Hi,

Today,I want to touch on a very interesting topic namely,paradoxes.

You may wonder why I'm posting this in the science section.The term "paradox" is often applied in the literary sense.For instance,saying "The son is the father of the man" is a typical example.The paradox is explained when one considers that it is the son who takes care of the father in his dotage.

To begin,what is a paradox? Let's see Wikipedia for insight.

"A paradox is a statement that apparently contradicts itself & yet might be true (or wrong at the same time)."

Still from Wikipedia,it goes on to say:

"Some logical paradoxes are known to be invalid arguments but are still valuable in promoting critical thinking".

The above is the crux of this topic,logical paradoxes.I am not concerned with literary paradoxes,but rather those that challenge our way of thinking and in general,logic.This is why this topic is in this section.

Get ready to be blown away...Science gurus and all lovers of rationality,this is for you.

Not again...

I am aware that in this section on various threads,certain paradoxes have been discussed.I remember commenting on the "Omnipotent Paradox" on a thread created by Teempakguy.I believe this thread is in response or shall I say,continuity of such a fascinating concept.

I shall write in parts rather than a lengthy essay.This way we get to discuss a paradox before moving on to the next one.I hope that I'm not the only one intrigued by this concept.If you are a logician in the house,your input will be appreciated.

I wanted to compile my favorite paradoxes,but I found out that they were too many.So I'll just start with one and see how it goes from there.In my next post,I shall discuss a very old paradox that stems from the ancient city of Greece.The Greeks were the greatest thinkers of their time,and even today we marvel at their genius which was far in advance of their time.

Brace yourself lads,I give to you "The Paradox of Protagoras' Pupil".....

PROTAGORAS'S PUPIL
A paradox which has its foundation-real or legendary-in antiquity concerns the sophist Protagoras,who lived and taught in the fifth century BC.
It is said that Protagoras made an arrangement with one of his pupils whereby the pupil was to pay for his instruction after he had won his first case.The young man completed his course,hung up the traditional shingle,and waited for clients.None appeared.Protagoras grew impatient and decided to sue his former pupil for the amount owed him.
'For',argued Protagoras,'either I win this suit,or you win it.
If I win,you pay me according to the judgement of the court.If you win you pay me according to our agreement. In either case I am bound to get paid'.
'Not so',replied the young man.'If I win,then by the judgement of the court I need not pay you.If you win,then by our agreement I need not pay you.In either case I am bound not to have to pay you.'

Whose argument was right?Who knows?

RobinHez:
Not again...

Has a thread of this nature been created before?

Sheik have come again.. Waiting for the Barber's paradox

yorex2011:
Sheik have come again.. Waiting for the Barber's paradox

Funny enough,I've discussed the Barber Paradox in a previous thread.I may yet discuss it again.

Is that the only paradox you are familiar with?

Sheikwonder:


Has a thread of this nature been created before?

No...I mean the science people have started again with all their gibberish talk

Sheikwonder:


Funny enough,I've discussed the Barber Paradox in a previous thread.I may yet discuss it again.

Is that the only paradox you are familiar with?

The lying and truth telling brothers, there are a boatload of them.. Remember da yr cellini and bellini

yorex2011:


The lying and truth telling brothers, there are a boatload of them.. Remember da yr cellini and bellini

Yay! I completely forgot about cellini & bellini...the good old days...anyway,tnx for that...

My favorite paradoxes though are those that centre on the concept of infinity.I would value your input on this thread,stay in touch.

RobinHez:


No...I mean the science people have started again with all their gibberish talk

Logic is the exact opposite of gibberish I assure you. If you have questions,be free to ask,your input is much welcome.

The Grelling-Nelson Paradox.


Suppose one interprets the adjectives
"autological" and "heterological" as
follows:

1. An adjective is autological (sometimes homological) if and only if it describes itself. For example "noun"
is autological, since the word "noun" is
itself a noun.
"English,"
"unhyphenated" and "pentasyllabic"
are also autological.

2. An adjective is heterological if it does not describe itself. Hence "long"
is a heterological word (because it is
not a long word), as are "unwritten" and
"monosyllabic".

All adjectives, it would seem, must be
either autological or heterological, for
each adjective either describes itself,
or it doesn't.

Problems arise in a
number of instances however,which leads us to our paradox....

