.
> I'm not normally this forthright,
I have no problem with people being forthright.
> you elected to "pull rank"
This is a lie. You elected to pull rank, and you falsely
claimed I had no education in logic. I, merely, rebutted
your claim. Don't blame me for your misinterpretting
my rebuttal of your false accusation. If it was
someone else who made this allegation, then you
mistook what was a clear rebuttal of a false accusation
as support for my contentions. In either case, you have
drawn utterly false conclusions, which doesn't surprise
me considering everything else you have claimed.
ArcticBonfire
>> My statement is not ill-defined.
>
> Yes it is. Yes it is. Ill defined. Ambiguous. Do you see it now?
Hello, Sammy Davis. Just repeating you're right and over again
again like a mantra is pointless. The burden of proof rests
with you. All I see is someone who thinks that if they
repeat a lie often enough, others might start believing it.
"I'm right, just because." You sound like a child.
ArcticBonfire
>The difficulty here is one that many students of elementary
> logic have
This is a false assumption as you have yet to realize
the true nature of the problem I am presenting. Sometimes
when we make a point, we need to progress one step at
a time.
> you have not properly defined the predicate "is"
I leave that up to you to define anyway you choose.
> which in this instance could be stated as "is_colored".
> If we define is_colored(A,color) as "A contains color
> and only color" then is_colored(albert,white) is false
> as is is_colored(albert,black). If, however, we define
> is_colored(A,color) as "A contains color" then is_colored
> (albert,white) is true.
This is the answer I was looking for and expecting.
I am so happy. Finally, I get someone who is intelligent.
Good, now we are making progress. Your post demands
a well thought out response. I think we are going to get
somewhere. Please bear with me for a few posts, and
I think you will understand the point I am trying to make
when we are finished. Don't jump the gun.
I have some business to attend to, but I will come back
to this post.
Termite of Temptation
Well, yes. PC doesn't tell us about the real world. The relevance is merely
that we can take assertions and make deductions ASSUMING those assertions
are true. You can't sit on your ass in your room and learn anything about
the world. It is circular. Once you starting plugging in well-accepted
assertions, you get interesting results. Or you plug in controversial ones,
and look for a contradiction (indicating false premises). This is what PC is
for.
> > And you really should have read Wittgenstein. Statements
> > can be true, false, or meaningless. It is so very easy to mistake
> > a meaningless statement for a proposition; that, in essence, is
> > what lies behind Russel's paradox; Wittgenstein cleared that up.
>
> Betrand Russell knew very well that statements can be true,
> false or meaningless. You do not seem to know what you
> are talking about.
Do you know Russell's paradox? It has nothing to do with Betrand's
ignorance. He just stated - imagine a book, B, containing a list of every
books that do NOT mention themselves at all (it doesn't list any others).
The question is, does B mention itself? If it does, then it shouldn't,
because it shouldn't mention books that mention themselves.
But if it doesn't, then it should.
Thus we deduce that no such book B exists. Simple really. Your answer wasn't
very helpful.
> > Your example was a silly one precisely because it was left
> > unclear what you meant. Did you mean that the ball was entirely
> > white, or partially white. (I would have interpreted it as "entirely
> > white", and so said that it is false.)
>
> No matter how you define the terms in my sentence, you will
> always be left with a contradiction in PC.
No. I define "Albert" to be "the Earth"
I define "white" to be "larger than the sun"
I define "half white and half black" to be "smaller than the sun"
The statement "Albert is white", if we assume "Albert is half white and half
black", is then false.
Easy.
Your problem is the re-use of the symbol "white" in two different contexts.
Mathematicians don't do that because of the ambiguity generated.
> > A better example of a meaningless statement is "Yesterday was
> > yellow." Clearly, something temporal cannot have colour
> > attributes.
>
> Your statement is meaningless, my statement is not meaningless.
> "Yesterday was yellow" conveys no information. "The ball is white"
> does convey information. If a statement conveys true information,
> it cannot be meaningless.
"The ball is white" might mean something in English, but that's not the same
as meaning something in another formal system.
> > You read Principia Mathematica when you were twelve? Are you
> > aware that what Russel and Whitehead were attempting to prove
> > with this work was proved false before they finished it,
>
> I don't believe this is true. Not only do I not believe this is true,
> I don't believe anything in Principia Mathematical has ever
> proven to be false. I think you have been taking too many drugs.
Stop attacking this guy, please. If you want to talk logic, let's talk
logic. If you want to slag people off, go on Jerry Springer.
[snip boring pissing contest]
Mike Smith
= ArcticBonfire <arctic...@aol.com> wrote:
= >mag...@math.berkeley.edu (Arturo Magidin) wrote:
= >> This from the man who complains when others mention
= >> their credentials...
= >
= >I only complain when others supply their credentials to
= >bolster their position. I did not supply my credentials
= >to bolster my position, but to refute the insult and
= >ad hominem attack that I was uneducated. If I had
= >accused you of being uneducated in the field of math,
= >then I would have found nothing wrong with your
= >supplying math credentials. But as I recall, you supplied
= >your math credentials to bolster your argument.
=
= [.rest deleted.]
=
= Your memory, I fear, is faulty.
=
= I mentioned my credentials in response to the following statement,
= made in article <20010204155655...@ng-fk1.aol.com>:
=
= "You wouldn't know a Schwarzschild metric from a
= Euclidean-Schwarzschild metric, you wouldn't know an eigenvalue from
= an eigenvector, and you wouldn't know a Calabi-Yau space from a
= Lobachevskian space."
Oops.
__________________________________________
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Mike Smith | aa #1164 | Founder of SMASH
(Sarcastic Middle-aged Atheist with a Sense of Humor)
__________________________________________
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
"Eat thou not the bread of him that hath an evil eye,
neither desire thou his dainty meats." - Pr.23:6
coffee
arctic...@aol.com (ArcticBonfire) wrote:
> Fred Stone fsto...@earthlink.net wrote:
> >The difficulty here is one that many students of elementary
> > logic have
>
> This is a false assumption as you have yet to realize
> the true nature of the problem I am presenting. Sometimes
> when we make a point, we need to progress one step at
> a time.
>
> > you have not properly defined the predicate "is"
>
> I leave that up to you to define anyway you choose.
>
> > which in this instance could be stated as "is_colored".
> > If we define is_colored(A,color) as "A contains color
> > and only color" then is_colored(albert,white) is false
> > as is is_colored(albert,black). If, however, we define
> > is_colored(A,color) as "A contains color" then is_colored
> > (albert,white) is true.
>
> This is the answer I was looking for and expecting.
Out of curiosity, were you looking for the somewhat more formal
format which Fred Stone used, or did you just not comprehend
or ignore (and if so which) the at least two other posts
which not only said that "is" is vague, but gave examples
of how with specific definitions of "is" the truth/falsity
of "Albert is white" would be non-ambiguous?
If you were just looking for the closer to formal answer,
why are you so special as to not need to approach formality?
Or ... is there any other info that you think would be
relavent to your skipping the issue that many people
raised feigning ignorance of how "is" was vague, yet
supposedly looking just for this?
-coffee
Peter van Velzen
For a true disprove of propositional calculus
we have to depent on greater thinkers than we are.
As far as I know a professor of mathematics succeeded in doing so,
and I heard a collegue of him found another way to do it.
I only heard about the first one, because he happened to be Dutch.
Your ball would only be a good disproof - I belief
If the ball would be infinitly small or something like that.
--
"Think for yourself"
Atheist #1107
Peter van Velzen
Amstelveen
The Netherlands
http://home-2.worldonline.nl/~pbamvv/petervve.htm
ArcticBonfire <arctic...@aol.com> wrote in article
<20010208164725...@ng-bd1.aol.com>...
Yang
<tw...@city-of-dis.com.eac> wrote:
>On 08 Feb 2001 21:47:25 GMT, arctic...@aol.com (ArcticBonfire)
>wrote in alt.atheism:
>
>>According to pc every statement is either true or false.
>>Suppose I have a ball called Albert that is exactly half
>>white and half black. Now, take the following statement:
>>"Albert is white." Such a statement can never be just
>>true or false.
>
>Betcha they say "Albert is white" isn't true or false, but
>meaningless.
A case of the false dilemma?
Scott Storm
John Hattan wrote:
> arctic...@aol.com (ArcticBonfire) wrote:
>
> >I beat college students at Wff n' Proof when I was nine. I read Principia
> >Mathematica when I was twelve. I took several formal, undergraduate
> >logic courses at University of Michigan when I was thirteen. I read just
> >about every book that Copi ever wrote. I took several more logic courses,
> >when I was fully matriculated. I sincerely doubt you have the formal
> >educational background in logic that I have or the fundamental grasp.
>
> Check out the big brain on bonfire!
>
Thanks man!
Now I gotta clean up all this friggin beer ;>o
Arturo Magidin
[.snip.]
>= Your memory, I fear, is faulty.
>=
>= I mentioned my credentials in response to the following statement,
>= made in article <20010204155655...@ng-fk1.aol.com>:
>=
>= "You wouldn't know a Schwarzschild metric from a
>= Euclidean-Schwarzschild metric, you wouldn't know an eigenvalue from
>= an eigenvector, and you wouldn't know a Calabi-Yau space from a
>= Lobachevskian space."
>
>Oops.
Isn't the easy checking of recent messages on Usenet so ->annoying<-
when one is trying to score a rhetorical point based on a double
standard?
William Barwell
ArcticBonfire <arctic...@aol.com> wrote:
>According to pc every statement is either true or false.
>Suppose I have a ball called Albert that is exactly half
>white and half black. Now, take the following statement:
>"Albert is white." Such a statement can never be just
>true or false.
