Paradoxes

[Scatty]

A lizard stole a father's child, and told the father that if the father would guess what happens to the child, then he would give the child back. What happens if the father says "You won't give me my child back."?

 

 

As you can see, this is a discussion about paradoxes. Tell what paradoxes you know, some random facts about them, and discuss paradoxes as a whole.

[✗Panda✗]

Ive got one:

 

what has a face and a tail, but no legs?

[NeoDemonX]

Wow here comes the flame war also here http://www.youtube.com/user/onisionspeaks?blend=1&ob=4&rclk=cti this will answer whats going on here.

[CrabHelmet]

I've always been fond of Tarski's solution.

[Scatty]

I've always been fond of Tarski's solution.

 

Frankly, I prefer Prior's approach.

[CrabHelmet]

I've always been fond of Tarski's solution.

 

Frankly' date=' I prefer Prior's approach.

[/quote']

 

Prior's approach is clever, but not terribly elegant - he essentially dodges the issue by changing what the statement says and then judging the new statement. Far better to use Tarski's approach and impose a blanket prohibition on any recursive truth values by means of tiered languages. Plus, Prior's approach produces odd results in other situations; for example, applying his method to Gödel's "This sentence is not provable" concludes that the statement is false, when the statement in question is almost universally considered to be true but not provably so, which is the basis of Gödel's First Incompleteness Theorem.

[Larxene]

Ive got one:

 

what has a face and a tail' date=' but no legs?

[/quote']

 

A snake.

 

Seriously, were you even trying?

[CrabHelmet]

Ive got one:

 

what has a face and a tail' date=' but no legs?

[/quote']

 

A snake.

 

Seriously, were you even trying?

 

I suspect the answer Panda wanted was "a coin", or something "clever" like that.

[Scatty]

I'm sorry, but I must contradict you. Prior does not change what the statement says, he merely adds a meta-language fragment that does not change the meaning at all. As for Tarski, he dodges the problem even MORE.

 

Now, let's look at Godel's theorem using prior's approach, ok? The sentence becomes:

 

This sentence is not provable and this sentence is true,

 

which means the same as:

 

It is true that this sentence is not provable.

 

Now, you could only consider this sentence false only if you follow the Logic rule that "insufficient information means truth". Take that, and even using Prior's approach, Godel's phrase is still true.

 

But I think these kind of discussions are common, people that do Logics rarely agree. By the way, you know the barber paradox?

[✗Panda✗]

Ive got one:

 

what has a face and a tail' date=' but no legs?

[/quote']

 

A snake.

 

Seriously, were you even trying?

 

I suspect the answer Panda wanted was "a coin", or something "clever" like that.

 

No, snake was the rite answer. i guess a coin would work to though...

[CrabHelmet]

I'm sorry' date=' but I must contradict you. Prior does not change what the statement says, he merely adds a meta-language fragment that does not change the meaning at all.

[/quote']

 

The statement has been transformed from "not A" to "A and not A". Call it what you like - a meta-language fragment, a direct edit - the statement under Prior means something that it does not state.

 

As for Tarski' date=' he dodges the problem even MORE.

[/quote']

 

Nonsense. Tarski strikes at the core of the problem. The core of the problem is not "What do we do with this statement?" but "Doesn't having self-referential statements make problems possible?" and resolves the matter by eliminating the fundamental problem of permitting such statements. It is the equivalent of the "mu" answer: "unask the question".

 

Now' date=' let's look at Godel's theorem using prior's approach, ok? The sentence becomes:

 

This sentence is not provable and this sentence is true,

 

which means the same as:

 

It is true that this sentence is not provable.

 

Now, you could only consider this sentence false only if you follow the Logic rule that "insufficient information means truth". Take that, and even using Prior's approach, Godel's phrase is still true.

 

But I think these kind of discussions are common, people that do Logics rarely agree.

[/quote']

 

Looking back over Gödel's unprovable statement, it seems to me that applying Prior takes the statement from "true but not provably so" and makes it instead "both completely true and completely false". It is false because, taking A = "This statement is unprovable", the statement reads "A AND A is unprovable". If A is false, the "A" portion is false, so the entire AND function is false and thus A is false. If A is true, the "A" portion is true (since it's true) and the "A is unprovable" portion is true (since, as above, A is also fine if it is false), so the entire AND function is true and thus A is true. Therefore, the statement is both true and false, and is consistently so in either case.

 

In fact, Prior's method allows us to consider any statement to be false as we wish. Why is it false? Because the portion that asserts its own truth is false, because it's false. Argument by contradiction becomes impossible because everything works out perfectly if everything is false, and so even true things are just as false as they are true. Something there is very wrong.

