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Liar Paradox (Eubulid or Epimenides 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.

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?
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.

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

Double Liar Paradox (Jourdain's paradox)

This version of a famous paradox was presented by English mathematician P. E. B. Jourdain in 1913.

The following is written on opposite sides of a card:

Back side
THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS TRUE.

Face side
THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS FALSE.

Barber Paradox (Russell's Paradox)

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

In a village, the barber shaves everyone who does not shave himself/herself, but no one else.
Who shaves the barber?

Lazy-bones Paradox

If destiny designed a master plan which defines everything that is to happen, isn't it useless, for example, to go to a doctor? If I am ill and it is my destiny to regain health, then I will regain health whether I visit a doctor or not. If it is my destiny to not regain my health, then seeing a doctor can't help me.

How could you question the presented opinion?

A few sentences from life

Nobody goes to that restaurant; it's too crowded.

Don't go near the water 'til you have learned how to swim.

The man who wrote such a stupid sentence can not write at all.

If you get this message, call me, and if you don't get it, don't call.

ADVERTISEMENT: Are you an analphabet? Write a letter and we will send you free of charge instructions how to undo it.

Think about these

Let's say there is a bullet which can shoot through any barrier. Let's also say there is an absolutely bullet-proof armor which no object can penetrate. What will happen if such a bullet hits such an armor?
Can a man drown in the fountain of eternal life?
Your mission is not to accept the mission. Do you accept?
A girl goes into the past and kills her Grandmother. Since her Grandmother is dead, the girl was never born. If she were never born, she never killed her grandmother.
If the temperature this morning is 0 degrees and the Weather Channel says, "It will be twice as cold tomorrow", what will the temperature be?
Answer truthfully (yes or no) to the following question: Will the next word you say be 'no'?
What happens if you are in a car going the speed of light and you turn the headlights on?

Oh!! I just remembered Zeno's famous paradox has been solved ?

@Alan McDougall,

Alan McDougall;73571 wrote:

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

No one 'always' does anything, our 'states' are time and context dependent. The question is in error.
They are telling the truth if they believe that they are.

Quote:

he following is written on opposite sides of a card:
Back side
THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS TRUE.
Face side
THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS FALSE

Only a fool would assume that both statements can be correct and true and thus present a paradox. Obviously, one or both are false. No paradox.
We handed the same cards in grade school to idiots. On one side was; "HOW DO YOU KEEP AN IDIOT BUSY? (over)". On the obverse side was; "HOW DO YOU KEEP AN IDIOT BUSY? (over)"
The biggest idiot was only amused for a moment. No attention span. I think that it fell, eventually, into the hands of some philosopher who, until this day, is pondering the 'paradox'...

Quote:

If destiny designed a master plan which defines everything that is to happen, isn't it useless, for example, to go to a doctor? If I am ill and it is my destiny to regain health, then I will regain health whether I visit a doctor or not. If it is my destiny to not regain my health, then seeing a doctor can't help me.

How could you question the presented opinion?

If your 'destiny' is to heal, what makes you disregard the contextual 'destiny' of being in the doctor's office? What is the point of arbitrarily choosing a visit to the doc to be 'outside destiny'? Why is the doctor visit less 'is' then the healing? Perhaps your 'destiny' of healing can only be found in the context of a universe where you visit the doctor?
If 'everything' is destiny, there are no options, no choices, no 'free-will', it is illogical to suddenly allow 'free-will' and the 'option' of a doctor's visit.

Quote:

A few sentences from life

Nobody goes to that restaurant; it's too crowded.

Don't go near the water 'til you have learned how to swim....

(etc...)

Yeah, there is no rules preventing idiots from speaking.
I cut it short as the list would be endless. Same thing. Poor thought patterns and linguistic skills...

@nameless,

nameless;73580 wrote:

No one 'always' does anything, our 'states' are time and context dependent. The question is in error.
They are telling the truth if they believe that they are.