The proposition is false. Albert is half white and half black, not white.
He could be black, or red, or colored like a kaleidoscope
scene, it matters not, except that Albert is not white.
White and black =\= white.
Pope Charles
SubGenius Pope of Houston
Slack!
Martin Thomas
> As I have stated again and again, as long as you can
> limit pc to mathematical statements or logical statements
> that do not apply to the real world, but are merely symbolic
> restatements of the hidden premise "p v -p", then this dirty
> hidden premise of PC is not violated, and the conclusion
> of any PC proof will be true.
Who is hiding it?
> But as soon as you try
> applying PC to the real world which contains shades of
> grey, object that are not discrete, scales that are continuum
> and not quantum, PC stumbles.
Why on Earth would anyone try to apply PC in such a way? Can you
name anybody who has actually tried to do that? It might be amusing
to look *briefly* at the work of such an idiot - but I am wondering
if you are attacking a straw dog here.
** Martin Thomas **
What does not kill me makes me stronger - Nietzsche
http://www.thehungersite.com/cgi-bin/WebObjects/HungerSite
To reply, turn off the light.
Martin Thomas
> mik...@moocow.math.nat.tu-bs.de (Mike Dowling) wrote:
> > It's just a pity that you obviously did not understand much of all this.
>
> It is a pity Mike Dowling that you still go around sodomizing little boys.
> Do you find this obvious, as well?
>
> > For a start, propositional calculus is about propositions, not
> > statements. And a proposition in most treatises is _defined_
> > as a statement that is either true or false.
>
> <big yawn> That was my point, genius. Try telling me something
> I don't know. Propositional calculus defines every statement as
> having only two truth values. Every statement in PC which
> restates this definition is true. Every statement in PC which
> disputes this definition is false. Every statement in PC which
> says nothing about this definition is neither true nor false. All PC
> does is literially rehash its definition that every statement is
> either T v F. Since in the real world, this premise is not
> always true, in order for PC to remain internally consistent,
> it must not accept any statements about the real world,
... except that part of the real world called PC!
> claiming that such statements are not valid statements.
> Every true statement in PC is circular logic.
Well if you want to look at it that way, so is every theorem in
mathematics. In fact, many advanced books on mathematics start off
by defining things in terms of set theory and use the language of
PC. Do you think that mathematics has anything to do with the real
world?
The Boolean logic used to design silicon chips is closely allied
with PC. Maybe that's why computers are not really intelligent!
I think the point you are making in this thread has some validity:
life certainly is far bigger than PC. But the example you gave was
not a useful one.
> Find a statement
> that refutes PC by being a counter-example, and PC claims
> that such a statement is not a statement by definition. So
> by definition every statement is either true or false,
Not every statement, just those statements that PC deals with.
> and any
> statement that defies this definition is not a statement, by
> definition. And every logical proof in PC is simply a reiteration
> or restatement of this definition. Totally circular.
It is your description of it that is circular.
> > And you really should have read Wittgenstein. Statements
> > can be true, false, or meaningless. It is so very easy to mistake
> > a meaningless statement for a proposition; that, in essence, is
> > what lies behind Russel's paradox; Wittgenstein cleared that up.
Russell's paradox arose because a proposed collection of axioms for
set theory were internally inconsistent. He found a way to modify
those axioms to get rid of the inconsistency. What did Wittgenstein
say about that?
ArcticBonfire
> Out of curiosity, were you looking for the somewhat
> more formal format which Fred Stone used, or did
> you just not comprehend or ignore (and if so which)
> the at least two other posts which not only said that
> "is" is vague
The vagueness of the statement is easily eliminated,
but eliminating the vagueness of the statement comes
at a cost. You will have to watch how I will answer
Fred to see why I expected and needed Fred's answer.
> but gave examples of how with specific definitions
> of "is" the truth/falsity of "Albert is white" would be
> non-ambiguous?
I don't remember those posts, but they weren't precise
and/or clear enough for me to be able to proceed with
my point. Fred gave the exact response I was looking
for. You will see from my answer to Fred, why I needed
an answer in exactly the form Fred gave it. In fact, it
didn't have to be stated so perfect. But what I needed
was the two possible meanings to proceed to the
next step.
> If you were just looking for the closer to formal answer,
> why are you so special as to not need to approach formality?
It was not exactly the formal form I was looking for, but the
two possible interpretations. Anyway, before you criticize
my approach, you first may want to wait till I finish making
my point.
> Or ... is there any other info that you think would be
> relavent to your skipping the issue that many people
> raised feigning ignorance of how "is" was vague, yet
> supposedly looking just for this? --coffee
If you ever became an airline stewardess, you could
say, "Coffee, tee or coffee."
The vagueness of the word "is" can be remedied in
the manner that Fred provided. Just saying that the
word "is" is vague is not a complete answer. That
leaves unending possibilities, when in reality there
are just two ways to interpret the sentence according
to PC, and Fred listed them both in impressive, beautiful
fashion. Which gives me the lead-in I need to continue
with my point. Fred made my job easy.
=========================================
I see we have a lot of Clinton supporters here.
"It all depends upon what the definition of 'is' is.
Clinton could have used you guys to defend him.
ArcticBonfire
> I beat college students at ... the fundamental grasp.
The above paragraph was in response to this statement,
"Come back when you have got a little bit of education"
by Lars Eighner eig...@io.com. I did not intend for it
to bolster my position.
ArcticBonfire
> It's just a pity that you obviously did not understand much of all this.
It is a pity Mike Dowling that you still go around sodomizing little boys.
Do you find this obvious, as well?
> For a start, propositional calculus is about propositions, not
> statements. And a proposition in most treatises is _defined_
> as a statement that is either true or false.
That was my point, genius. Try telling me something
ArcticBonfire
> Well, yes. PC doesn't tell us about the real world. The
> relevance is merely that we can take assertions and
> make deductions ASSUMING those assertions
> are true.
You missed my point. The question is can you
substitute statements about the real world for
"p" and "q." Since only valid, meaningful, precise
statement statements can be substituted for "p"
and "q" and since few English sentences qualify,
it seems that PC has very limited useage as far
as the real world is concerned.
> Do you know Russell's paradox?
I do. Do you?
> It has nothing to do with Betrand's ignorance.
I ***NEVER*** said it did.
> He just stated - imagine a book, B, containing a list of
> every books that do NOT mention themselves at all
> (it doesn't list any others). The question is, does B
> mention itself? If it does, then it shouldn't, because it
> shouldn't mention books that mention themselves.
This is not Betrand Russell's famous paradox, though
it sounds similar to it. Betrand Russell's famous
paradox is not about a books, but about the set of
all sets, and whether or not it contains itself. And
his paradox is not composed in English words, but
in the language of symbolic logic.
> Simple really. Your answer wasn't very helpful.
Sorry, but I don't know what you are talking about.
>> No matter how you define the terms in my sentence, you will
>> always be left with a contradiction in PC.
>
> No. I define "Albert" to be "the Earth" I define "white" to be
> "larger than the sun" I define "half white and half black" to
> be "smaller than the sun"
Your definitions do not comport with the ones I gave. When
I said, you could use any definitions you want, I meant you
could limit my definitions any way you desired to make them
more precise, like Fred Stone did. Not that you could just
completely change the definitions I provided.
... to be continued.
Termite of Temptation
> "Termite of Temptation" n...@telling.com wrote:
> > Well, yes. PC doesn't tell us about the real world. The
> > relevance is merely that we can take assertions and
> > make deductions ASSUMING those assertions
> > are true.
>
> You missed my point. The question is can you
> substitute statements about the real world for
> "p" and "q." Since only valid, meaningful, precise
> statement statements can be substituted for "p"
> and "q" and since few English sentences qualify,
> it seems that PC has very limited useage as far
> as the real world is concerned.
>
> > Do you know Russell's paradox?
>
> I do. Do you?
>
> > It has nothing to do with Betrand's ignorance.
>
> I ***NEVER*** said it did.
The misunderstanding comes from the original post, in which some guy
mentioned Russel's paradox and you started talking about Betrand Russell's
knowledge, or lack of.
> > He just stated - imagine a book, B, containing a list of
> > every books that do NOT mention themselves at all
> > (it doesn't list any others). The question is, does B
> > mention itself? If it does, then it shouldn't, because it
> > shouldn't mention books that mention themselves.
>
> This is not Betrand Russell's famous paradox, though
> it sounds similar to it. Betrand Russell's famous
> paradox is not about a books, but about the set of
> all sets, and whether or not it contains itself. And
> his paradox is not composed in English words, but
> in the language of symbolic logic.
The meaning does translate. And yes, I know about the set theory
formulation, but there are non-mathematicians present. Slinging about
unnecessary technical terms is not fair to them. The problem is equivalent
to my stated book, or a robot fixing all robots that do not fix themselves,
or any other similar formulation.
> > Simple really. Your answer wasn't very helpful.
>
> Sorry, but I don't know what you are talking about.
Refer to the original post. Your non-sequitur wrt Russell's Paradox prompted
me to explain the paradox in more detail.
> >> No matter how you define the terms in my sentence, you will
> >> always be left with a contradiction in PC.
> >
> > No. I define "Albert" to be "the Earth" I define "white" to be
> > "larger than the sun" I define "half white and half black" to
> > be "smaller than the sun"
>
> Your definitions do not comport with the ones I gave.
You gave NO definitions, which is exactly the problem in the first place!
> When
> I said, you could use any definitions you want, I meant you
> could limit my definitions any way you desired to make them
> more precise, like Fred Stone did. Not that you could just
> completely change the definitions I provided.
Provide definitions next time, and no-one will change them.
