Original Solution to the “Liars Paradox”

[TakenItSeriously]

If we can assume a person is lying when he says: “I am lying”.

 

Then it seems as if standard logic chains must yield an inconsistent result where his lie seems to also be provable to being the truth.

e.g.: If he is lying, then by saying he is lying means he must be telling the truth.

 

There is nothing wrong with the applied logic or even the postulate that assumes that the man is lying. nor is there any paradox. The problem is found in the statement of the problem itself which is not given in a valid form.

 

The statement “I am lying” is a meaningless statement as its used which implies a reference to something that is not there. When making an observation, simply using a valid sentence in English does not necisarily mean that the statement is valid. In this case the observer is making an empty statement unless he includes what he is lying about such as: “I am lying when I say you don’t look fat in those jeans.”

 

The error made in this problem is an error of misdirection where we are used to looking for an error in the premise, postulate, or in the applied logic. We may overlook the rest of the problem that we don’t often find error with and so we dont think to look there. 

 

Edited December 6, 2017 by TakenItSeriously

[studiot]

9 minutes ago, TakenItSeriously said:

So what could you conclude about the above?

 

That you have had too much Christmas spirit already?

 

 

Seriously I was unable to determine your beef from that ramblng post.

 

As regards paradoxes, I have not encountered all of them.

The ones I have encountered are usually formed by combining two (or more) statements inappropriately.

Resolution is achiveved by untangling them and taking one statemen at a time.

[TakenItSeriously]

26 minutes ago, studiot said:

 

That you have had too much Christmas spirit already?

 

 

Seriously I was unable to determine your beef from that ramblng post.

 

As regards paradoxes, I have not encountered all of them.

The ones I have encountered are usually formed by combining two (or more) statements inappropriately.

Resolution is achiveved by untangling them and taking one statemen at a time.

I’m not sure what your getting at.

Its a solution to a famous paradox with a few examples of problems that are similarly overlooked.

 

Ok, I removed the example that might look like a rant, though it was intended to be a common example of the same type of oversite.

Edited December 6, 2017 by TakenItSeriously

[John Cuthber]

13 minutes ago, TakenItSeriously said:

Its a solution to a famous paradox

No it isn't, because re.

47 minutes ago, TakenItSeriously said:

If we can assume a person is lying when he says: “I am lying”.

We can't.

 

And all you seem to have achieved is show that 

49 minutes ago, TakenItSeriously said:

“I am lying when I say you don’t look fat in those jeans.”

 

is not a paradox.

But nobody thought it was.

[pzkpfw]

I think the OP misses the point.

In day to day English I might say "I am seven feet tall, well, actually, I am lying".

Clearly the bit I'm saying is a lie, is the "7 feet tall", bit, and saying that I'm lying is not itself intended to be a lie.

 

But as a logic exercise, thinking about what "I am lying" - by itself, and referring to itself - really means, is a very different thing.

[TakenItSeriously]

8 minutes ago, pzkpfw said:

I think the OP misses the point

But as a logic exercise, thinking about what "I am lying" - by itself, and referring to itself - really means, is a very different thing.

Yes, that was my point.

The statement  “I am lying” must refer to what they’re lying about to have meaning.. Otherwise it’s an invalid statement as in its not a meaningful statement.

It may look kind of like a natural thing to say because such statements typically refer to something in the previous sentence but there’s nothing in the previous sentance to refer to.

Maybe you can think of it like using reference frames

If you dont provide an observer in their own reference frame and what their observing in the context of it’s reference frame. then the problem doesnt make sense.

“I am lying” is implying a referal to something that isnt there. so it doesnt make sense.

Edited December 6, 2017 by TakenItSeriously

[John Cuthber]

It's very difficult to generate a paradox without having something self-referential.

If you talk about the statement "you don’t look fat in those jeans.” then it doesn't refer to itself and it's not paradoxical

The issue of "I am lying" is that it juxtaposes language and metalanguage.

 

[studiot]

2 hours ago, TakenItSeriously said:

“I am lying” must refer to what they’re lying about to have meaning.

+1 for understanding the point.

 

and "I am lying" doesn't refer to anything.

The conventional way to phrase this is to first classify everyone as either liars or truthers in everything they say.

Then to offer the statement I am a liar.

 

[TakenItSeriously]

1 hour ago, John Cuthber said:

It's very difficult to generate a paradox without having something self-referential.

If you talk about the statement "you don’t look fat in those jeans.” then it doesn't refer to itself and it's not paradoxical

The issue of "I am lying" is that it juxtaposes language and metalanguage.

 

In math we try to prove a solution to a problem

In logic we see if it can be disproven through invalidity.

Once a statement is proven as being invalid its done. There’s no need to bring metalanguage into it.

3 minutes ago, studiot said:

+1 for understanding the point.

 

and "I am lying" doesn't refer to anything.

The conventional way to phrase this is to first classify everyone as either liars or truthers in everything they say.

Then to offer the statement I am a liar.

 

I think you may be thinking about a related problem with two characters: one that lies and one that tells the truth.

Edited December 6, 2017 by TakenItSeriously

[Strange]

4 hours ago, TakenItSeriously said:

The statement “I am lying” is a meaningless statement as its used which implies a reference to something that is not there. When making an observation, simply using a valid sentence in English does not necisarily mean that the statement is valid. In this case the observer is making an empty statement unless he includes what he is lying about such as: “I am lying when I say you don’t look fat in those jeans.”

The implied topic of the statement is the utterance itself.

It is, effectively, short for "I am lying when I speak this sentence."

Or, more concisely, "This statement is not true."

By your logic, the sentence, "I am happy" would be meaningless as well, because it doesn't state what it is referring to. But that is obviously an incorrect conclusion. 