The Grelling–Nelson paradox arises
when we consider the adjective
"heterological".

One can ask:

Is "heterological" a heterological word?

If the answer is 'no', "heterological" is
autological.

This leads to a contradiction, for in this case "heterological" does not describe itself:
it must be a heterological word.

But if the answer is 'yes', "heterological" is
heterological. This again leads to a
contradiction, because if the word "heterological" describes itself, it is
autological.


Does anyone get this paradox,or are we lost ?

HANGING OR
BEHEADING

Poaching on the hunting preserves of a
powerful prince was punishable by
death,but the prince further decreed that
anyone caught poaching was to be given the privilege of deciding whether he
should be hanged or beheaded.

The culprit was permitted to make a
statement-if it were false,he was to be
hanged;if it were true,he was to be
beheaded.


One logical rogue availed himself of this
dubious prerogative-to be hanged if he didn't say the truth and to be beheaded if
he did-by stating:

"I shall be hanged".


Here was a dillemma not anticipated.
For,as the poacher put it,

"If you now hang me,you break the laws made by the prince,for my statement is true,and I ought to be beheaded,but if
you behead me,you are also breaking the
laws,for then what I said was false and I
should therefore be hanged".



The prince on seeing his dilemma set the poacher free.

whoops! cool! i love paradoxes.
bring it on... sheik!

RobinHez:


No...I mean the science people have started again with all their gibberish talk

what is this?
are you saying you're not sciency again or that paradoxies are gibberish talk?

Some paradoxes come in the form of sophistry i.e arguments that sound convincing and clever but which are false on closer inspection.

The following is one of my favourites:

Question: Is there anything better than eternal bliss?

Answer: Nothing is better than eternal bliss.

Ok then.

Question:Which is better then,eternal bliss or half a loaf of bread?

Answer: Obviously it's eternal bliss....

But wait a minute... Half a loaf of
bread is better than nothing,and nothing is better than eternal bliss...

Therefore,half a loaf of bread is better
than eternal bliss.


The above argument is regarded as an example of sophistry.Not a paradox per se,as any right thinking person can see that the confusion stems from semantics.

The next paradox will be much logical I assure you...are you ready?

On second thought,I think I shall start with the more famous paradoxes and sophisms before moving on to the tougher,much logical ones...

We are back to Greece again.The following is the famous "liar paradox" or "Epimenedes Paradox".

This is a well known
paradox written by the great
stoical logician Chrysippos.

The poet, grammarian and
critic Philetus of Cos was said to have died of exhaustion attempting to
resolve it.


1. A Cretan sails to Greece and
says to some Greek men who are standing upon the shore:
"All Cretans are liars."

Did he speak the truth, or did he lie?


2. A week later, the Cretan sailed
to Greece again and said:

"All Cretans are liars and all I say
is the truth."

Although the
Greeks on the shore weren't aware of what he had said the first time, they were truly
puzzled.



The modern version of this paradox simply is:

If someone says "I always lie", are they telling the truth? Or are they lying?

Next is the famous "Barber Paradox".

Analogue paradox to the 'liar
paradox' formulated by
English logician, philosopher
and mathematician,Bertrand Russell.

There exists a village. In this village,there is a barber,a man,who shaves men and only those men who do
not shave themselves.

Question is,who shaves the barber?


Who shaves the barber?


Clue: It's not me....

Sheikwonder:
Next is the famous "Barber Paradox".
Analogue paradox to the 'liar
paradox' formulated by
English logician, philosopher
and mathematician,Bertrand Russell.
There exists a village. In this village,there is a barber,a man,who shaves men and only those men who do
not shave themselves.
Question is,who shaves the barber?
Who shaves the barber?
Clue: It's not me....

A woman?

Akanniade:

A woman?

#--#

First,understand the paradox.

There exists only one Barber in this village who is a MAN and as a matter of principle,he only shaves MEN that do not shave themselves.

So Mr. Akanniade,if you happen to be in this village and you needed a shave,there would be 2 ways to go about it:

1. Either you shave yourself,or;

2. The Barber shaves you.

However,you must recall that the Barber will only shave you IF AND ONLY IF YOU DO NOT SHAVE YOURSELF.

So,who shaves the Barber?

This is where the paradox becomes apparent.

