LarrySun:
I don't think it's exclusive to phones alone.

I thought you mentioned playstore

I could play you online,if you have a site where you usually play chess....

Sheikwonder:
Some other paradoxes while logical are also interesting because on first glance they do not look paradoxical. However they have practical applications in game theory,as well as in models that are predictive in nature.

Consider for example,"The Unexpected Hanging"....

A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day.

Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that the "surprise hanging" can't be on Friday, as if he hasn't been hanged by Thursday, there is only one day left - and so it won't be a surprise if he's hanged on Friday. Since the judge's sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday.

He then reasons that the surprise hanging cannot be on Thursday either, because Friday has already been eliminated and if he hasn't been hanged by Wednesday night, the hanging must occur on Thursday, making a Thursday hanging not a surprise either. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all.

The next week, the executioner knocks on the prisoner's door at noon on Wednesday — which, despite all the above, was an utter surprise to him. Everything the judge said came true.





The Paradox here,is that despite logically eliminating all possibilities of his date with death,when death came for the prisoner,he was still surprised- just like the judge predicted.

N.B: This Paradox also has variants e.g The Surprise Examination Paradox

This is not a paradox. It is just bad logic.

The prisoner knew that he would be hanged between monday to friday but it would be a surprise. Friday is eliminated because it would be the last day and after thursday night, there would be no surprise. Monday too would not be that surpising since it is the first day.

However, the three days of tuesday, wednesday and thursday will always be a surpise because he would never guess which of those days the hanging would happen within.

Sheikwonder:
Cc:AllNaijaBlogger

Good one there,striking similarities with LarrySun's grandfather paradox.


Ever heard of sorites paradox?
Interesting one,that.

Also known as paradox of the heap,it is a paradox centred on fuzziness and vague predicates.It goes thus:

1 million grains of sand make a heap.
If you take out one grain of sand from this i.e 999,999 grains,you are still left with a heap. If you yet take away another grain i.e 999,998 grains,you still have a heap of sand.

This process can be iterated until there is just one grain left. The paradox comes into play by calling that last grain a heap.

This is because if at 1 million it remains a heap,at 600,000 it remains a heap,at 200,000 it remains a heap;then for any given value save zero,you can refer to it as a heap.

The paradox arises because of vagueness: there is no accepted value for what constitutes a heap. Is it a million grains,100,000 grains or 1,000 grains?

Or simply put,at what point does a heap of sand stop being a heap of sand?

I too have always wondered about this.

You see, a community is a number of people. A hundred people are a community but when does it stop being a community? at 50 people? 30? 20? 10?

AllNaijaBlogger:



I too have always wondered about this.

You see, a community is a number of people. A hundred people are a community but when does it stop being a community? at 50 people? 30? 20? 10?

It stops being a community when there's nobody left in that community. Or may be when there is just one person left, just like sheikwonder said.

But we mustn't forget that man, as a single entity, is a community himself, because man comprises of body, mind and soul/spirit. All this makes up a man and functions for the benefit of man, just like a community.

Cc: AllNaijaBlogger

I am afraid Sir,I beg to disagree.

To understand the prisoner's logic better,let us analyse the judge's sentence.

The judge tells the prisoner that his death will come by noon of a weekday,and that his death will come as a surprise.


"Surprise" here means "Unexpected",hence the title of the paradox.


By your logic,you say that only Friday & Monday are the only days in which the prisoner's death will not come as a surprise,but this is you contradicting yourself!


Working from the top,If by Monday the prisoner is not dead,then death on Tuesday should come as no surprise-because he would be expecting it.And if by Tuesday,he is not dead,then death on Wednesday should come as no surprise,because he'd expect that too...and so on till Friday.

Yet his death was evidently still a surprise,which confirms the paradox and goes to show that even when all outcomes of a situation can be extrapolated,surprises are inevitable!


This paradox also has applications in game theory.

Sheikwonder, you're truly a wonder. I like how your mind works.

Sheikwonder:
Cc: AllNaijaBlogger

I am afraid Sir,I beg to disagree.

