WHAT IS A PARADOX: Fun With Definitions!
Snowmit
While us people types were arguing about paradoxes, we touched a lot on
what exactly is a paradox. I thought I'd present some definitions which
I found on the internet.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
MoneyWords Glossary:
http://cust2.iamerica.net/bplan/moneywords/p.htm
Paradox: A contradiction.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
WordNet 1.5 Vocabulary Helper
http://www.notredame.ac.jp/cgi-bin/wn.cgi
paradox -- ((in logic) a self-contradiction; ``I always lie'' ) ->
contradiction, contradiction in terms -- ((in logic) a statement that is
necessarily false; ``the statement `he is brave and he is not
brave' is a contradiction'' )
paradox -- ((in logic) a self-contradiction; ``I always lie'' )
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Webster's Revised Unabridged Dictionary, 1913 Edition
http://humanities.uchicago.edu/forms_unrest/webster.form.html
Paradox (Page: 1039)
Par`a*dox (?), n.; pl. Paradoxes (#). [F. paradoxe, L. paradoxum, fr. Gr.;
beside, beyond, contrary to + to think, suppose, imagine. See Para-, and
Dogma.] A tenet or proposition contrary to received opinion; an assertion
or sentiment seemingly contradictory, or opposed to common sense; that
which in appearance or terms is absurd, but yet may be true in fact.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Web Dictionary of Cybernetics and Systems
http://pespmc1.vub.ac.be/ASC/INdexASC.html
PARADOX
a tenet contrary to received opinion; a statement that is seemingly
contradictory or opposed to common sense and yet perhaps is true; a self-
contradictory statement that at first seems true; an argument that
apparently derives self-contradictory conclusions by valid deduction from
acceptable premises. (Webster's) A paradox is not the same as a
contradiction. "The shirt is blue; the shirt is not blue," and "It is
raining; it is not raining," are examples of contradictions. A
paradox occurs when one makes an assumption and, following a logical
argument, arrives at the converse. A paradox will always result when one
formulates a set that contains itself. Below are several examples:
l. Suppose there is a small town that consists only of men. There are two
kinds of men in this town--those who shave themselves and those who are
shaved by the barber. Who shaves the barber? If he shaves himself, then he
is shaved by the barber. But if he is shaved by the barber, then he shaves
himself. If the barber is assumed to be in one set, he appears in the
other. This situation occurs because the barber both appears in the set
and is used to define the set.
2. A person from the island of Crete asserts, "All Cretans are liars." We
can conclude that if he is telling the truth, then he is lying. But if he
is lying, then he is telling the truth. Once again an element of the set
is referring to the set.
3. Consider a businessman accused of accepting a bribe. He claims, "I did
not take the bribe." There are two possible interpretations of this
statement. Either he is a knowledgeable observer making a correct
statement, or he is a knowledgeable observer lying to avoid going to jail.
The businessman is both the observer and the person being observed. We
have no way of knowing which role he is playing.
As the third example indicates, paradox leads to "undecidability". When
two equally correct interpretations are possible, in the absence of
further information, no decision other than a random choice is possible.
(Umpleby)
From the Greek para + dokein, "to think more", conventionally, an argument
that apparently derives self-contradictory conclusions by valid deductions
from acceptable premises (Webster's). More generally, any description or
situation that is compelling enough to lead an observer into a vicious
cycle involving mutually exclusive interpretations, indications or acts,
force him to step out of or transcend the cycle and to CONSTRUCT a
logically more powerful (see ORDINALITY) COGNITIVE SYSTEM within which the
vicious cycle has disappeared. E.g., "This sentence is false" is false
when it is assumed to be true and true when it is assumed to be false. The
resolution of this vicious cycle requires a logic that accepts
SELF-REFERENCE which the prepositional calculus does not. Paradoxes appear
not only in logic but also in interpersonal COMMUNICATION, e.g.,
DOUBLE-BIND, in social ORGANIZATION and might be the stimulus for
MORPHOGENESIS. (Krippendorff)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Free On-line Dictionary of Computing
http://wagner.Princeton.EDU/foldoc/
<logic> An apparently sound argument leading to a contradiction.