Only a fool would assume that both statements can be correct and true and thus present a paradox. Obviously, one or both are false. No paradox.
We handed the same cards in grade school to idiots. On one side was; "HOW DO YOU KEEP AN IDIOT BUSY? (over)". On the obverse side was; "HOW DO YOU KEEP AN IDIOT BUSY? (over)"
The biggest idiot was only amused for a moment. No attention span. I think that it fell, eventually, into the hands of some philosopher who, until this day, is pondering the 'paradox'...

If your 'destiny' is to heal, what makes you disregard the contextual 'destiny' of being in the doctor's office? What is the point of arbitrarily choosing a visit to the doc to be 'outside destiny'? Why is the doctor visit less 'is' then the healing? Perhaps your 'destiny' of healing can only be found in the context of a universe where you visit the doctor?
If 'everything' is destiny, there are no options, no choices, no 'free-will', it is illogical to suddenly allow 'free-will' and the 'option' of a doctor's visit.

Yeah, there is no rules preventing idiots from speaking.
I cut it short as the list would be endless. Same thing. Poor thought patterns and linguistic skills...

Why be so serious loosen up a bit and smile. Smile

What about Zeno's paradox ?

@Alan McDougall,

He who laughs last, laughs last....

@Alan McDougall,

There's your sign. Compliments of the Blue Collar Comedy Company.

Welcome to Mc Donalds Drive through...............Will that be to have here or take away.

I am a stagnet onlooker to two men who walk into a bar immediately after one another. The man to my right lashes out at the other to his right for forcing this upon him. The man to his left shrugs the offence and clearly having had his fill leaves the establishment after having been there all day until now. The man left approaches right up to the bar, orders a bourbon and calmly goes about his buisness.

@Alan McDougall,

Alan McDougall;73571 wrote:

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?

Most statements have a single truth-value, but 'liar' statements like this have multiple, sequential truth-values. If all Cretans (including himself) have been liars up to now, then his statement is true in the first place. But since "all Cretans are liars" is now no longer true, his statement is false in the second place. Now "all Cretans are liars" becomes true again, so his statement is true in the third place, and so on ad infinitum. Thus the sequence of truth-values goes TFTFTF.....

Once this idea of multiple truth-values is accepted, and seen to be the only logically possible explanation, the paradox disappears. All 'liar' paradoxes can be solved in a similar way. Sometimes a statement is false in the first place, so the sequence goes FTFTFT..... And sometimes a statement is meaningless (i.e. has no truth-value) in the first place, but then logically acquires one. The sequence will then go MTFTFTF..... or MFTFTFT.....

Quote:

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.

Since he is a Cretan himself, he is contradicting himself, so his statement as a whole is false. This one doesn't flip over to 'true'; it is simply false.

Quote:

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

Assume that he/she has always lied in the past. Now, if the speaker is including his/her present statement (i.e. "and I am lying now"), then it is meaningless in the first place, since we cannot establish an initial truth-value for "I am lying now". But since it has no initial truth-value, "I am lying now" is not false, i.e. it is not a lie. So it now becomes false. Then it becomes true, and so on. So the sequence is MFTFTFT.....

[QUOTE]Let's say there is a bullet which can shoot through any barrier. Let's also say there is an absolutely bullet-proof armor which no object can penetrate. What will happen if such a bullet hits such an armor?[/QUOTE]It is logically impossible for both statements to be true together. So you cannot hypothesize that they are.
[QUOTE]Can a man drown in the fountain of eternal life?[/QUOTE]That depends on what "the fountain of eternal life" means.
[QUOTE]Your mission is not to accept the mission. Do you accept?[/QUOTE]This has no meaning if no other mission is being referred to.
[QUOTE]A girl goes into the past and kills her Grandmother. Since her Grandmother is dead, the girl was never born. If she were never born, she never killed her grandmother.[/QUOTE]She can't go into the past and kill her grandmother. Again, the scenario is logically impossible.
[QUOTE]If the temperature this morning is 0 degrees and the Weather Channel says, "It will be twice as cold tomorrow", what will the temperature be?[/QUOTE]
[QUOTE]Answer truthfully (yes or no) to the following question: Will the next word you say be 'no'?[/QUOTE]I can't answer it truthfully.
[QUOTE]What happens if you are in a car going the speed of light and you turn the headlights on?[/QUOTE]No physical object can travel at the speed of light.