To understand the prisoner's logic better,let us analyse the judge's sentence.

The judge tells the prisoner that his death will come by noon of a weekday,and that his death will come as a surprise.


"Surprise" here means "Unexpected",hence the title of the paradox.


By your logic,you say that only Friday & Monday are the only days in which the prisoner's death will not come as a surprise,but this is you contradicting yourself!


Working from the top,If by Monday the prisoner is not dead,then death on Tuesday should come as no surprise-because he would be expecting it.And if by Tuesday,he is not dead,then death on Wednesday should come as no surprise,because he'd expect that too...and so on till Friday.

Yet his death was evidently still a surprise,which confirms the paradox and goes to show that even when all outcomes of a situation can be extrapolated,surprises are inevitable!


This paradox also has applications in game theory.

I still disagree. This "paradox" is steeped in bad logic and semantics.

If we were to gamble on which day the prisoner would be hanged, the odds would be 1/5 for each day and it will reduce after each day passes. For us, any outcome (the day that is revealed to be the day of the hanging) will come as a surprise because we don't know the outcome- we have 80% (4/5) probability of failing or guessing wrong.


Also, the prisoner's hanging is not "unexpected"- the prisoner expects to be hanged within the week. However, the day of the hanging will be a surprise- this then illustrates the semantics and difference in using the words "surprise" and "unexpected".

AllNaijaBlogger, brilliant. Absolutely brilliant!

Cc: AllNaijaBlogger


#Sigh

You really should stop contradicting
yourself.

As each day passes,the probability of being hanged INCREASES,it doesn't
reduce because his death MUST occur at
some time during the week.


The hanging is unexpected,because the prisoner had logically eliminated all
possibilities of being hanged.


Imagine his surprise on a sunny
Wednesday afternoon,when he sees the hangman at the door of his prison cell.....

Sheikwonder:
Cc: AllNaijaBlogger


#Sigh

You really should stop contradicting
yourself.

As each day passes,the probability of being hanged INCREASES,it doesn't
reduce because his death MUST occur at
some time during the week.


The hanging is unexpected,because the prisoner had logically eliminated all
possibilities of being hanged.


Imagine his surprise on a sunny
Wednesday afternoon,when he sees the hangman at the door of his prison cell.....

@ the bolded part of your comment-

It is impossible for the prisoner or anyone to logically eliminate the possibilities of being hanged when it will be a gamble (probability) until thursday night.

On sunday night, the odds are 1/5, monday night is 1/4, tuesday night is 1/3, wednesday night is 1/2, thursday night is 1/1.


The prisoner or anyone (but the judge) cannot logically eliminate the possibilities of being hanged, they can only calculate the odds.

Cc: AllNaijaBlogger

You are failing to see the beauty of this paradox.Remove all preconceptions and sentiments that you have,and you will see reason with me.

-First,the Prisoner believed that EVERYTHING that the judge said would be true. It is important that you get that part,it is very germane to grasping the paradox.

-The judge said that he would die at noon on a weekday. This eliminates the Sunday you mentioned.

- The judge said the execution would be a SURPRISE and that he would not know when he would be hanged,until the executioner knocked at his cell door.

-The judge was CERTAIN that the prisoner would be hanged at some time during the week.

-Once again,I repeat the prisoner was CERTAIN that everything the judge said was true.






After the sentencing,the prisoner goes back to his cell and begins to logically eliminate days,arriving at the conclusion that he would not be hanged based on the premise that since the hanging would not come as a surprise to him,the judge's sentence would not hold.


Deep pause here.


THE PRISONER'S LOGIC


Remember,he was CERTAIN that everything the judge said was true. This therefore eliminates the gamble that you talked about;he was dead sure that he had gotten the judge in a fix and that his death would in no way come as a surprise. I mean if you think about it,it's easy to see the soundness of the prisoner's logic.

As you yourself stated,the hanging can in no way be unexpected because he would already know that he should die at some point in the week,and since he has naturally eliminated every day of the week,he believes that if the judge decides to sentence him,the judge would be invalidating the sentence because there would be no element of surprise and the judge would be forced to set him free.