Some famous examples are Russell's paradox and the liar paradox. Most
paradoxes stem from some kind of self-reference.
<database> Borland's IBM PC relational database.
Paradox 7 runs under Windows 95 and Windows NT. Paradox 5 runs on
Microsoft Windows and provides a graphical environment, a debugger, a data
modeling tool, and many "ObjectPAL" commands.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Bobs Byway GLOSSARY OF POETIC TERMS
http://shoga.wwa.com/~rgs/glossary.html
last stanza.
PARADOX
A passage which contains apparently opposing elements
contrary to common sense, yet full of significance when
viewed from another angle, for example, "make haste slowly."
Oscar Wilde was a master in the use of the paradox as a
rhetorical device.
(See also Catachresis,Malapropism,Mixed Metaphor,Oxymoron,
Synesthesia)
(Compare Hudibrastic Verse, Satire)
--
Take Air,
there are them that could Snowmit of the Loftie Mountain
and them that couldn't Chief Technician,
and them that do Founder of Cootm
who often shouldn't Truffles Like Him (shouldn't you?)
"I hate broccoli, but in a way I am broccoli."
-The Tick
___
{~o_o~} *****Needless Self-promotion*****
( ^ ) http://is2.dal.ca/~timmaly
()~:~() *****High Discordian Weirdness On-a-Stick*****
(_)-(_)
Is this sig block too long? ()yes ()no ()just right
John Baez
In article <5ojteq$rae$1...@News.Dal.Ca>, Snowmit <tim...@is.dal.ca> quoted
the following example of a "paradox" from the Web Dictionary of
Cybernetics and Systems:
>3. Consider a businessman accused of accepting a bribe. He claims, "I did
>not take the bribe." There are two possible interpretations of this
>statement. Either he is a knowledgeable observer making a correct
>statement, or he is a knowledgeable observer lying to avoid going to jail.
>The businessman is both the observer and the person being observed. We
>have no way of knowing which role he is playing.
This is the dumbest example of a "paradox" I've ever seen! Whoever
originally wrote this doesn't know know a paradox from a pair of
scissors.
Alexander Abian
In article <5p3b6p$d...@schauder.mit.edu>, John Baez <ba...@math.mit.edu> wrote:
>In article <5ojteq$rae$1...@News.Dal.Ca>, Snowmit <tim...@is.dal.ca> quoted
>the following example of a "paradox" from the Web Dictionary of
>Cybernetics and Systems:
>
Abian answers:
Discard all the definitions of a "Paradox" except the one that
I have given - namely:
PARADOX is a synonym of INCONSISTENCY
i.e., a statement whose truth implies its falsehood (non-truth) and
whose falsehood implies its truth.
A paradox is not a contradiction it is not a falsehood it is the
inconsistency itself!!
So, except for statements which in an intelligent interlocution must
be forbidden to be uttered or written (e.g., that paradoxical letter
of the Mayor to the Village Barber) THERE CANNOT BE A PARADOXICAL SITUATION
IN REAL LIFE !. The essence of Life is in its consistency!
--
--------------------------------------------------------------------------
ABIAN MASS-TIME EQUIVALENCE FORMULA m = Mo(1-exp(T/(kT-Mo))) Abian units.
ALTER EARTH'S ORBIT AND TILT - STOP GLOBAL DISASTERS AND EPIDEMICS
ALTER THE SOLAR SYSTEM. REORBIT VENUS INTO A NEAR EARTH-LIKE ORBIT
TO CREATE A BORN AGAIN EARTH (1990)
Snowmit
John Baez (ba...@math.mit.edu) wrote:
: >3. Consider a businessman accused of accepting a bribe. He claims, "I did
: >not take the bribe." There are two possible interpretations of this
: >statement. Either he is a knowledgeable observer making a correct
: >statement, or he is a knowledgeable observer lying to avoid going to jail.
: >The businessman is both the observer and the person being observed. We
: >have no way of knowing which role he is playing.
: This is the dumbest example of a "paradox" I've ever seen! Whoever
: originally wrote this doesn't know know a paradox from a pair of
: scissors.