I understand that some of these questions are meant light-heartedly, but I just wanted to show that some of these paradoxes are not as insoluble as they may appear at first sight.

@ACB,

The guy in the boats a liar not the Cretans as not all the Cretans need not be liars.We can assume just one of them is a liar by this statement.

@Alan McDougall,

Alan McDougall;73571 wrote:

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

This only becomes an issue, if one takes the perspective that there are statements that are true and false. In this case, I would say that the person believes that he always lies. Whether or not he is lying in this case, is a matter for him to ponder and resolve if he wishes. Whether or not an outsider chooses to believe this statement is another question. I would take him at his word, and choose not to believe anything he says, whether or not he is lying on this particular occasion. :perplexed:

Quote:

Double Liar Paradox (Jourdain's paradox)

Same issue as above. It would only bother someone who believes in truths of statements. In this case, I would say that each side has its own belief of the truth of their statement, and I don't believe either.

Quote:

In a village, the barber shaves everyone who does not shave himself/herself, but no one else.
Who shaves the barber?

His wife.

[QUOTE]If destiny designed a master plan which defines everything that is to happen, isn't it useless, for example, to go to a doctor? If I am ill and it is my destiny to regain health, then I will regain health whether I visit a doctor or not. If it is my destiny to not regain my health, then seeing a doctor can't help me.

How could you question the presented opinion? [/QUOTE]

Well, you can believe it is your destiny to go to the doctor, and you just go. Or you can do otherwise, if you feel that you don't want to go. Either way, it can be determined or free will, depending upon your perspective. I do agree though, that life gets boring if you think everything has already been done for you. So, I take a different perspective, that we have free will to choose a different direction.

Quote:

Let's say there is a bullet which can shoot through any barrier. Let's also say there is an absolutely bullet-proof armor which no object can penetrate. What will happen if such a bullet hits such an armor?

Penetrate the armor but I am able to deflect the bullet using my evolved telepathic powers.

Quote:

Can a man drown in the fountain of eternal life?

No, because no water is collecting. It is constantly moving.

Quote:

Your mission is not to accept the mission. Do you accept?

No, I am in retirement.

Quote:

Oh!! I just remembered Zeno's famous paradox has been solved ?

For some, but not for me. :bigsmile:

Rich

Well

@Alan McDougall,

Alan McDougall;73584 wrote:

Why be so serious loosen up a bit and smile. What about Zeno's paradox ?

This is in the 'logic' section of a philosophy forum, not comedy. I responed, I thought, appropriately. Sorry if I misinterpreted your intent and wasted my time in responding thoughtfully.
Zeno was correct, motion is not possible in timespace.
The only 'paradox', is that 'reality' contradicts our naive interpretations of sensory data (our reality).

The fast car is a common device to explain relativity. No matter the speed of the car, the light from the headlights will still be perceived by someone in the car to be going at 'light speed'. If someone riding one of those photons (from the car lights) had a flashlight, the photons from that light would still be emmiting at 'light speed'.
I wonder how that light would appear from the Perspective of the car?
In actuality, nothing 'moves' (Zeno was correct). Not even photons.
But thats another story...

@nameless,

nameless;73746 wrote:

This is in the 'logic' section of a philosophy forum, not comedy. I responed, I thought, appropriately. Sorry if I misinterpreted your intent and wasted my time in responding thoughtfully.
Zeno was correct, motion is not possible in timespace.
The only 'paradox', is that 'reality' contradicts our naive interpretations of sensory data (our reality).

The fast car is a common device to explain relativity. No matter the speed of the car, the light from the headlights will still be perceived by someone in the car to be going at 'light speed'. If someone riding one of those photons (from the car lights) had a flashlight, the photons from that light would still be emmiting at 'light speed'.
I wonder how that light would appear from the Perspective of the car?
In actuality, nothing 'moves' (Zeno was correct). Not even photons.
But thats another story...