THE JUDGE'S LOGIC

The judge knew that the prisoner would hold on to every word of his sentencing. He therefore had to be careful in his wording. In my opinion,the judge was a genius.

The judge simply told him for effect,that his hanging would come as a surprise. The prisoner must have thought,"how in hell is this judge going to surprise me? Already he has told me that I ought to die sometime between Monday and Friday. Surely such a death would be expected and thus not surprising".

The real surprise came on Wednesday afternoon,when the hangman was waiting at the prisoner's cell door. I can only imagine the look on the prisoner's face when he is being led to the noose,he'd be like:

"I don't understand,this hanging should not be happening at all"......

I can see the judge smiling from afar,with a knowing nod saying "Exactly,my friend....exactly"





I honestly hope you understand it now. There is no need for calculating odds,the clue is in seeing that the prisoner was only seeing the surprise aspect from one angle,he never banked on the fact that the judge would capitalize on this.

LarrySun:
Sheikwonder, you're truly a wonder. I like how your mind works.

Thank you Sir,thank you.....

Sheikwonder:
Cc: AllNaijaBlogger

You are failing to see the beauty of this paradox.Remove all preconceptions and sentiments that you have,and you will see reason with me.

-First,the Prisoner believed that EVERYTHING that the judge said would be true. It is important that you get that part,it is very germane to grasping the paradox.

-The judge said that he would die at noon on a weekday. This eliminates the Sunday you mentioned.

- The judge said the execution would be a SURPRISE and that he would not know when he would be hanged,until the executioner knocked at his cell door.

-The judge was CERTAIN that the prisoner would be hanged at some time during the week.

-Once again,I repeat the prisoner was CERTAIN that everything the judge said was true.






After the sentencing,the prisoner goes back to his cell and begins to logically eliminate days,arriving at the conclusion that he would not be hanged based on the premise that since the hanging would not come as a surprise to him,the judge's sentence would not hold.


Deep pause here.


THE PRISONER'S LOGIC


Remember,he was CERTAIN that everything the judge said was true. This therefore eliminates the gamble that you talked about;he was dead sure that he had gotten the judge in a fix and that his death would in no way come as a surprise. I mean if you think about it,it's easy to see the soundness of the prisoner's logic.

As you yourself stated,the hanging can in no way be unexpected because he would already know that he should die at some point in the week,and since he has naturally eliminated every day of the week,he believes that if the judge decides to sentence him,the judge would be invalidating the sentence because there would be no element of surprise and the judge would be forced to set him free.


THE JUDGE'S LOGIC

The judge knew that the prisoner would hold on to every word of his sentencing. He therefore had to be careful in his wording. In my opinion,the judge was a genius.

The judge simply told him for effect,that his hanging would come as a surprise. The prisoner must have thought,"how in hell is this judge going to surprise me? Already he has told me that I ought to die sometime between Monday and Friday. Surely such a death would be expected and thus not surprising".

The real surprise came on Wednesday afternoon,when the hangman was waiting at the prisoner's cell door. I can only imagine the look on the prisoner's face when he is being led to the noose,he'd be like:

"I don't understand,this hanging should not be happening at all"......

I can see the judge smiling from afar,with a knowing nod saying "Exactly,my friend....exactly"





I honestly hope you understand it now. There is no need for calculating odds,the clue is in seeing that the prisoner was only seeing the surprise aspect from one angle,he never banked on the fact that the judge would capitalize on this.

So the claim that there is a paradox lies on the semantic change in the usage of "surprise" as a word.


Again. This is not necessarily a paradox.

AllNaijaBlogger:


So the claim that there is a paradox lies on the semantic change in the usage of "surprise" as a word.


Again. This is not necessarily a paradox.

You most certainly did not read what I wrote,as it is your prerogative you can choose to infer what you like,though I fail to see the role of semantics in this matter.

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

Thank you for your contribution.