Yeah, I know.
It kind of gets accross the point that there really isn't a strict
well agreed upon definition for paradox out there though. This is what I
wanted to point out.
--
Take Air,
there are them that could Snowmit of the Loftie Mountain
and them that couldn't Chief Technician,
and them that do Founder of Cootm
who often shouldn't Truffles Like Him (shouldn't you?)
"Don't worry ma'am, I'm disturbing but asexual."
-Bathtime Bob (The Hygiene Cowboy)
Shane Hitching
Alexander Abian <ab...@iastate.edu> wrote in article
<5p3kst$659$1...@news.iastate.edu>...
> In article <5p3b6p$d...@schauder.mit.edu>, John Baez <ba...@math.mit.edu>
wrote:
> >In article <5ojteq$rae$1...@News.Dal.Ca>, Snowmit <tim...@is.dal.ca>
quoted
> >the following example of a "paradox" from the Web Dictionary of
> >Cybernetics and Systems:
> >
>
> Abian answers:
>
> Discard all the definitions of a "Paradox" except the one that
> I have given - namely:
>
>
> PARADOX is a synonym of INCONSISTENCY
>
> i.e., a statement whose truth implies its falsehood (non-truth) and
> whose falsehood implies its truth.
>
> A paradox is not a contradiction it is not a falsehood it is the
> inconsistency itself!!
>
> So, except for statements which in an intelligent interlocution must
> be forbidden to be uttered or written (e.g., that paradoxical letter
> of the Mayor to the Village Barber) THERE CANNOT BE A PARADOXICAL
SITUATION
> IN REAL LIFE !. The essence of Life is in its consistency!
May I ask what country you come from? I ask this because your statement
regarding the definition of the word paradox is akin to saying that apple
is a synonym of orange. Is it possible that you have made a simple error
in your use of english?
You demand that people "Discard all the definitions of a "Paradox" except
the one that I have given - namely: PARADOX is a synonym of
INCONSISTENCY". Why should we do this? Why should I suddenly say that an
apple is an orange?
You really should go and visit the library ASAP, you will then see that I
can create a paradox in real life as easily as I can post this message...
* * * * *
Shane Hitching
Sh...@XX.Demon.co.uk - replace XX with GAMyNet
www.GAMyNet.Demon.co.uk
dann corbit
Snowmit <tim...@is.dal.ca> wrote in article <5p90ms$lj1$3...@News.Dal.Ca>...
> John Baez (ba...@math.mit.edu) wrote:
> : >3. Consider a businessman accused of accepting a bribe. He claims, "I
did
> : >not take the bribe." There are two possible interpretations of this
> : >statement. Either he is a knowledgeable observer making a correct
> : >statement, or he is a knowledgeable observer lying to avoid going to
jail.
> : >The businessman is both the observer and the person being observed. We
> : >have no way of knowing which role he is playing.
>
> : originally wrote this doesn't know know a paradox from a pair of
> : scissors.
>
> Yeah, I know.
>
> It kind of gets accross the point that there really isn't a strict
> well agreed upon definition for paradox out there though. This is what I
> wanted to point out.
The prosecution says, "You did it!"
The defense says, "I did not do it!"
Can both statements be true? [Well, maybe under certain circumstances]
The interesting thing about a court case is that unless sufficient facts
come out, we are unable to RESOLVE the paradox.
me...@cars3.uchicago.edu
In article <01bc8636$6e041ad0$c961e426@backslash>, "dann corbit" <dco...@solutionsiq.com> writes:
>EVERY court case is a paradox.
>The prosecution says, "You did it!"
>The defense says, "I did not do it!"
>Can both statements be true? [Well, maybe under certain circumstances]
>
>The interesting thing about a court case is that unless sufficient facts
>come out, we are unable to RESOLVE the paradox.