> ... to be continued.
I look forward to it.
Regards,
Duncan
Fred Stone
I shall eat a herring in your honor.
>
>
> > Or ... is there any other info that you think would be
> > relavent to your skipping the issue that many people
> > raised feigning ignorance of how "is" was vague, yet
> > supposedly looking just for this? --coffee
>
> If you ever became an airline stewardess, you could
> say, "Coffee, tee or coffee."
>
> The vagueness of the word "is" can be remedied in
> the manner that Fred provided. Just saying that the
> word "is" is vague is not a complete answer. That
> leaves unending possibilities, when in reality there
> are just two ways to interpret the sentence according
> to PC, and Fred listed them both in impressive, beautiful
> fashion. Which gives me the lead-in I need to continue
> with my point. Fred made my job easy.
Why thank you. Glad to oblige.
You may wish to include fuzzy logic and non-deterministic
automata in the domain of your argument.
--
Fred Stone
ArcticBonfire
> Why thank you. Glad to oblige. You may wish to include
> fuzzy logic and non-deterministic automata in the domain
> of your argument.
You spoiled the ending. But basically, the need for fuzzy
logic is where I am headed. But I think it is instructive
to see how I get there, and why I think it is necessary.
I don't believe fuzzy logic is just a restatement of
probability theory, I think it is an important way of
thinking.
Fred Stone
I kind of thought that might be where you were heading.
By the way, for those who haven't studied this:
Fuzzy logic says that instead of fixed truth values of 0 and 1 (false
and true)
a statement can have a truth value in between (such as 0.5).
This isn't probabilistic. A truth value of 0.5 doesn't imply "odds of
50-50."
It's more like "you're half right."
This site:
http://www.abo.fi/~rfuller/fuzs.html
has a pretty extensive resource list.
I've been working with some Lisp AI code incorporating fuzzy
logic, and the results can be surprising. I'm quite optimistic that
FL automata could lead to progress on "artificial sentience"
if I can coin a phrase.
--
Fred Stone
aa # 1369
Noah Simoneaux
Then you were just making idle conversation? Figures.
Noah Simoneaux
Education is the process of moving from cocksure ignorance to thoughtful uncertainty.- Utvich's Observation
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keith_jo...@my-deja.com
But Arctic, the statement "Albert is white" can mean "Albert is nothing
but white" in which case it is false or it could mean "Albert has white
as well as other colors" in which case it is true. The truth or falsity
of the statemetn depends on what you meant when you said it; since there
are multiple intepretations the statement is ambiguous.
Keith
keith_jo...@my-deja.com
(snip)
>
> > Definitions in everyday language are slippery
>
> When you say, "everday language," you don't say
> what you really mean. You mean any language that
> pertains to the real world which contains things that
> are not pure, that are not 0-1, that are partly black
> and partly white, that are shades grey. Say what
> you really mean. Don't decieve!
>
> > Using only the symbols of propositional calculus, write
> > out the statements 'Albert is half white', 'Albert is half black',
and
> > 'Albert is white', and show your disproof. I dare you. Clearly
> > you've taken plenty of propositional calculus, and converting
> > these statements (which you claim are not ill-defined) into
> > statements of propositional calculus should be a trivial job.
> > Let's see it.
>
> So what you are saying is that you can only substitute
> symbolic propositional calculus statements for "p" and "q,"
> you can't insert statements about the real world for "p"
> and "q." Then I quite agree. But this proves my point
> that you can only substitute for "p" and "q" statements
> from Boolean logic and such, but not any statement that
> applies to the real world. As such, propositional calculus
> would be quite useless. Actually, I don't have as dim a
> view of propositional calculus as you. I maintain that
> English statements can be substituted for "p" and "q"
> so long as all the underlying reality is binary, discrete,
> and digital. Propositional calculus can be used
> effectively for describing the position of billard balls,
> because every billard ball is either at a certain position
> or its not.
I would say your title is a little misleading (not that there's anything
wrong with that:-) when it implies you have a DISPROOF of the
propositional calculus. What you are arguing is that reality is to
slippery to be captured with propositional calculus. In the example you
used, the hypothetical ball is half white and half black; in this case
the statement "the ball is white" is true depending on what you mean you
say that; if another person understands what you mean then this person
can examine the ball and determine the truth value of your claim. You
said that the terms in your example were clearly defined, but (as our
most recent ELECTED President said) "it all depends on what the word
'is' means". The ambiguous term you used was the verb "is".
So I guess I am asking: what significance do you draw from your
observation?
Ted King
<fsto...@earthlink.net> wrote:
Earlier today I was going through some old books trying to decide if I
should keep them or not. I came across "Cybernetics" (1961 edition) by
Norbert Wiener and was thumbing through a section he wrote about self
organizing systems in which non-linear phenomena play a part - really
fascinating (not that I grasped the mathematical details). I wonder what
he would have thought of your and others current research.
Ted
Fred Stone
"Cybernetics" is a seminal work in process control. Much of it's
content deals with feedback systems and has been absorbed into
standard EE courses. It's like standard material now.
Fuzzy logic has been used to create a generalized approach to
process controllers. Rather like feedback systems with adaptive
control of parameters. Also, it's possible to define FL systems
where complete knowledge of the problem domain is not available.
I'm sure that Weiner would have found it irresistable.
FL Automata is actually a different field. Has to do with generalizing
the "non-deterministic finite-state automaton" to fuzziness. Plug that
phrase into Google for some references.
In a nutshell, the CPU of a computer is a deterministic finite-state
automaton. Kind of a generalized Turing machine.
An FL automaton is capable of acting upon vague inputs, and of
generalizing and selecting outputs ("behaviors") according to less-than
perfect internal-state information.
This is way beyond the scope of a.a. and I'm not ready to publish anything
for sci.math yet. I'm just a dilettante, not a PhD.
Ted King
<fsto...@earthlink.net> wrote:
Reading his book it is fascinating to see the broad range of areas from
which he drew - in one section he describes the difference in strategy
between the mongoose and the cobra and how the adaptive behavior of the
mongoose is able to overcome the nonadaptive behavior of the cobra. It
does seem certain that he would have been delighted to "play" with fuzzy
logic systems.
> FL Automata is actually a different field. Has to do with generalizing
> the "non-deterministic finite-state automaton" to fuzziness. Plug that
> phrase into Google for some references.
> In a nutshell, the CPU of a computer is a deterministic finite-state
> automaton. Kind of a generalized Turing machine.
> An FL automaton is capable of acting upon vague inputs, and of
> generalizing and selecting outputs ("behaviors") according to less-than
> perfect internal-state information.
> This is way beyond the scope of a.a. and I'm not ready to publish anything
> for sci.math yet. I'm just a dilettante, not a PhD.
>
> --
> Fred Stone
> aa # 1369
>
Thanks for the lucid and concise summary. I will look up
"non-deterministic finite-state automoton", it sounds really
interesting. You may be "just a dilettante" but I have always
appreciated that people with much greater knowledge in philosophy,
theology, mathematics and physics have been willing to take the time to
scrum with those of us who don't know as much. I'm amazed at how much
I've learned in this newsgroup just by reading, asking a lot of
questions and keeping an open mind on things I thought I had figured
out. (I have had to work, though, at winnowing out and ignoring
emotively charged chaf from the kernals with value.)
Ted
ArcticBonfire
> I kind of thought that might be where you were heading.
> By the way, for those who haven't studied this: Fuzzy logic
> says that instead of fixed truth values of 0 and 1 (false
> and true) a statement can have a truth value in between
> (such as 0.5). This isn't probabilistic. A truth value of 0.5
> doesn't imply "odds of 50-50." It's more like "you're half right."
> This site: http://www.abo.fi/~rfuller/fuzs.html has a pretty
> extensive resource list. I've been working with some Lisp
> AI code incorporating fuzzy logic, and the results can be
> surprising. I'm quite optimistic that FL automata could lead
> to progress on "artificial sentience" if I can coin a phrase.
I believe that fuzzy logic computers will soon be able to solve
any problem humans can solve. I believe fuzzy logic will
create true artificial intelligence and create computers
that will replace university professors, judges, engineers,
and any occupation that requires intelligence. These
computers or fuzzy logic automata will not be sentient
to the slightest degree. They will communicate like
humans, process information and solve problems like
humans, but they will not possess any degree of
sentience. And they will be the first to tell you this.
They will not even know what you are talking about.
Fuzzy logic computers will have I.Q.s that are off the
scales. They will solve all the remaining solvable problems
in physics, they will speak every language on the planet.
But they will have zero sentience. Sentience comes from
a different part of the brain than the parts that are
responsible for human intelligence, memory and information
processing. Intelligence is one axis, sentience is another.
Humans will become more intelligent and less sentient.
Humans may eventually evovle into some highly intelligent
species that possesses no sentience. Humans may
eventually evolve into a species of organic robots that
only have a will to reproduce in the most efficient way
possible. The cereberal cortex and frontal lobes are
responsible for human intelligence. The hypothalamus
is responsible for human sentience. These two organs
are at odds with each other and fight each other
constantly for control over the body. When this happens
humans are conflicted and say they can't make up
their mind. Some humans have a more evolved cereberal
cortex, some humans have a more evolved hypothalamus.
Evolution will decide which humans will finally populate
the Earth. The future human may well have an atavistic
or shrunken hypothalamus, and very little emotional
and feeling apparatus, like Bill Gates.
Fred Stone
Well, we agree on the potential for AI.
I can't agree or disagree with you about "sentience" because I don't
understand your definition. The dictionary defines sentience
as "feeling or perception."
