The Liar Paradox

[which doctor]

Okay, okay, I was joking about how it tears apart the universe, but I think that it proposes some interesting ideas.

For those of you unaware of the idea I will give you a typical example of it for you.

"A person who always lies, says that he always lies."
or
"I am lying right now"

The statements seem to present truths that contradict themselves. This isn't like some paradoxes that can be solved mathmatically or others that rely on the presence of a supernatural being.

The statement, "I am lying right now." cannot be true, yet it can't be false. It lies within that other "zone". It isn't really a middle ground, but more like an entirely different plane.

It's nuts, this is what I think about all day and night.

Any comments?
or
Am I full of bullshit?

[Rosa Lichtenstein]

Easy: it is neither true nor false, since it is not a proposition.

The dangling indexical "I'm" prevents it from being one.

[Monty Cantsin]

It’s a called a 'performative contradiction', like post-modern truth theoires...making a truth-claim while denying truth. it can't be resoved it's a contradiction.

[Rosa Lichtenstein]

Sorry, Monty; it cannot be a contradiction if no proposition is involved.

[Hegemonicretribution]

Originally posted by Rosa [email protected] 15 2006, 06:54 PM
Sorry, Monty; it cannot be a contradiction if no proposition is involved.
It could be seen as propositional; "I know that I am lying right now." It is still meaningless however. What is contained within the claim cannot be verified, it is much like, "All 2 sided triangles contain no right angles." The statement may be propositional, yet non-sensical. This is because there are no 2 sided triangles, and statements about them are false.

I know that the examlpe is different in nature to the one initially proposed, but it still serves its purpose. If a claim cannot be viewed as true or false, then it is not a claim.

Not all post modern theories reject truth, they claim that it is contextual. It is true that when dealing with language that many claims are only true or false within a certain context.

Even as a relative truth FoB's statement is non-sensical, and therefore different from PM theories.

[Rosa Lichtenstein]

Well, it contains an indexical term, and once the reference of that has been fixed, it does indeed become a proposition. But then the paradox disappears.

You example is not a very good one, however.

"I know I am lying" since it is reflexive, and so would involev problems as to whether you could know something paradoxical.

If it meany "I know I sometimes lie" or "I know I am lying now", there is no problem. But no paradox.

Classical forms of this paradox remove the individual who is supposed to be lying, so that such niggles vanish.

So, this might become : "The very next sentence is false"; "The last sentence is true".

Now that pair is very much more difficult to resolve, but I think it can be.

Check out:

L Goldstein, (2001), ‘Truth-Bearers And The Liar – A Reply To Alan Weir’, Analysis 61, 2, pp.115-26.

And Hartley Slater's work at:

http://www.philosophy.uwa.edu.au/staff/slater/publications

For example:

http://www.philosophy.uwa.edu.au/staff/sla...f_the_paradoxes (http://www.philosophy.uwa.edu.au/staff/slater/publications/the_uniform_solution_of_the_paradoxes)

http://www.iep.utm.edu/p/par-log.htm

[Gonzo Journalism]

Here's another kind of one that's always irritated me:

The statement below this is false.
The statement above this is true.

[Monty Cantsin]

Originally posted by Rosa [email protected] 15 2006, 10:51 AM
Easy: it is neither true nor false, since it is not a proposition.

The dangling indexical "I'm" prevents it from being one.
"I am lying right now" is not a truth claim?

[Rosa Lichtenstein]

It's not a proposition, since the temporal indexical is vague, and the personal identifying pronoun is unassigned.

I'd say nice try, but it isn't.

[patrickbeverley]

Originally posted by Rosa [email protected] 15 2006, 11:52 AM
Easy: it is neither true nor false, since it is not a proposition.

The dangling indexical "I'm" prevents it from being one.
:huh: ?

[Chrysalis]

I'd say, no, there isn't a contradiction, or it isn't a paradox, because the statement "I am lying right now" isn't a knowledge claim. Meaning, you cannot validly follow that claim with, "He is lying" ---you being the person listening to the person making the statement. Rosa is correct, btw.

[Rosa Lichtenstein]

Let's try again, without the typos!

Patrick, don't be puzzled, a dangling indexical is an expression like "I'm", which in normal conversational contexts has a clear reference. You can point (i.e., indicate, hence 'indexical') to whom your refer, or someone else can (even if no one actually choses to do so). In that case, something would be being proposed.