>
Reminds me of a statement (by Oscar Wilde, I think) that goes like:
"Our legal system is based on the belief that you can get to the truth
by listening to the lies of all sides involved"
Mati Meron | "When you argue with a fool,
me...@cars.uchicago.edu | chances are he is doing just the same"
cybe...@hotmail.com
On 28 Jun 1997 18:24:29 GMT, ab...@iastate.edu (Alexander Abian)
wrote:
> So, except for statements which in an intelligent interlocution must
>be forbidden to be uttered or written (e.g., that paradoxical letter
>of the Mayor to the Village Barber) THERE CANNOT BE A PARADOXICAL SITUATION
>IN REAL LIFE !. The essence of Life is in its consistency!
Hey, why don't you start your own language? To simply discard a very
common and traditional definition for something and to replace it with
your own is egotistical, stupid, and pointless.
Mercurius
Alexander Abian wrote in article <5p3kst$659$1...@news.iastate.edu>...
>Abian answers:
>
> Discard all the definitions of a "Paradox" except the one that
> I have given - namely:
>
> PARADOX is a synonym of INCONSISTENCY
Not really, while a paradox necessarily contains an inconsistency, an
inconsistency is not always enough to guarantee a paradox. If I say "I am
not a crook" today, and then confess tomorrow, it would be inconsistent of
me, but not paradoxical. I am either a crook or not, but never both
simultaneously, regardless of what I say on the matter.
> i.e., a statement whose truth implies its falsehood (non-truth) and
>whose falsehood implies its truth.
This is a stronger and more accurate definition, but note that it does not
follow from your "paradox is a synonym of inconsistency" definition, for
the reasons given above. Also note that this stronger definition only
admits paradoxes of the "this sentence is false" variety, which are very
small in number.
> So, except for statements which in an intelligent interlocution must
>be forbidden to be uttered or written (e.g., that paradoxical letter
>of the Mayor to the Village Barber) THERE CANNOT BE A PARADOXICAL
>SITUATION IN REAL LIFE !.
Um. You're begging the question. If you want to demonstrate that "there
cannot be a paradoxical situation in real life", you can't start by
insisting on the exclusion of certain statements which may give rise to
paradoxes.
It's true that many situations people call "paradoxical" are not strict,
logical paradoxes of the "this sentence is false" variety. Many are
oxymorons, inconsistencies, contradictions, necessary falsehoods, whatever.
Of course, if people call them paradoxes, then it demonstrates a poor
understanding of the term; but it also tends to become the accepted
definition.
It seems true that a "barber that always and only cuts the hair of people
who don't cut their own hair" couldn't possibly exist. But the *idea* of
such a barber *does* exist. Bertrand Russell called it "the set of all
things which are not sets of themselves", which is a fancy way of saying
"this sentence is false".
And all that suggests possible problems with our understanding of "true"
and "false". Or, if not, then paradoxes are just the "shadows" cast by the
existing system of logic, truth and knowledge that our understanding of the
world is based upon.
>The essence of Life is in its consistency!
Don't bite off more than you can chew. When people are dead, they stay
dead, consistently. ;->
Mercurius
me...@isp.com.au
Mercurius
Mercurius
Mercurius
Gus Gassmann
Alexander Abian wrote:
> A paradox is not a contradiction it is not a falsehood it is the
> inconsistency itself!!
>
> So, except for statements which in an intelligent interlocution must
> be forbidden to be uttered or written (e.g., that paradoxical letter
> of the Mayor to the Village Barber) THERE CANNOT BE A PARADOXICAL SITUATION
> IN REAL LIFE !. The essence of Life is in its consistency!
Yeah right! Like Raymond Smullyan, I am a Gemini. I think he has a
wonderful
explanation for why he doesn't believe in astrology: Geminis never do...
-------------------------------------------------------
gus gassmann (Horand....@dal.ca)
School of Business Administration, Dalhousie University
Halifax, Nova Scotia, Canada , B3H 1Z5
ph. (902) 494-1844
fax (902) 494-1107
John Baez
In article <5p90ms$lj1$3...@News.Dal.Ca>, Snowmit <tim...@is.dal.ca> wrote:
>John Baez (ba...@math.mit.edu) wrote:
>: >3. Consider a businessman accused of accepting a bribe. He claims, "I did
>: >not take the bribe." There are two possible interpretations of this
>: >statement. Either he is a knowledgeable observer making a correct
>: >statement, or he is a knowledgeable observer lying to avoid going to jail.