The hypothalamus is involved with basal brain mechanism
and deals with autonomic regulatory function. It also connects
the nervous and endocrine systems. And possibly, has some
effects upon emotional response.
Is it necessarily the case that "intelligence" must develop at
the expense of "feeling?" Quite the contrary, I think that
"feeling" is enhanced as intelligence grows and broadens.
No doubt, if AI proceeded strictly along classical "expert system"
lines, then such structures would not develop. But these would not
be self-aware systems. I think that self-awareness is a function
of feedback through internal states of the organism. A truely
self-aware AI system would indeed "feel" in the sense of being
aware of internal states, positive or negative, and would be
capable of expressing such "feelings."
You may of course deny that such expression would be "true sentience"
but I don't know how you'd distinguish the two.
As to the more mystical aspects of your exposition above,
I cannot agree. Different "organs" of the brain do not "fight...
for control over the body" unless the individual affected has
lost some essential integrative capacity due to trauma or lack
of development. One example might be a severed corpus callosum.
Humans may be conflicted for many different reasons, some of
which may involve deep brain structure, other involving unresolved
symbol mappings or unintegrated "subroutines" of the mind.
Psychoanalysis has found much of this type of conflict to arise
strictly within the conscious and subconscious and to be related
to development of the person from infancy through adulthood.
This type of conflict could not arise from basal levels such as
the hypothalamus.
--
Fred Stone
ArcticBonfire
> I can't agree or disagree with you about "sentience"
> because I don't understand your definition. The dictionary
> defines sentience as "feeling or perception."
As always, my definition and the dictionary definition
coincide. Computers have no feeling or perception.
Feeling is pain, pleasure, hate, love, fear, anxiety.
Perception is red, green, blue, sweet, sour, and
any number of smells.
> The hypothalamus is involved with basal brain mechanism
> and deals with autonomic regulatory function. It also connects
> the nervous and endocrine systems. And possibly, has some
> effects upon emotional response.
" Hypothalamus also plays a role in emotion.
For example...
LATERAL PORTION
involved in pleasure and rage
activates bodily responses to threat (fight-or-flight reactions)
MEDIAL PORTION:
involved with aversion (displeasure), uncontrolled laughter and rage
Hypothalamus is also closely connected with structures of the limbic system."
Many neuroscientists consider the limbic system
to be part of the hypothalamus. It is clear that the hypothalamus
and the limbic system have little or no connection to human
intelligence. Also, note that the endocrine system has a
great influence over human emotion and is intimately
connected with human emotion.
> Is it necessarily the case that "intelligence" must develop at
> the expense of "feeling?"
No, they can and have developed together. But intelligence and
feeling can also develop at the expense of the other. Some
very bright people can have retarded emotions, and many
people with highly developed, mature emotions often have
little intellect. Contrast your average mathematician or
accountant with your average pop singer, line backer, or
rock star. You really have two completely different animals.
I am surprised they are able to mate.
> Quite the contrary, I think that "feeling" is enhanced as
> intelligence grows and broadens.
This has so far been an evolutionary trend.
> I think that self-awareness is a function of feedback
> through internal states of the organism.
There is no evidence for this. If what you say were
true there would be some experimental computers
today that are "self-aware." In any event, there are
two types of "self-awareness." Today's computers
are self-aware in some trivial sense. I try to avoid
the word "self-aware" because it is misleading. Let's
stick with pain and pleasure.
> A truely self-aware AI system would indeed "feel"
> in the sense of being aware of internal states,
> positive or negative,
Pleasure is not positive, and pain is not negative.
Let's not confuse the stimulus which typically
induces pain and pleasure with the sensations
of pain and pleasure. Pain is not directly
connected to the avoidance of negative stimuli.
Masochists crave pain. Pain is "sensation."
> A truely self-aware AI system would indeed "feel"
> in the sense of being aware of internal states,
> positive or negative, and would be capable of
> expressing such "feelings."
You are personifying and anthropomorphizing.
You could say a tape recorder "feels" the
sound waves that impact its microphone, but
this is simply yielding to the "pathetic fallacy."
pathetic fallacy (p-thtk fl-s) n. The attribution
of human emotions or characteristics to inanimate
objects or to nature.
> You may of course deny that such expression
> would be "true sentience"
I would deny that such expression is any kind
of sentience.
> but I don't know how you'd distinguish the two.
At this point in time we couldn't. There is
no way to very that a tape recorder does
not hear music, but no person in their right
mind would suggest it does.
> Different "organs" of the brain do not "fight...
> for control over the body" unless the individual
> affected has lost some essential integrative
> capacity due to trauma or lack of development.
There are all kinds of wars and all kinds of
fights. I submit that the human decision
making process is vector addition of various
electrical signals.
> Humans may be conflicted for many different reasons, some of
> which may involve deep brain structure, other involving unresolved
> symbol mappings or unintegrated "subroutines" of the mind.
> Psychoanalysis has found much of this type of conflict to arise
> strictly within the conscious and subconscious and to be related
> to development of the person from infancy through adulthood.
> This type of conflict could not arise from basal levels such as
> the hypothalamus.
The submit the hypothalamus and the limbic system comprise
the subconscious. I further submit that much of psychoanalysis
is mere conjecture with very little scientific corroboration.
Carl Funk
>
> FL Automata is actually a different field. Has to do with generalizing
> the "non-deterministic finite-state automaton" to fuzziness. Plug that
> phrase into Google for some references.
> In a nutshell, the CPU of a computer is a deterministic finite-state
> automaton. Kind of a generalized Turing machine.
Sorry to pick nits, but you have that backwards. A CPU is a specialized
Turing machine. Or to put it another way, every CPU can be modeled
abstractly as a Turing machine, but no particular CPU will represent
every Turing machine. (Now a CPU coupled with the right software *can*
do that, but that's a fish of a different color. I suspect that's what
you meant, though.)
--
Carl Funk
a.a atheist #1229
Arturo Magidin
ArcticBonfire <arctic...@aol.com> wrote:
[.snip.]
>> You read Principia Mathematica when you were twelve? Are you
>> aware that what Russel and Whitehead were attempting to prove
>> with this work was proved false before they finished it,
>
>I don't believe this is true. Not only do I not believe this is true,
>I don't believe anything in Principia Mathematical has ever
>proven to be false. I think you have been taking too many drugs.
You misunderstood the comment.
The _Principia Mathematica_ was Russell and Whitehead's attempt to
fulfill the Hilbert Programme of putting all of mathematics on a solid
axiomatic basis.
Unfortunately, before the work was finished, along came Kurt Goedel,
who proved that a decidable axiomatic system with a decidable set of
rules of inference, all of which could be modeled by general recursive
function, could not capture all of mathematics, and that it would
never be able to formally prove its own consistency, provided it
included simple arithmetic.
In fact, Goedel's paper was a direct attack on the formalism in the
Principia, which is why it is called _On formally undecidable
propositions in "Principia Mathematica" and related systems
I_. Because the formalism he uses as a model is precisely the one in
_Principia_.
Since the final objective of the Principia was shown to be moot, it
was abandoned as a work in progress by Russell and Whitehead.
In addition, much of the formalism in the Principia was later
abandoned, since it introduced many unwanted
complications. Originally, it was thought that it was a fair trade-off
if it would fullfill the Hilbert Programme, but it is unwarranted if
you aren't going to get all the way anyway. Thus, Russell's
axiomatization of Set Theory has been all but abandoned in favor of
Zermelo-Fraenkel, and his notion of 'levels and categories' for
statements has also been abandoned.
Nobody claims there is an ->error<- in _Principia_, which is how you
interpreted the comment. The point is that the ultimate objective of
the Principia was shown to be impossible while the work was in
progress.
There are a number of sources in which you can verify the
claim. There's Nagel and Newman's _Goedel's Proof_; there's _Goedel's
Theorem in Focus_; there's Newman's _World of Mathematics_; and there
are a couple of essays by Russell and Goedel in _Philosophy of
Mathematics_.
Brian E. Clark
> And you are an unfunny, fat slob.
Why is it we hear so little about the skinny slobs? ;-)
--
--------------
Brian E. Clark
brian -at- telerama -dot- com
Cats do stumble, yes, but no cat has yet
acknowledged it.
Arturo Magidin
Brian E. Clark <lo...@sig.for.address> wrote:
>ArcticBonfire (arctic...@aol.com) wrote:
>
>> And you are an unfunny, fat slob.
>
>Why is it we hear so little about the skinny slobs? ;-)
Equal opportunity. The exclusion of skinny slobs is just the
equivalent of the exclusion of chubby and fat air in disappearance
cases.
Fred Stone
Yes of course, you are correct. I didn't quite get that final paragraph the way
I wanted it. A Turing machine has an *infinite* tape doesn't it?
I was trying to get that to parse as "a DFA is a (sorta, kinda) generalized
Turing machine"
Oh well, the perils of using english to talk about math. :-)
Or to counter-pick, any particular CPU represents only ONE
(equivalence class of) Turing machine(s). :-)
--
Fred Stone
aa # 1369
This is why I don't have a PhD in Computer Science...
Fred Stone
ArcticBonfire wrote:
> Fred Stone fsto...@earthlink.net wrote:
> > I can't agree or disagree with you about "sentience"
> > because I don't understand your definition. The dictionary
> > defines sentience as "feeling or perception."
>
> As always, my definition and the dictionary definition
> coincide. Computers have no feeling or perception.
> Feeling is pain, pleasure, hate, love, fear, anxiety.
> Perception is red, green, blue, sweet, sour, and
> any number of smells.
This is true *at present*. I see no reason to assume that
such mechanism of intellect can never be developed upon
computer hardware.