Sheik taking time to explain, you trying man.. Thumbs up

Sheikwonder:



You most certainly did not read what I wrote,as it is your prerogative you can choose to infer what you like,though I fail to see the role of semantics in this matter.

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

Thank you for your contribution.

A paradox is a statement that contradicts itself but still remains true and logically valid.

Conversely, a sophism is a statement that seems true at first but is actually based on bad logic and faulty arguments.


What you have shown so far is a sophism

Feraz:
Nice one there OP! Fascinating topic. I'm enjoying every bit of it. How about these (saw it somewhere):

The crocodile sophism

A slim crocodile living in the Nile took a child. His mother begged to have him back. The crocodile could not only talk, but was also a great sophist and stated, "If you guess correctly what I will do with him, I will return him. However, if you don't predict his fate correctly, I'll eat him."
What statement should the mother make to save her child?

Can a man drown in a fountain of eternal life?

This is truly a paradox. I love it!

LarrySun:


In that regard, the Fibonacci sequence may be considered a numerical paradox.

However, there is one particular kind of paradox that always fascinates. It's The Grandfather Paradox.

It is a proposed paradox of time travel which results in an inconsistency through changing the past. It explains the age-old argument of preventing your birth by killing your grandparents.

For example, a time traveller goes back in time and kills his grandfather before his grandfather meets his grandmother.

As a result, the time traveller is never born. But, if he was never born, then he is
unable to travel through time and kill his grandfather, which means the traveller
would then be born after all, and so on.

Yes, I play chess.

Fascinating...

LarrySun:
A thread for great thinkers. The OP must be a good chess player.

One life for a thousand years, or ten lives for a hundred years each?

All is a logic of choice and belief. To be, or not to be?

Logically, which came first: The chicken or the egg?

Can the immediate question above be regarded as a paradox? There are paradoxical situations all around us. I extensively studied paradoxes when I was about to begin my 'The Paradox of Abel'. In my research, I arrived at the conclusion that paradoxes are basically spiral cats chasing their own tails.

Thanks, my Ishilove, for the mention.

With the way your mind works I knew this thread will be right up your alley

I would like to know if this, too, is a paradox:

A certain village was invaded with a plague of vermin, farmers complained of the damage done to their crops, houseowners lamented about how they had to battle with mice everyday. The king decided to find a lasting solution about how to get rid of the mice. He sent a message to the townspeople that they should begin to hunt the animals for a price. When you catch or kill a mouse, you shall be paid a certain amount of money. You would get twice the amount when you catch or kill two, and so on.

This was an idea meant to eradicate the invasion of vermin in the village. And because money was involved, villagers attacked any mouse with gumption. But instead of the mice to reduce, their number was actually growing, exponentially. Some villagers had to be smuggling mice into the village from other villages. Some were even keeping them and making them multiply so that they could receive more money.

In a few days after the king had promised a reward for every mouse caught or killed, the village was filled with ten times more mice than the initial number.

The solution to the problem turned out to worsen the problem.

yorex2011:
Sheik taking time to explain, you trying man.. Thumbs up

Thank you boss... It still beats me how some still find the concept of paradoxes hard to grasp...

I came up with this paradox myself


The paradox of technological problems.



We use technology to solve problems. We innovate in order to create solutions.


However, with technology we get more problems.



For instance,


We invented stoves to cook food better than firewood. But kerosene stoves give a nasty flavour to certain foods.


We invented gas cookers to overcome the problems of kerosene stoves but gas cookers are less portable and are more dangerous to use in terms of scale of explosion.


We invented electric cookers to overcome the limitations of gas cookers. Yes electric cookers can't explode but they can still shock you and cause fires if tampered with. Electric cookers cook slower than gas cookers.


The greatest irony here is that firewood beats all the cookers and stoves when it comes to cooking jollof rice for huge number of people.



This is the paradox- the solution is also a problem.


The very technology one uses as a solution to the problem is the problem.

"I'll help you out.....but there's a catch".

Even in the world of paradoxes there seems to be a catch,literally speaking.