>: >The businessman is both the observer and the person being observed. We
>: >have no way of knowing which role he is playing.
>
>Yeah, I know.
>It kind of gets across the point that there really isn't a strict
>well agreed upon definition for paradox out there though.
Maybe it gets across the point that there are people who don't know
shit about the concept of "paradox". :-)
It's certainly true that there is some fuzziness in the definition of
a paradox: for example, some people use it to mean only an argument
leading logically from certain axioms to a contradiction, while others
freely use it to mean any argument with a conclusion that puzzles or
disturbs them. The distinction is fuzzy because you can always turn
the latter kind of paradox into the former kind by making your reasons
for being disturbed or puzzled into new axioms.
What bugged me was that in the "paradox" above, the author above
doesn't seem to be reaching a contradiction, and he doesn't even seem
particularly disturbed or puzzled. He seems to think one has a
"paradox" when there is something one doesn't know about a situation!
At least that was my first impression. Thinking about it further, I
suppose the above snippet is a reasonable example of a "paradox" if
the author takes it for granted that one can always tell if someone is
telling the truth or not, and is shocked to discover that this is not
the case.
If you start with funny axioms like this, it is easy to get paradoxes.
Some ancient Greek and Chinese paradoxes seem a little bit funny to us
now for similar reasons. My favorite example is the famous Chinese
"white horse" paradox, which goes: "How is a `white horse' possible,
since it would have to be both white and horse?" When I first heard
this I didn't get it. Then I learned more about Chinese grammar and
it made more sense.
ca314159
John Baez wrote:
>
> In article <5p90ms$lj1$3...@News.Dal.Ca>, Snowmit <tim...@is.dal.ca> wrote:
> >John Baez (ba...@math.mit.edu) wrote:
> >: >not take the bribe." There are two possible interpretations of this
> >: >statement. Either he is a knowledgeable observer making a correct
> >: >statement, or he is a knowledgeable observer lying to avoid going to jail.
> >: >The businessman is both the observer and the person being observed. We
> >: >have no way of knowing which role he is playing.
> >
>
> >Yeah, I know.
>
> >It kind of gets across the point that there really isn't a strict
> >well agreed upon definition for paradox out there though.
>
> doesn't seem to be reaching a contradiction, and he doesn't even seem
> particularly disturbed or puzzled. He seems to think one has a
> "paradox" when there is something one doesn't know about a situation!
Kind of like the zero frequency problem. If you have no idea about
the degrees of freedom, how do you assign probabilities ? In his
example the assumption is that there are only two states and hence
a 1/2 division of probabilities.
The problem with his example is that he forgot about insanity. The
businessman might very well believe to be true what the majority
find to be false; and, that's another kind of paradox.
Terry Moore
In article <01bc8636$7d48a4c0$fb3d9593@elh-s-hitching>, "Shane Hitching"
<Sh...@XX.Demon.co.uk - replace XX with GAMyNet> wrote:
> > Abian answers:
> >
> > Discard all the definitions of a "Paradox" except the one that
> > I have given - namely:
> >
> >
> > PARADOX is a synonym of INCONSISTENCY
> May I ask what country you come from? I ask this because your statement
> regarding the definition of the word paradox is akin to saying that apple
> is a synonym of orange. Is it possible that you have made a simple error
> in your use of english?
>
> You demand that people "Discard all the definitions of a "Paradox" except
> the one that I have given - namely: PARADOX is a synonym of
> INCONSISTENCY". Why should we do this? Why should I suddenly say that an
> apple is an orange?
It is totally irrelevant whether Abian's definiton agrees with your
dictionary or not. The question is whether we can avoid the
classical paradoxes by adopting his definition. If you can give
a reasoned argument on that, then that will be progress. Pointing
out that Abian's definition is not in your dictionary is not progress,
it is a waste of effort.
--
Terry Moore, Statistics Department, Massey University, New Zealand.
Theorems! I need theorems. Give me the theorems and I shall find the
proofs easily enough. Bernard Riemann
Shane Hitching
Mercurius <me...@isp.com.au> wrote in article
<5pcjfd$f...@news.mel.aone.net.au>...