> > The hypothalamus is involved with basal brain mechanism
> > and deals with autonomic regulatory function. It also connects
> > the nervous and endocrine systems. And possibly, has some
> > effects upon emotional response.
>
> " Hypothalamus also plays a role in emotion.
> For example...
> LATERAL PORTION
> involved in pleasure and rage
> activates bodily responses to threat (fight-or-flight reactions)
> MEDIAL PORTION:
> involved with aversion (displeasure), uncontrolled laughter and rage
> Hypothalamus is also closely connected with structures of the limbic system."
>
> Many neuroscientists consider the limbic system
> to be part of the hypothalamus. It is clear that the hypothalamus
> and the limbic system have little or no connection to human
> intelligence. Also, note that the endocrine system has a
> great influence over human emotion and is intimately
> connected with human emotion.
Indeed. What makes this subsystem impervious to computer simulation?
> > Is it necessarily the case that "intelligence" must develop at
> > the expense of "feeling?"
>
> No, they can and have developed together. But intelligence and
> feeling can also develop at the expense of the other. Some
> very bright people can have retarded emotions, and many
> people with highly developed, mature emotions often have
> little intellect. Contrast your average mathematician or
> accountant with your average pop singer, line backer, or
> rock star. You really have two completely different animals.
> I am surprised they are able to mate.
I think that you oversimplify the mentalities of mathematicians and
pop singers. There is tremendous variation in mental talents among
humans. Some have more of one, some more of another. Some
more or less of both.
> > Quite the contrary, I think that "feeling" is enhanced as
> > intelligence grows and broadens.
>
> This has so far been an evolutionary trend.
>
> > I think that self-awareness is a function of feedback
> > through internal states of the organism.
>
> There is no evidence for this. If what you say were
> true there would be some experimental computers
> today that are "self-aware." In any event, there are
> two types of "self-awareness." Today's computers
> are self-aware in some trivial sense. I try to avoid
> the word "self-aware" because it is misleading. Let's
> stick with pain and pleasure.
Ah, but "self-awareness" is key to this whole disagreement.
What is the "feeling of pain" other than an awareness of
potential harm to "oneself?"
> > A truely self-aware AI system would indeed "feel"
> > in the sense of being aware of internal states,
> > positive or negative,
>
> Pleasure is not positive, and pain is not negative.
> Let's not confuse the stimulus which typically
> induces pain and pleasure with the sensations
> of pain and pleasure. Pain is not directly
> connected to the avoidance of negative stimuli.
> Masochists crave pain. Pain is "sensation."
Masochism (and it's counterpart sadism) result from
getting pain and/or humiliation reactions confused with internal
states representing parental care and love, later further confused
with sexual states.
Most masochists do not crave pain except in sexual situations.
Their pain response is convoluted with sexual response.
I would suggest "Lady Slings the Booze" by Spider Robinson for a
really quite accurate characterization of S-M personalities.
> > A truely self-aware AI system would indeed "feel"
> > in the sense of being aware of internal states,
> > positive or negative, and would be capable of
> > expressing such "feelings."
>
> You are personifying and anthropomorphizing.
> You could say a tape recorder "feels" the
> sound waves that impact its microphone, but
> this is simply yielding to the "pathetic fallacy."
You are oversimplifying my argument, leading to
a "strawman fallacy." We are talking about a hypothetical
computer system which would be "personified", though
not necessarily anthropomorphized.
> pathetic fallacy (p-thtk fl-s) n. The attribution
> of human emotions or characteristics to inanimate
> objects or to nature.
>
> > You may of course deny that such expression
> > would be "true sentience"
>
> I would deny that such expression is any kind
> of sentience.
>
> > but I don't know how you'd distinguish the two.
>
> At this point in time we couldn't. There is
> no way to very that a tape recorder does
> not hear music, but no person in their right
> mind would suggest it does.
More strawman. A tape recorder cannot report
upon it's subjective states as to what it has experienced
upon hearing music.
> > Different "organs" of the brain do not "fight...
> > for control over the body" unless the individual
> > affected has lost some essential integrative
> > capacity due to trauma or lack of development.
>
> There are all kinds of wars and all kinds of
> fights. I submit that the human decision
> making process is vector addition of various
> electrical signals.
In general perhaps, though I think it's more complicated
than that. There are processes very much like the operation
of an "expert system" going on in there.
> > Humans may be conflicted for many different reasons, some of
> > which may involve deep brain structure, other involving unresolved
> > symbol mappings or unintegrated "subroutines" of the mind.
> > Psychoanalysis has found much of this type of conflict to arise
> > strictly within the conscious and subconscious and to be related
> > to development of the person from infancy through adulthood.
> > This type of conflict could not arise from basal levels such as
> > the hypothalamus.
>
> The submit the hypothalamus and the limbic system comprise
> the subconscious. I further submit that much of psychoanalysis
> is mere conjecture with very little scientific corroboration.
I think that the subconscious conveys inputs from the hypothalamus
and the limbic system, but it's symbol generation and manipulation
originate in the cortex.
Psychoanalysis has been much maligned over the years, and it certainly
cannot address issues arising from actual brain physiology. However,
it does bear consideration when dealing with internal states of a
well-functioning mind.
--
Fred Stone
aa # 1369
Since when is ignorance a point of view?
ArcticBonfire
> "Is" -- one of the most slippery words in the language.
Didn't I hear this once before from someone? Didn't
it become a national joke?
ArcticBonfire
> I would say your title is a little misleading
> (not that there's anything wrong with that:-)
Exactly, a book titled "The Deflowering
of Jenifer Flowers" sells more copies than
copies than "Gardening tips by Jenifer."
> What you are arguing is that reality is to
> slippery to be captured with propositional
> calculus
True. Actually, what I was going to argue
is that there are many legitimate statements
that don't succumb to the law of the excluded
middle, because everything in reality cannot
accurately be described as black OR not black.
Some things are both black AND not black.
> In the example you used, the hypothetical ball
> is half white and half black; in this case the
> statement "the ball is white" is true . . .
Actually, I never finished what I wanted to say.
But most multi-racial people would understand
where I was going. They have a problem with
someone who says they are either black or not
black, white or not white. You may artificially
put them in one classification or another, but
if you do, your classifications will not be true to
a continuum reality. In a universe where every
object is newspaper grey, you do not tell
the truth when you say every object is either
black or not black. You distort the truth if you
say newspaper grey is not black, and you distort
the truth if you say news paper grey is black.
As I am sure you know newspaper grey part
black and part white.
But I really didn't finish with what I was going
to say. I need to take Fred's obervation to
the next step, and I haven't posted this reply
yet.
ArcticBonfire
posted in extra large print. This was not intentional
on my part. I've tried to correct it here. This is an
old post.
After a string of insults, Mike Dowling wrote:
> For a start, propositional calculus is about propositions, not
> statements. And a proposition in most treatises is _defined_
> as a statement that is either true or false.
Propositional calculus defines every statement as
having only two truth values. Every statement in PC which
restates this definition is true. Every statement in PC which
disputes this definition is false. Every statement in PC which
says nothing about this definition is neither true nor false. All PC
does is literially rehash its definition that every statement is
either T v F. Since in the real world, this premise is not
always true, in order for PC to remain internally consistent,
it must not accept any statements about the real world,
claiming that such statements are not valid statements.
Every true statement in PC is circular logic. Find a statement
that refutes PC by being a counter-example, and PC claims
that such a statement is not a statement by definition. So
by definition every statement is either true or false, and any
statement that defies this definition is not a statement, by
definition. And every logical proof in PC is simply a reiteration
or restatement of this definition. Totally circular.
> And you really should have read Wittgenstein. Statements
> can be true, false, or meaningless. It is so very easy to mistake
> a meaningless statement for a proposition; that, in essence, is
> what lies behind Russel's paradox; Wittgenstein cleared that up.
Betrand Russell knew very well that statements can be true,
false or meaningless. You do not seem to know what you
are talking about.
> Your example was a silly one precisely because it was left
> unclear what you meant. Did you mean that the ball was entirely
> white, or partially white. (I would have interpreted it as "entirely
> white", and so said that it is false.)
No matter how you define the terms in my sentence, you will
always be left with a contradiction in PC.
> A better example of a meaningless statement is "Yesterday was
> yellow." Clearly, something temporal cannot have colour
> attributes.
Your statement is meaningless, my statement is not meaningless.
"Yesterday was yellow" conveys no information. "The ball is white"
does convey information. If a statement conveys true information,
it cannot be meaningless.
> You read Principia Mathematica when you were twelve? Are you
> aware that what Russel and Whitehead were attempting to prove
> with this work was proved false before they finished it,
I don't believe this is true. Not only do I not believe this is true,
I don't believe anything in Principia Mathematical has ever
proven to be false. I think you have been taking too many drugs.
> Are you aware that what Russel and Whitehead were attempting
> to prove with this work was proved false before they finished it,
ArcticBonfire
>> claiming that such statements are not valid statements.
>> Every true statement in PC is circular logic.
>
> mathematics.
Not every theorem in mathematics proves its definitions.
If every proof in Euclidean geometry proved that "parallel
lines" are lines that never meet, then Euclidean geometry
would be analagous to PC. Every true statement in PC
is not just consistent with it premisses, every true statement
in PC is an exact restatement for the very definition of what
consitutes a statement in PC.
> In fact, many advanced books on mathematics start off
> by defining things in terms of set theory and use the language
> of PC.
PC is valid for the universe of mathematics.
> Do you think that mathematics has anything to do with the real
> world?
Yes. But mathematics is more than PC.
> The Boolean logic used to design silicon chips is closely allied
> with PC. Maybe that's why computers are not really intelligent!