[TakenItSeriously]

19 minutes ago, Strange said:

The implied topic of the statement is the utterance itself.

It is, effectively, short for "I am lying when I speak this sentence."

Or, more concisely, "This statement is not true."

By your logic, the sentence, "I am happy" would be meaningless as well, because it doesn't state what it is referring to. But that is obviously an incorrect conclusion. 

ok, I guess you see meaning where I don’t. if someone told me “I am lying” Id ask him ”about what?”

but if someone said “I’m happy”, Id say “good for you” 

To me one makes sense the other doesn’t.but thats not the point

Either could have validity  as a statement of logic or not depending on the context, but not making sense is a valid point of invalidity.

Otherwise it’s like trying to make sense out of nothing.

 

Edited December 7, 2017 by TakenItSeriously

[Strange]

1 hour ago, TakenItSeriously said:

ok, I guess you see meaning where I don’t. if someone told me “I am lying” Id ask him ”about what?”

OK. So that's a problem with your understanding.

Instead, focus on the simpler example: "this statement is false"

 

Edited December 7, 2017 by Strange

[TakenItSeriously]

5 hours ago, Strange said:

OK. So that's a problem with your understanding.

Instead, focus on the simpler example: "this statement is false"

 

It still makes no sense to me, sorry. 

It looks like a self conflicting statement

I guess Id describe it like a statement that 2+2=5 which I understand, isn’t the best analogy, maybe divide by zero is closer.

Better still, it’s an infinite recursive loop maybe?

Edited December 7, 2017 by TakenItSeriously

[TakenItSeriously]

.I still cant see anywhere stating if those problems have discovered solutions or not. Other than the millet problem which Aristotle  had successfully refuted back in the same era it was proposed. Which suggests that they should have all been solved.by now. 

Does anyone know for certain the state of those problems?

I used to think that there wer no more unsolved paradoxes until I discovered the balance paradox still had no solution so I dont make that assumption anymore, and I’m not going to keep posting known solutions.

That would be like posting solutions that prove the earth is round.or something.

Edited December 7, 2017 by TakenItSeriously

[studiot]

I have to observe that TIS is correct here.

I meant to add exactly this to my post but it somehow got lost.

8 hours ago, TakenItSeriously said:

ok, I guess you see meaning where I don’t. if someone told me “I am lying” Id ask him ”about what?”

 

The verb "to be happy" is a reflexive verb, so the subject and object are the same.

So both are clear if someone says "I am happy".

On the other hand, the verb to lie is transitive as it requires an object (the subject of the lie).

So the question "about what ?" is valid, unless the subject has already been stated, as I said above.

The paradox is a somewhat artificial construct in that people don't normally lie about everything.

[Strange]

40 minutes ago, studiot said:

On the other hand, the verb to lie is transitive as it requires an object (the subject of the lie).

No it isn't.

Do you think this is ungrammatical: "What did Trump do today?" "He lied."

But don't take my word for it:https://www.merriam-webster.com/dictionary/lie

Quote

3lie

verb   \  ˈlī \

Definition of lie

lied; lying play  \ˈlī-iŋ\

intransitive verb

1: to make an untrue statement with intent to deceive  

(They do also list a transitive sense, but it is not relevant to this discussion.)

 

Happy might not have been the best example (it is not a reflexive verb, it is an adjective). Maybe "I am swimming" or "I am talking" would be better.

 

Edited December 7, 2017 by Strange

[studiot]

54 minutes ago, Strange said:

Happy might not have been the best example (it is not a reflexive verb, it is an adjective)

Where exactly did I suggest it was?

[Strange]

39 minutes ago, studiot said:

Where exactly did I suggest it was?

Here:

2 hours ago, studiot said:

The verb "to be happy" is a reflexive verb, so the subject and object are the same.

The verb "be" in that sentence is a copula.

[studiot]

 

1 hour ago, Strange said:

Here:

The verb "be" in that sentence is a copula.

 

Thank you Strange, I have learned a new word today. +1

 

[TakenItSeriously]

There is some profound misunderstanding about the significance of the roll that validity or more importantly invalidity plays in logic.

Aside from the laws of logic or the roles that axioms play, You can think of validity/invalidity as the only rule in logic.

The consequence of it being the only rule and the fact that logic basically represents all thinking outside of math, then its fair to say that the scope of invalidity covers every type of error mankind has ever made since the dawn of consciousness. so it needs to be taken a little more seriously than just the proper usage of English.

If you think rigor is important in math, then think of invalidity at least with the same importance as the rigor you apply to math. because the lack of respect for invalidity is literally just plain ignorance. and every thing that comes from ignorance.

I’ll try to write something up on logic later but for now there is an easy trick that we can use when dealing with paradoxical problems.

The source of every paradoxical problem is an intuitive error. Thats what makes them seem so paradoxical. Its the conflict between logic and intuitiive error. So you can start by mulling over how that applies to these problems

Edited December 7, 2017 by TakenItSeriously

[Strange]

1 hour ago, TakenItSeriously said:

There is some profound misunderstanding about the significance of the roll that validity or more importantly invalidity plays in logic.

Can I just check exactly what you mean by "validity" here. Do you mean the technical sense (that a logical argument is valid if the consequence inevitably follows from the premises, whether they are true or not)?

1 hour ago, TakenItSeriously said:

The source of every paradoxical problem is an intuitive error.

Not necessarily true. There are some cases where that is true, such as the so-called "paradoxes" in relativity theory, which aren't paradoxes, just counter intuitive.

But there are many paradoxes that can be expressed in formal logic (including the liar paradox) and therefore have nothing to do with intuition.

Edited December 8, 2017 by Strange