> >
> > Discard all the definitions of a "Paradox" except the one that
> > I have given - namely:
> >
> > PARADOX is a synonym of INCONSISTENCY
>
> inconsistency is not always enough to guarantee a paradox. If I say "I am
> not a crook" today, and then confess tomorrow, it would be inconsistent
of
> me, but not paradoxical. I am either a crook or not, but never both
> simultaneously, regardless of what I say on the matter.
>
<SNIP>
> Mercurius
> me...@isp.com.au
I agree with you except on one point, inconsistency is not a requirement
for a paradox. The only requirement is the *appearance* of contradiction;
although I admit that its much easier to come up with an inconsistant
paradox than it is a consistant paradox.
* * * * *
Shane Hitching
Sh...@XX.Demon.co.uk - replace XX with GAMyNet
Patrick Herring
John Baez wrote:
-
- In article <5p90ms$lj1$3...@News.Dal.Ca>, Snowmit <tim...@is.dal.ca>
wrote:
- >John Baez (ba...@math.mit.edu) wrote:
- >: >3. Consider a businessman accused of accepting a bribe. He claims,
"I did
- >: >not take the bribe." There are two possible interpretations of
this
- >: >statement. Either he is a knowledgeable observer making a correct
- >: >statement, or he is a knowledgeable observer lying to avoid going
to jail.
- >: >The businessman is both the observer and the person being
observed. We
- >: >have no way of knowing which role he is playing.
- >:
- >: This is the dumbest example of a "paradox" I've ever seen!
-
- >Yeah, I know.
-
- >It kind of gets across the point that there really isn't a strict
- >well agreed upon definition for paradox out there though.
-
- Maybe it gets across the point that there are people who don't know
- shit about the concept of "paradox". :-)
-
- It's certainly true that there is some fuzziness in the definition of
- a paradox: for example, some people use it to mean only an argument
- leading logically from certain axioms to a contradiction, while others
- freely use it to mean any argument with a conclusion that puzzles or
- disturbs them. The distinction is fuzzy because you can always turn
- the latter kind of paradox into the former kind by making your reasons
- for being disturbed or puzzled into new axioms.
Surely a contradiction is just false - nothing paradoxical about it.
IMHO a paradox is when a valid argument from believed premises has a
disbelieved conclusion.
- What bugged me was that in the "paradox" above, the author above
- doesn't seem to be reaching a contradiction, and he doesn't even seem
- particularly disturbed or puzzled. He seems to think one has a
- "paradox" when there is something one doesn't know about a situation!
-
- At least that was my first impression. Thinking about it further, I
- suppose the above snippet is a reasonable example of a "paradox" if
- the author takes it for granted that one can always tell if someone is
- telling the truth or not, and is shocked to discover that this is not
- the case.
From Abian's other writings perhaps the paradox he sees is the conflict
between believing that p must be true or false but not being able to
believe which one obtains 'out there' ie you can have a priori knowledge
but not a posteriori, and, as you say, he seems to believe that all
knowledge of the 'world' is a posteriori. Abian needs to read Kant in a
big way, though I wouldn't like to watch it happening.
- If you start with funny axioms like this, it is easy to get paradoxes.
- Some ancient Greek and Chinese paradoxes seem a little bit funny to us
- now for similar reasons. My favorite example is the famous Chinese
- "white horse" paradox, which goes: "How is a `white horse' possible,
- since it would have to be both white and horse?" When I first heard
- this I didn't get it. Then I learned more about Chinese grammar and
- it made more sense.
Not heard this one: can you say more?
yours, Patrick
________________________________________________________
Patrick Herring at work, herr...@rlsclare.agw.bt.co.uk
Disclaimer: The form is BT but the essence is me.
"Occam's razor is so sharp, I bought the whole argument"
Graham Walmsley
Gus Gassmann <HGAS...@MGMT.Dal.CA> wrote in article
<33BA92...@MGMT.Dal.CA>...
> Alexander Abian wrote:
>
> > A paradox is not a contradiction it is not a falsehood it is the
> > inconsistency itself!!