 

By the way' date=' you know the barber paradox?

[/quote']

 

It is the set theory equivalent, with the most widely-accepted solution being analogous to Tarski's method by ruling that sets are not permitted to contain themselves as elements.

[Scatty]

Umph...ok, you win. God you're good...

[JG.]

You come to a crossroads. Both have a counter showing how many people have walked down it. Both say 17 ATM. You must take the path less travelled by.

 

Simple paradox. I used to trick my friends with that one. They know all my paradoxes now T.T

[Dark]

You come to a crossroads. Both have a counter showing how many people have walked down it. Both say 17 ATM. You must take the path less travelled by.

 

Simple paradox. I used to trick my friends with that one. They know all my paradoxes now T.T

 

Hey' date=' thanks for [s']stealing[/s] taking my paradox without even asking me. :/

[Scatty]

You come to a crossroads. Both have a counter showing how many people have walked down it. Both say 17 ATM. You must take the path less travelled by.

 

Simple paradox. I used to trick my friends with that one. They know all my paradoxes now T.T

 

Hey' date=' thanks for stealing my paradox without even asking me. :/

[/quote']

 

Of course he didn't ask you if he stole it, silly :D

 

Your phrase is like saying "God exists because God exists". (although,, on that matter, that might be the best thing one might think to prove it)

[Dark]

I fixed it. Are you happy now? I made "stealing" into "taking".

[Scatty]

Fine by me. Ever heard of "fake net anger"? Yup, I was faking it just as an excuse to add another quote about how proud am I of being an Atheist.

[Twig]

Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves, some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves.

 

Under this scenario, we can ask the following question: Does the barber shave himself?

 

Asking this, however, we discover that the situation presented is in fact impossible:

 

* If the barber does not shave himself, he must abide by the rule and shave himself.

* If he does shave himself, according to the rule he will not shave himself.

[Dark]

Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves' date=' some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves.

 

Under this scenario, we can ask the following question: Does the barber shave himself?

 

Asking this, however, we discover that the situation presented is in fact impossible:

 

* If the barber does not shave himself, he must abide by the rule and shave himself.

* If he does shave himself, according to the rule he will not shave himself.

[/quote']

 

Barber by day, normal man who shaves himself by night. :/

 

Pretty much, the paradox is broken if you consider the barber and the person as different people.

 

The person shaves himself, so the barber doesn't need to shave the person.

[Skuldur]

This sentence is a lie.

[CrabHelmet]

Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves' date=' some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves.

 

Under this scenario, we can ask the following question: Does the barber shave himself?

 

Asking this, however, we discover that the situation presented is in fact impossible:

 

* If the barber does not shave himself, he must abide by the rule and shave himself.

* If he does shave himself, according to the rule he will not shave himself.

[/quote']

 

This is the Barber Paradox mentioned above, and is an analogy for the set theory problem of the set defined as containing a set if and only if that set does not contain itself, which produces the same problem of whether that set itself contains itself. The standard solution to this problem is to declare that it is simply not permissible for sets to contain themselves as elements.

[Womi]

Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves' date=' some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves.

 

Under this scenario, we can ask the following question: Does the barber shave himself?

 

Asking this, however, we discover that the situation presented is in fact impossible:

 

* If the barber does not shave himself, he must abide by the rule and shave himself.

* If he does shave himself, according to the rule he will not shave himself.

[/quote']

 

This is the Barber Paradox mentioned above, and is an analogy for the set theory problem of the set defined as containing a set if and only if that set does not contain itself, which produces the same problem of whether that set itself contains itself. The standard solution to this problem is to declare that it is simply not permissible for sets to contain themselves as elements.

 

Or the barber grows a beard.

[Scatty]

Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves' date=' some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves.

 

Under this scenario, we can ask the following question: Does the barber shave himself?

 

Asking this, however, we discover that the situation presented is in fact impossible:

 

* If the barber does not shave himself, he must abide by the rule and shave himself.

* If he does shave himself, according to the rule he will not shave himself.

[/quote']

 

This is the Barber Paradox mentioned above, and is an analogy for the set theory problem of the set defined as containing a set if and only if that set does not contain itself, which produces the same problem of whether that set itself contains itself. The standard solution to this problem is to declare that it is simply not permissible for sets to contain themselves as elements.

 

Um...you do realise that ALL paradoxes are self-referential, don't you? From your logic it derives that no correct paradox exists.

[Bull3tM0nk3y]

The below statement is true.

The above statement is false.

 

/thread

[Raylen]

God. It's propositional logic... I though I'd never see this again.

 

It's all based on some tricks where you get p and NOT p to be true at the same time.