I am fascinated with movement and once wrote a paper on it. I look for it It went something like this, "Nothing ever really moved it only jumps through spacetime"

Wikipedea

Mathematicians today tend to regard the paradoxes as resolved, but some philosophers disagree. Bertrand Russell, who was both a mathematician and a philosopher, wrote Georg Cantor invented a theory of continuity and a theory of infinity which did away with all the old paradoxes upon which philosophers had battened. ... Philosophers met the situation by not reading the authors concerned.[16]

The paradoxes certainly pose no practical difficulties.

However, some philosophers insist that the deeper metaphysical questions, as raised by Zeno's paradoxes, are not addressed by the calculus. That is, while calculus tells us where and when Achilles will overtake the Tortoise, philosophers do not see how calculus takes anything away from Zeno's reasoning that there are problems in explaining how motion can happen at all.[17]

Philosophers also point out that Zeno's arguments are often misrepresented in the popular literature. That is, Zeno is often said to have argued that the sum of an infinite number of terms must be infinite itself, which calculus shows to be incorrect.

However, Zeno's problem wasn't with any kind of infinite sum, but rather with an infinite process: how can one ever get from A to B, if an infinite number of events can be identified that need to precede the arrival at B? Philosophers claim that calculus does not resolve that question, and hence a solution to Zeno's paradoxes must be found elsewhere.[18]

Physicists point out that in the race, after a few dozen steps, we will have to deal with dimensions where quantum mechanics can't be disregarded. According to the uncertainty principle those distances are so small that taking a measurement would be pointless, even from a theoretical point of view: uncertainty would be too prominent.[19]

Infinite processes remained theoretically troublesome in mathematics until the early 20th century. L. E. J. Brouwer, a Dutch mathematician and founder of the Intuitionist school, was the most prominent of those who rejected arguments, including proofs, involving infinities.[citation needed] In this he followed Leopold Kronecker, an earlier 19th century mathematician.[citation needed]

However, modern mathematics, with tools such as 's proof of the logical independence of the axiom of choice and the epsilon-delta version of Weierstrass and Cauchy (or the equivalent and equally rigorous differential/infinitesimal version by Abraham Robinson), argues rigorous formulation of logic and calculus has resolved theoretical problems involving infinite processes, including Zeno's.[20]

@Alan McDougall,

Alan McDougall;73832 wrote:

I am fascinated with movement and once wrote a paper on it. I look for it It went something like this, "Nothing ever really moved it only jumps through spacetime"

Once upon a time, there was this thing called an electron, an atom and a quantum leap.
An electron occupying a particular energy level was 'seen' to 'leap' to another energy level. That was a quantum leap. Something 'leapt' from 'here' to 'there'.

Now, with devices capable of allowing us to see deeply into this 'process', we have found that there is not anything 'leaping'! There is not anything between the energy levels, ever!
There is (momentarily) a Universe with an electron on one level. Another moment, there is no more electron on that level and there is an electron appeared on the next level. It didn't 'come from' anywhere. It is an inherent feature of the Universe as perceived at that moment.
There is nothing to indicate that they are one and the same electron!
Like a movie, if you flash the moments in a certain order (linear Perspective/memory), we see a 'cogent' meaningful 'movie'. Our 'lives'.
But not anything is 'moving', it is simply a matter of Perspective. The electron only appears to 'jump' and it was assumed, naively, that it is the same electron now on the next level.
This is what we 'naively' perceive as 'motion'.
Zeno was correct. The only 'paradox' is that his irrefutable logic confounded our naively accepted and believed 'sensory data'. Thats the way i see it/ thats the way that it appears to me now, must be 'right'! Every perception is a feature of the complete Universe, and in that context, is correct, but only a small part of the complete picture.
The Universe is not like a movie (it appears so, though, to some Perspectives), it is more like a tapestry of perceptions available to Conscious Perspectives.

@Alan McDougall,

Alan McDougall;73571 wrote:

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

Double Liar Paradox (Jourdain's paradox)

Barber Paradox (Russell's Paradox)

Lazy-bones Paradox

Think about these

Let's say there is a bullet which can shoot through any barrier. Let's also say there is an absolutely bullet-proof armor which no object can penetrate. What will happen if such a bullet hits such an armor?

Can a man drown in the fountain of eternal life?

Your mission is not to accept the mission. Do you accept?

A girl goes into the past and kills her Grandmother. Since her Grandmother is dead, the girl was never born. If she were never born, she never killed her grandmother.