Well, that is where I was headed. In order to create true AI you
need neurel net computers based on fuzzy logic, and possessing
the ability to use inductive logic to form generalizations.
> I think the point you are making in this thread has some validity:
> life certainly is far bigger than PC. But the example you gave was
> not a useful one.
I didn't get to finish making my point.
>> Find a statement
>> that refutes PC by being a counter-example, and PC claims
>> that such a statement is not a statement by definition. So
>> by definition every statement is either true or false,
>
> Not every statement, just those statements that PC deals with.
I don't think you understood what I was trying to say. I was trying
to say, that if you find a counter-example to the main premiss of
PC, PC dismiss that counter-example as being meaningless.
PC is not falsifiable.
Take Euclidian Geometry. You can show that our universe is not
not Euclidian by showing two parallel lines that meet. But there
is no way to prove that our world is not PC, because anytime
you find a statement that is partly true and partly false, PC claims
be definition, such a statement is not a statement.
> It is your description of it that is circular.
You have not shown this to be the case.
> > And you really should have read Wittgenstein. Statements
> > can be true, false, or meaningless. It is so very easy to mistake
> > a meaningless statement for a proposition; that, in essence, is
> > what lies behind Russel's paradox; Wittgenstein cleared that up.
>
> Russell's paradox arose because a proposed collection of axioms
> for set theory were internally inconsistent. He found a way to modify
> those axioms to get rid of the inconsistency. What did Wittgenstein
> say about that?
The quote above that you attribute to me was not made by me. They
are words that were addressed to me by someone who was disputing
what I said.
Russell conconcted the ramified theory of types to solve his paradox.
Russell's solution eliminated branches of mathematics, and was
generally not accepted by others.
ArcticBonfire
> The _Principia Mathematica_ was Russell and Whitehead's attempt to
> fulfill the Hilbert Programme of putting all of mathematics on a solid
> axiomatic basis.
I was aware of this.
> Unfortunately, before the work was finished, along came Kurt Goedel,
> who proved that a decidable axiomatic system with a decidable set of
> rules of inference, all of which could be modeled by general recursive
> function, could not capture all of mathematics, and that it would
> never be able to formally prove its own consistency, provided it
> included simple arithmetic.
That is a nice statement of what Goedel did. I thought Goedel
came along with his undecidability principle long after Principia
was finished. I am thinking Prinicpia was written around 1910,
and Goedel came twenty years latter. Let me do a Google
search, . . . on second thought let me look it up in Britannica
. . . . . . . . . . . .
........................................................
..........................................................................
.........
......................................
"Gödel's proof first appeared in an article in the Monatshefte für
Mathematik und Physik, vol. 38 (1931)"
"The three-volume Principia Mathematica (1910-13) was
optimistically named after the Philosophiae naturalis principia
mathematica."
Is there something here you care to clarify?
> Since the final objective of the Principia was shown to be moot, it
> was abandoned as a work in progress by Russell and Whitehead.
> . . . The point is that the ultimate objective of the Principia was
> shown to be impossible while the work was in progress.
All of math and science is a work in progress. But Principia was
published and copyrighted in 1910 through 1913. How can you say
it was not finished when nothing was added to it in the next 15
years, before Goedel came out with his theorem? Three volumes
in three years and then nothing for 15+ years. It sounds to me like
it was finished. Didn't Russell accomplish anything worth publishing
in the ten years following its publication. Do you mean that in 1913
Russell published an unfinished work because of what Goedel was
going to do 15+ years latter?
> his notion of 'levels and categories' for statements has also
> been abandoned.
You mean his ramified theory of types.
> There are a number of sources in which you can verify the claim. There's
> Nagel and Newman's _Goedel's Proof_; there's _Goedel's Theorem in
> Focus_; there's Newman's _World of Mathematics_; and there are a
> couple of essays by Russell and Goedel in _Philosophy of Mathematics_.
Hmmm. I still think it is a stretch to say that Principia was published
unfinished because Goedel. Russell may have been working on another
book that attempted to complete what he started in Principia. But even
if Goedel never came along, he still may never have published his sequel.
> that it would never be able to formally prove its own consistency,
> provided it included simple arithmetic.
How was Goedel able to formally "prove" this? It is my understanding
that at the heart of Goedel's proof is proof that any system that tries
to prove its own consistency will result in an infinite regress as to
what constitutes a proof in the system. I stated this years ago in
alt.atheism, and I was met with hail of bronx cheers. Everyone
claimed that this was an old idea dating back to the Greeks. And
that Goedel only proved his theorem for a very limited case. And
so in effect Goedel really didn't do much of anything, and that
everyone makes much to much out of what Goedel did accomplish.
The gist of what I got from Goedel's proof was that no meaningful
logical system could prove itself self-consistent, therefore,
nothing can really be proved by logic, as the rules necessary
to determine what constitues a valid proof, themselves can never
be proven to be sufficient to establish a valid proof. This statement
was loudly jeered, by several resident soi disant logicians. They
claimed that Goedel's proof meant very little since it only applied
to a vary limited case. Perhaps, you could clear up my confusion
on this. There is some famous logician who extended Turings work,
I forget his name now, but I asked him to help me clarify this issue,
but he was unable to do so.
ArcticBonfire
ArcticBonfire
format is not good. I can't find the rest of Fred's post to
respond to the rest of it, so I will post what I have now,
and look for the rest of his post latter.
Fred Stone fsto...@earthlink.net wrote:
> You may wish to include fuzzy logic and
> non-deterministic automata in the domain
> of your argument.
Actually, I think humans are deterministic. And
without free will, you really can't have God, or good
and evil.
Fred Stone fsto...@earthlink.net wrote:
>> Many neuroscientists consider the limbic system
>> to be part of the hypothalamus. It is clear that the hypothalamus
>> and the limbic system have little or no connection to human
>> intelligence. Also, note that the endocrine system has a
>> great influence over human emotion and is intimately
>> connected with human emotion.
>
> Indeed. What makes this subsystem impervious to computer
> simulation?
Why can't pain and fear be created in a calculator or in a
camcorder? Pain and fear are not software programs. There
is no part of a computer designed to reproduce pain and fear.
If we wanted to reproduce pain and fear using electrical circuits,
we wouldn't know even how to take the first step. ***Maybe"""
inanimate circuit boards can be made to feel pain with a special
kind of circuit that reproduces the kind of energy field the limbic
system produces. But it is unlikely that it would happen by
chance, and we wouldn't have the vaguest idea where to start
in designing such a board.
I have no doubt that computers can be made to simulate human
emotions to the point where someone outside not knowing how
the simulation was being produced could not tell the simulation
from the real thing. But underneath there would be a world of
difference.
The problem here is that we strongly associate intelligence
with sentience because humans have a high degree of
intelligence and a high degree of sentience. But they are
really two separate entities. Take a human with Alzheimer
disease who doesn't know what world he is in, who needs
help eating, who can't find their way to the bathroom door
two feet in front of them, who has an IQ just somewhere
above a slug. Such a person I imagine can still feel extreme
amounts of pain.
There is something very strange and paradoxical about all
feelings, sensations, color and image perception, and
consciousness. Words are not really adequate here. At
this time there is no way to scientifically describe the color
humans see when a specific frequency of light contacts
their retina and sends an electrical signal to the visual
cortex. What is the color red that humans perceive?
Theoretically, we could perceive the color red when light
with a frequency which we typically associate with green
contacts our retina. We need to be able to differentiate
red light from the color red we perceive. Now how would
we go about creating a computer that would experience
the color red? Of course we could create a computer that
can see red light, but this is not the same as experiencing
the color red. It is easy to confuse the two, red light with
the color red; pain with negative stimuli; fear with
something threatening; but in reality these are all causes
and effects. Two humans with the same nervous system
can experience different sensations to the exact same
stimuli. One person may feel hot, while another person
feels cold. Once we understand that the color red really
has nothing to do with red light, we understand how
difficult it would be to create a computer to experience
the color red. And so on with each smell, taste, and
emotion. There are people who experience certain
emotions when the normal stimuli for such emotions
are not present. Touch an electrical probe to one part
of the brain, a person feels sad, to another a person
feels fright. If you ask them what they fear, they will
say nothing, they are just experiencing this thing
they call fright. So how do you build a computer to
simulate such a feeling when we know absolutely
nothing as to what fright or the experience of color
really is. All we know is how to create these entities
by stimulating different parts of the brain. This is
hardly much of a road map for building an electrical
circuit. Now intelligence is entirely a different matter.
Intelligence is objective. Calculators possess true intelligence.
Intelligence is rather ordinary. The real thing that separates
human intelligence from the intelligence of calculators
and ordinary computers is that calculators and ordinary
computers are only able to employ deductive logic.
Whereas humans use their associative powers and
inductive reasoning to generalize. Once computers
are made that can generalize on their own, and can
employ fuzzy logic there will be really nothing stopping
computers from outstripping the human brain as
far as problem solving is concerned.
> I think that you oversimplify the mentalities of
> mathematicians and pop singers. There is tremendous
> variation in mental talents among humans. Some have
> more of one, some more of another. Some more or less
> of both.
That is why I qualified my statement with the words "on average."
Most people associate with people like themselves. I don't
know if most people realize how different some people are
than others. Some people are completely controlled by one
part of their brain, other people are completely controlled
by other parts of their brain. Some make decisions almost
exclusively with their emotions, and some people make
decisions almost exclusively with their intellect. Some
people's entire lives are devoted to feeding their physical
appetites. Some people's entire life is dedicated to
exercising their cerebral cortex. Do a CAT scan of
Stephen Hawking's brain and that of an emotional female
who has been a crack-addicted prostitute for the last 30
years, and you will see two completely different brains.