A catch-22 is a paradoxical situation from which an individual cannot escape because of contradictory rules.

Coined by author,Joseph Heller,it is also the eponymous name of his book which discusses the paradox. The original catch-22 is given here,as an excerpt from his book. Here Orr, who is a soldier,wants to get out of combat duty and asks the doctor to help him out.The doctor tells him how to go about it but with a catch,catch-22:


"You mean there's a catch?"

"Sure there's a catch", Doc Daneeka replied. "Catch-22. Anyone who wants to get out of combat duty isn't really crazy."

There was only one catch and that was Catch-22, which specified that a concern for one's own safety in the face of dangers that were real and immediate was the process of a rational mind. Orr was crazy and could be grounded. All he had to do was ask; and as soon as he did, he would no longer be crazy and would have to fly more missions. Orr would be crazy to fly more missions and sane if he didn't, but if he was sane, he had to fly them. If he flew them, he was crazy and didn't have to; but if he didn't want to, he was sane and had to. [wikipedia]



We experience catch-22 in real life. For instance,to apply for a job, you need to have a few years of experience; but in order to gain experience you need to get a job. This is the paradox of the job seeker,and is a typical example of a catch-22 situation.

Cc: LarrySun

It is by all means a paradoxical situation,and a nice example at that.


Once avarice enters the picture,there is no telling how much havoc man can cause to himself,as is the case with the villagers and the vermins.

Is getting run down by an ambulance a paradox?

LarrySun:
Is getting run down by an ambulance a paradox?

Haha,funny one that... I suppose in a weird kind of way,it is...

Ever heard of the raven paradox? I have intentionally decided not to share it because it is quite logical... I'll share it anyway...

The raven paradox is an example of a confirmation paradox.

While taking a group of benefactors on a tour through the new aviary they had just helped to build, a noted ornithologist commented, "And here we have two of the finest examples of ravens that I have ever seen. Notice the lustrous black plumage for which all ravens are famous." The ornithologist continued his lecture, commenting on the corvine feeding and nesting habits as well as on the birds' legendary role as harbingers of ill fortune. When the ornithologist had finished, a young man said, "Sir, excuse me, but did you say that 'All ravens are black'?" "I don't know if I said exactly that, but it's true. All ravens are black." "But, how do you know that - for certain, I mean?" asked the young man. "Well, I've seen a few hundred ravens in my day and every one of them has been black." "Yes, but a few hundred are not all. How many ravens are there, anyway?" "I would guess several million. As for your question, many other scientists, and non-scientists for that matter, have observed ravens over thousands of years and so far the birds have all been black. At least, I don't know of a single instance in which someone has produced a non-black raven." "That's true, but it's still not all - just most." "True, but there is other evidence. For example, take all these lovely multicolored birds we have seen today - the parrots, toucans, the peacocks -" "They're lovely, but what do they have to do with your claim that all ravens are black?" "Don't you see?" asked the ornithologist. "No, I don't see. Please explain." "Well, you accept the idea that every new instance of another black raven that is observed adds to the support of the generalization that all ravens are black?" "Yes, of course." "Well then, the statement 'All ravens are black' is logically equivalent to the statement 'All non-black things are non-ravens.' This being so and because whatever confirms a statement also confirms any logically equivalent statement, it's clear that any non-black non-raven supports the generalization 'All ravens are black.' Hence, all these colorful, non-black non- ravens also support the generalization." "That's ridiculous," chided the young man. "In that case you might as well say that your blue jacket and gray pants also confirm the statement 'All ravens are black.' After all, they're also non-black non- ravens." "That's correct," said the ornithologist. "Now you're beginning to think like a true scientist." Who is reasoning correctly, the ornithologist or the young man?

Give me time to think. After much thoughts, I shall come back to answer the question.

LarrySun:
Give me time to think. After much thoughts, I shall come back to answer the question.

Goodluck!

LarrySun:
Is getting run down by an ambulance a paradox?

It is quite ironic. It is an irony but not a paradox.