If the temperature this morning is 0 degrees and the Weather Channel says, "It will be twice as cold tomorrow", what will the temperature be?

Answer truthfully (yes or no) to the following question: Will the next word you say be 'no'?

What happens if you are in a car going the speed of light and you turn the headlights on?

Oh!! I just remembered Zeno's famous paradox has been solved ?

If one says "I always lie", he is lying, because he cannot be saying the truth. Its true that he lies, but it is false that he always lies.

Double Liar: I dont think this one has a logical solution, except saying that neither sentence is worth of trust Smile

Barber: Nobody

Lazy-bones: Thinking about destiny is included into destiny, so if you go to the doctor anyway it means you are destined to live, if you dont it means you are destined to die: destiny doesnt offers many paths with the same end, it offers one path and one end. You cannot avoid the path no matter what you do.

*The sentences are contradictory
*Depends of how it works Smile

*No
*That cant happen Smile

*"0 degrees is a human measurement, absolute zero cannot be reached"
*Impossible Smile

*I will trust nameless here Smile

@manored,

manored;74367 wrote:

*I will trust nameless here

That's scary... :eek:

@nameless,

nameless;74476 wrote:

That's scary... :eek:

Why, exactly? Smile

@manored,

manored;74587 wrote:

Why, exactly?

I'm here to offer food for thought, a 'different' Perspective.
The last thing that I desire is the responsibility of someone accepting or adopting my words and thoughts without the application of their own critical thought. If, after his own critical examination, one can accept what I offer, then fine, whatever...
I don't need disciples, I'm here to demonstrate and encourage 'critical thought' among those that are capable.
I understand that my response is probably much more serious than your probably light-hearted statement. But, you went on further to ask this question, so...

@nameless,

nameless;74702 wrote:

I'm here to offer food for thought, a 'different' Perspective.
The last thing that I desire is the responsibility of someone accepting or adopting my words and thoughts without the application of their own critical thought. If, after his own critical examination, one can accept what I offer, then fine, whatever...
I don't need disciples, I'm here to demonstrate and encourage 'critical thought' among those that are capable.
I understand that my response is probably much more serious than your probably light-hearted statement. But, you went on further to ask this question, so...

Dont worry, I wont be following anyone like sapient pearwood (I hope you have played this game Smile

) I just dont know much about lightspeed movement and decided your view was probally correct.

@manored,

manored;74780 wrote:

Dont worry, I wont be following anyone like sapient pearwood (I hope you have played this game ) I just dont know much about lightspeed movement and decided your view was probally correct.

http://www.scientificpsychic.com/graphics/
Word Color Test
In this test DO NOT READ the words, say aloud the COLOR of each word.

YELLOW BLUE ORANGE
BLACK RED GREEN
PURPLE YELLOW RED
ORANGE GREEN BLACK
BLUE RED PURPLE
GREEN BLUE ORANGE

@Alan McDougall,

Alan McDougall;74793 wrote:

http://www.scientificpsychic.com/graphics/
Word Color Test
In this test DO NOT READ the words, say aloud the COLOR of each word.

YELLOW BLUE ORANGE
BLACK RED GREEN
PURPLE YELLOW RED
ORANGE GREEN BLACK
BLUE RED PURPLE
GREEN BLUE ORANGE

Interesting post Alan. Thanks.

Rich

@Alan McDougall,

Alan McDougall;74793 wrote:

http://www.scientificpsychic.com/graphics/
Word Color Test
In this test DO NOT READ the words, say aloud the COLOR of each word.

YELLOW BLUE ORANGE
BLACK RED GREEN
PURPLE YELLOW RED
ORANGE GREEN BLACK
BLUE RED PURPLE
GREEN BLUE ORANGE

English is not my first language so its easy for me... I already did this test in my home language and totally failed though Smile

It was probally easy because I was "thinking in portuguese", but sometimes I "think in english" too. I wonder how things will go if I try to make the portuguese test thinking in english Smile

@Alan McDougall,

It does tax you brain does it not, you musts look at the blue lettered word typed in as red and say red

My mind does not like being confused like that

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