1. If we say the Barber shaves himself,then he does not shave himself for as the rule goes,HE ONLY SHAVES MEN WHO DO NOT SHAVE THEMSELVES.

2. If we say the Barber does not shave himself,then he shaves himself because HE SHAVES MEN WHO DO NOT SHAVE THEMSELVES.

A WOMAN can therefore not shave him because as is the rule there exists only one Barber,a MAN,who only shaves men who do not shave themselves.



I hope you are confused ""...

Sheikwonder:


#--#

First,understand the paradox.

There exists only one Barber in this village who is a MAN and as a matter of principle,he only shaves MEN that do not shave themselves.

So Mr. Akanniade,if you happen to be in this village and you needed a shave,there would be 2 ways to go about it:

1. Either you shave yourself,or;

2. The Barber shaves you.

However,you must recall that the Barber will only shave you IF AND ONLY IF YOU DO NOT SHAVE YOURSELF.

So,who shaves the Barber?

This is where the paradox becomes apparent.

1. If we say the Barber shaves himself,then he does not shave himself for as the rule goes,HE ONLY SHAVES MEN WHO DO NOT SHAVE THEMSELVES.

2. If we say the Barber does not shave himself,then he shaves himself because HE SHAVES MEN WHO DO NOT SHAVE THEMSELVES.

A WOMAN can therefore not shave him because as is the rule there exists only one Barber,a MAN,who only shaves men who do not shave themselves.



I hope you are confused ""...

Can't the barber just have a full ass beard?

Sheikwonder:
HANGING OR
BEHEADING

Poaching on the hunting preserves of a
powerful prince was punishable by
death,but the prince further decreed that
anyone caught poaching was to be given the privilege of deciding whether he
should be hanged or beheaded.

The culprit was permitted to make a
statement-if it were false,he was to be
hanged;if it were true,he was to be
beheaded.


One logical rogue availed himself of this
dubious prerogative-to be hanged if he didn't say the truth and to be beheaded if
he did-by stating:

"I shall be hanged".


Here was a dillemma not anticipated.
For,as the poacher put it,

"If you now hang me,you break the laws made by the prince,for my statement is true,and I ought to be beheaded,but if
you behead me,you are also breaking the
laws,for then what I said was false and I
should therefore be hanged".



The prince on seeing his dilemma set the poacher free.

What is your fixation with paradoxes?

Ishilove:

What is your fixation with paradoxes?

I would prefer to answer that question using the socratic method: Tell me,do you have any special interests,likes,inclinations? etc... Do share,I'd like to know....

Ishilove:

Can't the barber just have a full ass beard?

He could,but that would in no way solve the dilemma that would come when the need arises for him to shave his beard....

Sheikwonder:



I would prefer to answer that question using the socratic method: Tell me,do you have any special interests,likes,inclinations? etc... Do share,I'd like to know....

Yels, literature.

Likes, literature

Inclinations, literature

Special interest, LITERATURE!!

What's Socratic method?

Sheikwonder:



He could,but that would in no way solve the dilemma that would come when the need arises for him to shave his beard....

What if he is a hair fetish? What if he has no intention of EVER shaving his beard?

See, we have to open our minds to a world of possibilities

Ishilove:

Yels, literature.

Likes, literature

Inclinations, literature

Special interest, LITERATURE!!

What's Socratic method?

I sent you a mail...do check it out....


Socratic method, also known as method of elenchus, elenctic method, or Socratic debate, is named after the classical Greek philosopher Socrates. It is a form of inquiry and discussion between individuals, based on asking and answering questions to stimulate critical thinking and to illuminate ideas.

Sheikwonder:




I sent you a mail...do check it out....


Socratic method, also known as method of elenchus, elenctic method, or Socratic debate, is named after the classical Greek philosopher Socrates. It is a form of inquiry and discussion between individuals, based on asking and answering questions to stimulate critical thinking and to illuminate ideas.

Oh

Hokay.

Seen and replied sir.

So is my answer illuminating enough?

Ishilove:

What if he is a hair fetish? What if he has no intention of EVER shaving his beard?

See, we have to open our minds to a world of possibilities

One cannot argue with this point....1-0,Ishilove....

Sheikwonder:



One cannot argue with this point....1-0,Ishilove....