I guarantee it.
> Ah, but "self-awareness" is key to this whole disagreement.
> What is the "feeling of pain" other than an awareness of
> potential harm to "oneself?"
<big sigh> The feeling of pain has nothing to do with awareness
of potential harm to 'oneself', pain has nothing at all to do with
harm, potential or otherwise. Imagine for second, that I have
created an electrical circuit that plays "Mother had a little lamb"
every time I shine a yellow light at a particular sensor
connected to the circuit. Does that mean that the rhyme
"Mary had a little lamb" has anything to do with yellow light?
Humans are programmed to feel pain in certain circumstances,
say when subjected to the heat from a flame thrower. But this
is just the way the human brain is wired. The yellow light
is like the heat of the flame thrower. The pain that is felt
is the rhyme Mary had a little lamb. Clearly, the connection
between the pain and the heat is arbitrary. The human
brain can easily be rewired so that people would feel the
sensation of tasting chocolate ice cream while their flesh
is melting off their bones. One can imagine why evolution
did not favor this combination. But there is nothing inherent
in the feeling of pain that has anything to do with "harm"
or negative stimuli. You can be made to feel pain when
no harm is present by electrically stimulating a part of your
brain. This same electrical stimulation to another part of
your brain can cause you to feel the sensation of
chocolate ice cream on your tongue.
When I was in high school taking honors geometry, I provoked
the class with a simple question. If Jack had a brain transplant
would he still be Jack. Of course, we have had lots of movies
about such a thing, but this was before all these movies. And
of course, there was the story of Frankenstein. In any event,
what surprised me was the number of students who were
confused by this situation, and thought that Jack would still
be Jack. I just couldn't understand how anyone could be
confused with this hypothetical. Likewise, I am astounded at
how many people confuse red light with the color red, pain
with the heat from a flame thrower, the taste of chocolate with
chocolate. It is a fluke that we taste chocolate ice cream as
the sensation we know as chocolate. Had evolution proceeded
a little different, we might experience vanilla whenever we bite
into to chocolate. There is no direct connection between the
stimuli that produce sensations, and the sensations themselves.
I once had confidence that once I explained this others would
understand what I am trying to say. But I have explained this
so many times to no avail, that I no longer have any confidence
that what I am saying will make any sense to others.
Ernie DiMicco, Jr.
definition of "is" for this to work... strange but true). If you made a more
explicit statement such as "Albert is mostly white" then of course it would be
false.
"ArcticBonfire" <arctic...@aol.com> wrote in message
news:20010208164725...@ng-bd1.aol.com...
> According to pc every statement is either true or false.
> Suppose I have a ball called Albert that is exactly half
> white and half black. Now, take the following statement:
> "Albert is white." Such a statement can never be just
> true or false.
Ernie DiMicco, Jr.
> > A> According to pc every statement is either true or false.
> > Yes, because unless it is either true or false, it is not a statement.
> > It is, in other words, the definition of a statement. It does not
> > follow that every declarative English sentence is a pc statement. . . .
> > Because it is not a statement. Neither is "Albert is honest" if Albert
> > is a marble. Come back when you have got a little bit of education.
> I beat college students at Wff n' Proof when I was nine. I read Principia
> Mathematica when I was twelve. I took several formal, undergraduate
> logic courses at University of Michigan when I was thirteen. I read just
> about every book that Copi ever wrote. I took several more logic courses,
> when I was fully matriculated. I sincerely doubt you have the formal
> educational background in logic that I have or the fundamental grasp.
Then you have apparently learned nothing from any of these courses, because you
have made a fundamental mistake in your logic that several posters on here all
reported, and refused to correct it or acknowledge that it could be corrected.
Steve
<arctic...@aol.com> ArcticBonfire says...
> Google has taken over DejaNews.com. The new "beta"
> format is not good. I can't find the rest of Fred's post to
> respond to the rest of it, so I will post what I have now,
> and look for the rest of his post latter.
I agree with you here. The new format is for shit. I hope it is
temporary. Google definitely jumped the shark big time.
--
Steve
Director EAC Crop Circle Division
Arturo Magidin
ArcticBonfire <arctic...@aol.com> wrote:
>mag...@math.berkeley.edu (Arturo Magidin) wrote:
>> The _Principia Mathematica_ was Russell and Whitehead's attempt to
>> fulfill the Hilbert Programme of putting all of mathematics on a solid
>> axiomatic basis.
>
>I was aware of this.
>
>> Unfortunately, before the work was finished, along came Kurt Goedel,
>> who proved that a decidable axiomatic system with a decidable set of
>> rules of inference, all of which could be modeled by general recursive
>> function, could not capture all of mathematics, and that it would
>> never be able to formally prove its own consistency, provided it
>> included simple arithmetic.
>
>That is a nice statement of what Goedel did. I thought Goedel
>came along with his undecidability principle long after Principia
>was finished. I am thinking Prinicpia was written around 1910,
>and Goedel came twenty years latter. Let me do a Google
>search, . . . on second thought let me look it up in Britannica
[.snip.]
>
>"Gödel's proof first appeared in an article in the Monatshefte für
>Mathematik und Physik, vol. 38 (1931)"
>"The three-volume Principia Mathematica (1910-13) was
>optimistically named after the Philosophiae naturalis principia
>mathematica."
>
>Is there something here you care to clarify?
Sure, since apparently the actual history is not known.
The ->express<- purpose of the _Principia_ was to establish a solid
foundation for mathematics. It was the ->express<- hope of Whitehead
and of Russell that the work there would end in a proof of
consistency of the system of mathematics.
The work stalled after a few years for a variety of reasons, and was
left quite short of its goal. For one, it became apparent that it
wouldn't be as easy as Russell and Whitehead had hoped to extend the
system of the Principia to a proof of consistency. In 1914, Russell
became active in the anti-war movement. He started publishing
pamphlets, was fined, and even arrested for being a pacifist. His
lectureship was revoked. While in prison, he worked on _Introduction
to Mathematical Philosophy.
After the war, his interest had gone away from the _Principia_, on
which he hadn't worked for a number of years, and went on to his
written critique of Bolshevism in 1920, books on atomic theory and
relativity in 1923 and 1925, and a book on education in 1926. He then
also spent some time editing the second edition of the already
published volumes of the Principia, and wrote on philosophy. The
second edition of the Principia was to be the first step towards
reacquainting himself with the work in preparation to continuing it
(now on his own, as Whitehead, see below, had already moved on as
well). By the time it was all done, and with little but a few notes
for volume four ready, Goedel came along.
Whitehead, in the meantime, also moved from the study of the
foundations of mathematics and logic to the study of the basic
concepts of nature, publishing _The Concepts of Nature_ in 1920,
having started studying this while Russell was having his own problems
related to the War. He later went on to _Religion in the Making_
(1926), _The Aims of Education_ (1929), and _The Function of Reason_
(1929 as well). By the time both Whitehead and Russell were again at
their leisure to continue the work, Goedel had come and shown that the
ultimate goal would be, in any case, unacheivable, and they never got
together again to continue it.
>> Since the final objective of the Principia was shown to be moot, it
>> was abandoned as a work in progress by Russell and Whitehead.
>> . . . The point is that the ultimate objective of the Principia was
>> shown to be impossible while the work was in progress.
>
>
>All of math and science is a work in progress. But Principia was
>published and copyrighted in 1910 through 1913. How can you say
>it was not finished when nothing was added to it in the next 15
>years, before Goedel came out with his theorem? Three volumes
>in three years and then nothing for 15+ years. It sounds to me like
>it was finished. Didn't Russell accomplish anything worth publishing
>in the ten years following its publication. Do you mean that in 1913
>Russell published an unfinished work because of what Goedel was
>going to do 15+ years latter?
I have now explained how the circumstances in the world
intervened. The work fell quite short of its express intent; the
authors wanted to take the work a long way further than where it
stopped.
(A similar phenomenon can be found in Donald Knuth's _The Art of
Computing Programming_, which stopped at three volumes in the 60's
because the author moved on to other interests and because of other
real-world concerns, and the planned and promised fourth volume has
not appeared in the intervening 30 years; none-the-less, _The Art of
Computing Programming_ is understood to be an incomplete work, even
though the author, still alive and still working, hasn't published or
worked at the next volume).
It is a known fact what the objective of the Principia was. It is also
a fact that the Principia stops far short of that objective. And the
timing indicates that the authors had other things to do in the
intervening 15 years.
>> his notion of 'levels and categories' for statements has also
>> been abandoned.
>
>You mean his ramified theory of types.
Yes. I mistranslated. Thanks.
>> There are a number of sources in which you can verify the claim. There's
>> Nagel and Newman's _Goedel's Proof_; there's _Goedel's Theorem in
>> Focus_; there's Newman's _World of Mathematics_; and there are a
>> couple of essays by Russell and Goedel in _Philosophy of Mathematics_.
>
>Hmmm. I still think it is a stretch to say that Principia was published
>unfinished because Goedel.
Nobody said the Principia was "published unfinished", just as nobody
said the Principia contained errors. What was said was that the work
in the Principia was ->left unfinished<-. It was not intended to stop
at 3 volumes; it was intended to continue on to a proof of consistency.
> Russell may have been working on another
>book that attempted to complete what he started in Principia. But even
>if Goedel never came along, he still may never have published his sequel.
True enough. In which case, it would still be an incomplete work,
stopping short of its authors' plans and desires for the work.
>> that it would never be able to formally prove its own consistency,
>> provided it included simple arithmetic.
>
>How was Goedel able to formally "prove" this? It is my understanding
>that at the heart of Goedel's proof is proof that any system that tries
>to prove its own consistency will result in an infinite regress as to
>what constitutes a proof in the system.