> >
> > So, except for statements which in an intelligent interlocution must
> > be forbidden to be uttered or written (e.g., that paradoxical letter
> > of the Mayor to the Village Barber) THERE CANNOT BE A PARADOXICAL
SITUATION
> > IN REAL LIFE !. The essence of Life is in its consistency!
>
> Yeah right! Like Raymond Smullyan, I am a Gemini. I think he has a
> wonderful
> explanation for why he doesn't believe in astrology: Geminis never do...
Hang on...
There's two possible situations here. Either you were born on a certain
date and you do believe in astrology. Or you were born on a certain date
and you don't believe in astrology. Neither of those situations is, in
itself, inconsistent.
What is inconsistent is the *description* of that situation: the two
statements that "I am a Gemini" and "Geminis never believe in astrology".
So the real life situation is perfectly consistent - the paradox arises in
the description.
Graham
John Baez
In article <33BC18...@rlsclare.agw.bt.co.uk>,
Patrick Herring <herr...@rlsclare.agw.bt.co.uk> wrote:
>John Baez wrote:
>- Some ancient Greek and Chinese paradoxes seem a little bit funny to us
>- now for similar reasons. My favorite example is the famous Chinese
>- "white horse" paradox, which goes: "How is a `white horse' possible,
>- since it would have to be both white and horse?" When I first heard
>- this I didn't get it. Then I learned more about Chinese grammar and
>- it made more sense.
>
>Not heard this one: can you say more?
Well, in classical Chinese there is no sharp distinction between mass
nouns, count nouns, and even what we would consider adjectives.
A mass noun is something like "mud" or "water", while a count noun is
something like "apple" or "horse": in English one can grammatically
say "I saw one horse" or "There was a large amount of mud in the
woods" but not "I saw one mud" or "There was a large amount of horse
in the woods". (You can, however, say "there was a large amount of
livestock in the woods".)
In classical Chinese this distinction is weak or absent. Even
adjectives like "white" can act like nouns - perhaps the closest
example I can come up with in English is "I saw white all around me",
where one can with a stretch sort of think of "white" as a mass noun.
So, putting yourself into the frame of mind where adjectives, mass
nouns, and count nouns are all sort of the same, you can imagine
wondering which sorts of things can coexist:
can horse be cow?
can black be white?
can horse be white?
and so on. (I should add that classical Chinese has no words
for "a" and "the"!)
Clearly horse can't be cow, and white can't be black. But the idea
that a thing can be only itself and nothing else, while simple and at
first reasonable, runs into trouble with examples like "white horse".
On the other hand, maybe in fact there is no such thing as a "white
horse"! You've got the whiteness and the horseness in close
association, but is the white ever really horse, and is the horse ever
really white?
I believe that the Mohists were the ones who were the most interested
in such paradoxes. You will also find similar issues raised in Plato's
"Parmenides", where they discuss how things can participate in forms.
Terry Moore
In article <5pcjhr$f...@news.mel.aone.net.au>, "Mercurius"
<me...@isp.com.au> wrote:
> Alexander Abian wrote in article <5p3kst$659$1...@news.iastate.edu>...
> >Abian answers:
> >
> > Discard all the definitions of a "Paradox" except the one that
> > I have given - namely:
> >
> > PARADOX is a synonym of INCONSISTENCY
>
> Not really, while a paradox necessarily contains an inconsistency, an
> inconsistency is not always enough to guarantee a paradox.
It is if your definition of "Paradox" is Abian's one.
We all know that his definition is not the one most
used. But that's irrelevant to his argument. Discuss
his argument. But only once please - sending the
same message three times does not guarantee three
times as much acceptance. Or do you work on the
Bellman principle?
Dann Corbit
[snip]
> I agree with you except on one point, inconsistency is not a requirement
> for a paradox. The only requirement is the *appearance* of contradiction;
> although I admit that its much easier to come up with an inconsistant
> paradox than it is a consistant paradox.
statements were paradoxical. They really aren't paradoxes now, since we have
calculus to prove the results. When Galileo said the earth moved, it was a
paradox for two different frameworks. One system said it was possible, the
other impossible. Imagine if Einstein had never discovered the principles of
relativity, and we simply MEASURED that we could not accelerate an electron
past the speed of light or MEASURED light bending past a star, or one of
those gravitational lenses discovered by the Hubble Telescope. Then we would
have a paradox until we refined one of our frameworks to reach agreement.