Sheikwonder:
While taking a group of
benefactors on a tour through
the new aviary they had just
helped to build, a noted
ornithologist commented, "And
here we have two of the finest examples of ravens that I have
ever seen. Notice the lustrous
black plumage for which all
ravens are famous." The
ornithologist continued his
lecture, commenting on the corvine feeding and nesting
habits as well as on the birds'
legendary role as harbingers of ill
fortune.
When the ornithologist had
finished, a young man said, "Sir, excuse me, but did you say that
'All ravens are black'?"
"I don't know if I said exactly
that, but it's true. All ravens are
black."
"But, how do you know that - for certain, I mean?" asked the
young man.
"Well, I've seen a few hundred
ravens in my day and every one
of them has been black."
"Yes, but a few hundred are not all. How many ravens are there,
anyway?"
"I would guess several million. As
for your question, many other
scientists, and non-scientists
for that matter, have observed ravens over thousands of years
and so far the birds have all been
black. At least, I don't know of a
single instance in which someone
has produced a non-black raven."
"That's true, but it's still not all - just most."
"True, but there is other
evidence. For example, take all
these lovely multicolored birds
we have seen today - the
parrots, toucans, the peacocks -"
"They're lovely, but what do they
have to do with your claim that
all ravens are black?"
"Don't you see?" asked the
ornithologist. "No, I don't see. Please explain."
"Well, you accept the idea that
every new instance of another
black raven that is observed
adds to the support of the
generalization that all ravens are black?"
"Yes, of course."
"Well then, the statement 'All
ravens are black' is logically
equivalent to the statement 'All
non-black things are non-ravens.' This being so and because
whatever confirms a statement
also confirms any logically
equivalent statement, it's clear
that any non-black non-raven
supports the generalization 'All ravens are black.' Hence, all
these colorful, non-black non-
ravens also support the
generalization."
"That's ridiculous," chided the
young man. "In that case you might as well say that your blue
jacket and gray pants also
confirm the statement 'All
ravens are black.' After all,
they're also non-black non-
ravens." "That's correct," said the
ornithologist. "Now you're
beginning to think like a true
scientist."
Who is reasoning correctly, the
ornithologist or the young man?

Again, this is not a paradox. This is just bad logic.

At first, it seems paradoxical but considering that the original premise that "all ravens are black" is faulty, the whole argument breaks down.

If you do further reading on this raven paradox, you will find that it is only a tool in exposing the limits of inductive logic.


If all ravens are black, then it automatically means that all non black things are not ravens. This is logically sound based on the rules of inductive reasoning and it could have paradoxical consequences, however, inductive reasoning has its limits and can lead you to faulty arguments if not carefully examined.

---------------------------------------------------------------------------------------------


If you go on philosophy blogs, you would see people saying that it is not necessarily a paradox. It is only a paradox within the context of its inductive reasoning. But in general terms, it is not a paradox.

Remember what a paradox is- it contains two statements or two ideas that are contradictory but also true. For instance;

Predestination paradox
1) Changing the past will automatically change the future
2) However, going back in time was predestined for Mr. A and it didnt change but ensured his future.

Which came first, chicken or egg? Chicken/egg paradox
1) All chickens come from eggs
2) All eggs come from chickens

You've used the term "bad logic" for another paradox,wow!
You must be a master logician!


So,the original premise:

"All ravens are black" is faulty.

Normally,I'd ask you if you've ever seen a non-black one before,and I expect that your answer would be along the line of:

"Because I haven't seen a non-black raven before does not mean that all ravens are black,absence of evidence must not be misconstrued as evidence of absence".


The problem of course with this reasoning of yours is that anything can be disproved in this way.

For example,consider the statement:

"All men are mortal"

One could by your logic,argue that it is a faulty statement,because its logical equivalent would be:

"All non-men are non-mortal"

So summarily,one can conclude that "dogs are immortal".

But of course,you and I know that the above is absurd. The paradox arises because of logical equivalence. Your claim that the premise is wrong is wrong.

Various solutions to this paradox abound,see wikipedia for