You are in fact incorrect. After proving the formal undecidability of
the Goedel statement G, assuming S is consistent, Goedel proves, quite
formally, that the statement "If the system S is consistent, then G is
true" is formally provable in the system.
Therefore, if you were to find a formal proof that the system S is
consistent in S, then you would have a formal proof of G in the system
S. Therefore, if the system is consistent, no formal proof of the
consistency of S can exist inside of S, as that would yield a formal
proof of the undecidable proposition G.
> I stated this years ago in
>alt.atheism, and I was met with hail of bronx cheers. Everyone
>claimed that this was an old idea dating back to the Greeks.
The statement G is what goes back to an idea dating badk to the
Greeks, to wit the liars paradox.
> And
>that Goedel only proved his theorem for a very limited case. And
>so in effect Goedel really didn't do much of anything, and that
>everyone makes much to much out of what Goedel did accomplish.
Goedel proved it in a fairly limited case: the argument only works for
an axiomatic system in which the set of axioms is decidable, which
uses only rules of inference which can be modeled by generalized
recursive functions (think Turing machines if you want), and a
decidable set of rules of inference; and which is complicated enough
to contain a model for (Peano) arithmetic. It is fairly restricted. It
does not apply to the "real world" in any sense. You need each and
every hypothesis for the argument to work.
However, it is a very general statement from the point of view of
formal axiomatic systems. All axiomatic systems we know have decidable
sets of axioms; they all use very simple rules of inference, all of
which can be traced to Modus Ponens, which can be modeled by a Turing
machine; and arithmetic is the first "comlicated" theory. It deals a
deathblow to the Hilbert Programme because the hypothesis of the
theorem match almost perfectly with the description in the Programme
of how "easy" the axiomatic system to prove consistency ought to
be. The only gap is that Hilbert spoke of "algorithmic" rules of
inference, without a formal definition of algorithm. Church's thesis
says that general recursive functions actually capture the notion, so
module Church's thesis, the hypothesis of Goedel's theorem math
perfectly the kind of thing Hilbert wanted to start with.
>The gist of what I got from Goedel's proof was that no meaningful
>logical system could prove itself self-consistent, therefore,
>nothing can really be proved by logic, as the rules necessary
>to determine what constitues a valid proof, themselves can never
>be proven to be sufficient to establish a valid proof.
This a gross oversimplification. It is impossible for a complex enough
system to prove its own consistency in simple terms, but this is far
cry from "nothing can be proved by logic." In fact, proofs of the
consistency of arithmetic have been furnished since shortly after
Goedel... they simply use infinite recursion or transfinite induction,
which is an easy enough pill to swallow if you are willing to swallow
regular induction.
> This statement
>was loudly jeered, by several resident soi disant logicians.
And rightly so. The claim "nothing can be proved by logic" is a gross
over simplification of a fairly complicated matter, and it invites a
rather mistaken appreciation of what is going on. If you found
criticism hard to bear, that's hardly the fault of Goedel's Theorem.
> They
>claimed that Goedel's proof meant very little since it only applied
>to a vary limited case.
Goedel's proof is, in the end, about the limitations of the axiomatic
method of the algorithmic proof-making techniques. It is a very
general theorem (as axiomatic methods go) but at the same time it is a
limited theorem, since it only applies to certain kinds of axiomatic
systems (but is rich enough to encompass everything we have ever
thought of as a 'good' and 'useful' axiomatic method).
> Perhaps, you could clear up my confusion
>on this.
I hope I have. Yours and others'.
[.snip.]
Mike Smith
= eyele...@my-deja.com wrote:
= > "Is" -- one of the most slippery words in the language.
=
= Didn't I hear this once before from someone? Didn't
= it become a national joke?
Maybe. No.
__________________________________________
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Mike Smith | aa #1164 | Founder of SMASH
(Sarcastic Middle-aged Atheist with a Sense of Humor)
__________________________________________
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
"The LORD stood upon a wall made by a plumbline,
with a plumbline in his hand." - Amos 7:7
Mark Richardson
wrote:
<snip stuff about sensation / "qualia">
Good post AB.
Interesting and articulate.
I hope you do this kind of post more often - I, for one, will read it.
Mark.
--------------------------------------------
Mark Richardson. m.rich...@utas.edu.au
Member of SMASH
(Sarcastic Middle-aged Atheist with a Sense of Humor)
--------------------------------------------------
Noah Simoneaux
>arctic...@aol.com (ArcticBonfire) wrote:
>
>= eyele...@my-deja.com wrote:
>= > "Is" -- one of the most slippery words in the language.
>=
>= Didn't I hear this once before from someone? Didn't
>= it become a national joke?
>
>Maybe. No.
Maybe that's where ArcticBonehead got his command of logic. :/
Noah Simoneaux
Anyone who thinks there is some good in everyone hasn't interviewed enough people.
Eastman's Personnel Director's Law
Mike Dowling
>> > And you really should have read Wittgenstein. Statements
>> > can be true, false, or meaningless. It is so very easy to mistake
>> > a meaningless statement for a proposition; that, in essence, is
>> > what lies behind Russel's paradox; Wittgenstein cleared that up.
>
>Russell's paradox arose because a proposed collection of axioms for
>set theory were internally inconsistent. He found a way to modify
>those axioms to get rid of the inconsistency. What did Wittgenstein
>say about that?
I cannot remember the precise details, unfortunately, but the argument
was along the following lines.
The question is as to whether or not the set of all sets that are not
members of themselves is a member of itself or not. It is if and only
if it isn't.
Sets are defined with a proposition, for example the set of even numbers
is the set of all integers that are divisible by two. The defining
proposition is "n is divisible by two".
The defining proposition for the set of all sets that are not members of
themselves is "X is not a member of itself."
As I recall, and it's along time ago, "X is not a member of itself" can
engender meaningless statements when checked with the defining
proposition for many sets X. I just cannot recall how it was done.
Cheers,
Mike
--
My email address mi...@moocow.math.tu-bs.de above is a valid email
address. It is a mail alias. Once spammed, the alias is deleted, and
the integer 'N' incremented. Currently, mike[49,50] are valid. If
email to mikeN bounces, try mikeN+1.
Mike Dowling
>Not every theorem in mathematics proves its definitions.
It must be hard being a misunderstood genius!
For mere mortals, this is complete nonsense. ("definitions of
theorems"? Perhaps "definitions of concepts appearing in the statements
of theorems? But how do you prove a definition?)
0/10 for logic!
>Take Euclidian Geometry. You can show that our universe is not
>not Euclidian by showing two parallel lines that meet.
Silly me; I thought that two lines are parallel if and only if they
never meet, and that _one_ way of showing that a given _geometry_ (not
universe) is to show that there are lines taht have no parallel lines.
Still, I bow to your superior wisdom.
Mike Dowling
>In article <20010209123446...@ng-mp1.aol.com>,>>> This from the man who complains when others mention
>>> their credentials...
>I mentioned my credentials in response to the following statement,
>made in article <20010204155655...@ng-fk1.aol.com>:
>
> "You wouldn't know a Schwarzschild metric from a
> Euclidean-Schwarzschild metric, you wouldn't know an eigenvalue from
> an eigenvector, and you wouldn't know a Calabi-Yau space from a
> Lobachevskian space."
Don't worry about him. It this were not a mathematical topic, I'd think
that that this ArcticBonfire chappie is a troll. Unfortunately, he is
probably a much sadder sort of person, a trisectionist.
There he is, an unknown genius, and he has come up with this fantastic
proof that propositional calculus is flawed, no nobody from the
mathematical "establishment" will believe him. Like a typical
trisectionist, he runs around claiming discrimination, and conspiracy
amongst the "establishment".
Trisectionist _never_ give up, it's time we gave upon him.
Martin Thomas
> On Sat, 10 Feb 2001 02:53:44 +0000, Martin Thomas <mar...@albedosystems.light.com> wrote:
> >> > And you really should have read Wittgenstein. Statements
> >> > can be true, false, or meaningless. It is so very easy to mistake
> >> > a meaningless statement for a proposition; that, in essence, is
> >> > what lies behind Russel's paradox; Wittgenstein cleared that up.
> >
> >Russell's paradox arose because a proposed collection of axioms for
> >set theory were internally inconsistent. He found a way to modify
> >those axioms to get rid of the inconsistency. What did Wittgenstein
> >say about that?
>
> I cannot remember the precise details, unfortunately, but the argument
> was along the following lines.
>
> The question is as to whether or not the set of all sets that are not
> members of themselves is a member of itself or not. It is if and only
> if it isn't.
>
> Sets are defined with a proposition, for example the set of even numbers
> is the set of all integers that are divisible by two. The defining
> proposition is "n is divisible by two".
>
> The defining proposition for the set of all sets that are not members of
> themselves is "X is not a member of itself."
>
> As I recall, and it's along time ago, "X is not a member of itself" can
> engender meaningless statements when checked with the defining
> proposition for many sets X. I just cannot recall how it was done.
If there is a set of all sets, which used to be thought reasonable,
then we can define the set of all sets that are not members of
themselves, call it M.
Then is M a member of M?
If it isn't, then it a set that isn't a member of itself, so by
definition it is a member of M.
But if it is a member of M then it fails the definition!
Oh dear - the world of logic was horrified. This was about 1895 I
think - they had to somehow amend their axioms to stop any such
unsightly contradiction!
So now the set of all sets is not generally regarded as being a set!
** Martin Thomas **
What does not kill me makes me stronger - Nietzsche
http://www.thehungersite.com/cgi-bin/WebObjects/HungerSite
To reply, turn off the light.