Here's another sort of paradox (in my mind anyway -- could simply be
confusion on my part...)
a implies not b
b implies not a
Then we have some partial conditions which partly imply either a or b must be
true.
The Barber's paradox is of this sort. If we make either assumption, it
negates the possibility of the other.
Ken Livingston
"Graham Walmsley" <gra...@xara.com> wrote:
> Hang on...
>
> There's two possible situations here. Either you were born on a certain
> date and you do believe in astrology. Or you were born on a certain date
> and you don't believe in astrology. Neither of those situations is, in
> itself, inconsistent.
But what happens if you were born on an *uncertain* date? Say that
there is no definitive record of your birthdate. Are you inconsistent?
> What is inconsistent is the *description* of that situation: the two
> statements that "I am a Gemini" and "Geminis never believe in astrology".
> So the real life situation is perfectly consistent - the paradox arises in
> the description.
I do not know what it means to "believe in astrology" or *not* to "believe
in astrology." One might be undecided on the matter. Or, one might believe
in some aspects of astrology and not believe in other aspects of astrology.
Regards,
Ken
--
Ken Livingston
ken...@pcug.org.au
mahipa...@orbital.fsd.com
In article <33BC18...@rlsclare.agw.bt.co.uk>,[trim]
> - Maybe it gets across the point that there are people who don't know
> - shit about the concept of "paradox". :-)
> -
> - It's certainly true that there is some fuzziness in the definition of
> - a paradox: for example, some people use it to mean only an argument
> - leading logically from certain axioms to a contradiction, while others
> - freely use it to mean any argument with a conclusion that puzzles or
> - disturbs them. The distinction is fuzzy because you can always turn
> - the latter kind of paradox into the former kind by making your reasons
> - for being disturbed or puzzled into new axioms.
>
> Surely a contradiction is just false - nothing paradoxical about it.
> IMHO a paradox is when a valid argument from believed premises has a
> disbelieved conclusion.
Or a believed conclusion?
Excellent definition. Though I might joke, I'm one of those people who've
never fully appreciated the difference between a contradiction and a
paradox. Apparently, I haven't got the time to invest appreciating.
Nevertheless, here's a paradox, hopefully a new one, for your e(y)es
only:
The |meforce> Paradox: Why do Newton's F=pdot and Einstein's E=mc2,
the two foundations of modern physics, result in this |meforce>?
Possible questions/resolutions:
1. Purely accidental?
2. A byproduct of mixing literature with physics? I think maybe!
3. Is Nature absurd? Let's hope not.
If you're even *remotely* interested in physics' paradoxes, this one's
neat! Maybe it isn't even a "paradox" by the "definition"?
> - What bugged me was that in the "paradox" above, the author above
> - doesn't seem to be reaching a contradiction, and he doesn't even seem
> - particularly disturbed or puzzled. He seems to think one has a
> - "paradox" when there is something one doesn't know about a situation!
[trim]
Forgive me if I appear rude by/for sharing my thoughts. :-( Sometimes I
truly wish I didn't stumble on this *weird* formulation/paradox. Anyway,
don't hate me just the same. :-| I'm just this writer with a pen. Well,
some ink too.
The details of the paradox are at the http address below. It's about three
standard size pages of really fast reading. You don't have to be a rocket
scientist to get it. Though it couldn't hurt, I imagine. :-)
/\ "If the line between science fiction and
/ science fact doesn't drive you crazy,
/\ \ then you're just not tr(y)ing!"
\ /\/\ / \ \/ Mahipal
/ == \ / \/\/ The |meforce> Paradox
\/ http://www.geocities.com/Athens/3178/mew3.html
-------------------==== Posted via Deja News ====-----------------------
http://www.dejanews.com/ Search, Read, Post to Usenet