Short of that, in written contexts, for example, this is not so easy to establish.

Hence the 'dangling'; so this indicative sentence is not proposing anything until these ambiguities are cleared up.

The 'now' is similarly indexically-challenged, but far more difficult to resolve.

So, if this sentence lacks a truth-value, no paradox can follow. [The paradox allegedly depends on the sentence oscillating between truth and falsehood all the time -- which it cannot now do. The problem is that when we see such sentences we bend over backwards to accommodate them (and lock into the usual steps we would take to interpret them), when we should reject them as bogus.]

Now, if someone actually says, "I'm lying right now" and it is clear from what they say who is meant and when, then we would have a different problem (which it is also possible to defuse, but in other ways). But Monty failed to do this, he slipped up by typing his sentence.

You can find more details on the in Sybil Wolfram's book 'Philosophical Logic' (Oxford, 1989).

[apathy maybe]

Hey Rosa, use the edit button. Then you don't double post.

And apart from that I am not going to add much to the conversation. Apart from, I love this forum. I been around so long that I see when topics come up again :).

http://www.revolutionaryleft.com/index.php...hl=liar+paradox (http://www.revolutionaryleft.com/index.php?act=ST&f=6&t=6215&hl=liar+paradox)
http://www.revolutionaryleft.com/index.php...c=20050&hl=liar (http://www.revolutionaryleft.com/index.php?showtopic=20050&hl=liar)

I am the friend referenced (I think) in the first post of the first topic.

[Rosa Lichtenstein]

Apathy, thanks for that tip, I did not spot the edit button.

Will do so from now on!

[Zingu]

This has been solved by a logician, I'll give the answer once I run off and find the book tommorow morning.

[Commie Rat]

tears my brain apart, which is actually the universe

[Commie Rat]

damn gifs that dont work.*shakes fist*

[Iroquois Xavier]

You're all liars! :D

[Rosa Lichtenstein]

Not me, I just fib.

[Iroquois Xavier]

whereas i bend the truth! :P

[Rosa Lichtenstein]

If I said I believed you, would you believe me?

[Angry Young Man]

Originally posted by Fist of [email protected] 15 2006, 01:41 AM

"I am lying right now"


This doesn't really hold any water unless it is put into context. You have not made any comment that could be perceived as a lie or truth.
The real paradox would be, for example, "I could kick your arse. I have a massive penis. I am lying right now". This is paradoxical because there are two statements that could either be true or false.
Nonetheless, size is a matter of each individual, much like sensibility. For example, the Londoner, on a dull day, may say "Gaw Blimey, Gavna, it's bladdy freezin'", but a neighbour who was raised in Leeds would be more used to a colder climate. Thusly, he would not feel cold and would reply by going "It's not cold, you big Jesse".
Sorry to have taken us a bit far afield.

[Rosa Lichtenstein]

Mick, the dangling temporal indexical (i.e., "now"), among other things, prevents this from being a paradox (except in a parlour game sort of way).

As I pointed out above, since you have typed these sentences, the indexicals lack a reference, and so they are truth-value-less. They are not propositions -- they are proposing nothing.

Now, if these words were spoken, reference could be assigned to these indexicals, but we would not be forced to assign ones that created a paradox -- the choice is ours.

So, one way to avoid paradox here is to assign references that do not collapse them into paradox (unless we merely want to amuse ourselves -- and even then, there are other ways to avoid these problems).

However, I wasn't too sure what point you were making about the guy from Leeds (my home town, by the way!).

[ComradeRed]

Wait what about "A liar never tells the truth and says 'This statement is false'."

Would that be a contradiction? :huh:

[Rosa Lichtenstein]

Again, since you typd this, it contains dangling indexicals.

Nice try.

And...liars sometimes tell the truth.

[Hegemonicretribution]

Originally posted by Rosa [email protected] 12 2006, 09:41 PM
And...liars sometimes tell the truth.
Exactly, it could be that the person claiming that this particular lier always lies, was in fact lying themselves.

I am coming round to the view that paradoxes, whilst they exist (inevitably temporarily) serve to show shortfalls in our current understanding. It is once these are resolved, or shown to not actually be a meaningful statement that we further our understanding.

You are far more familiar with set theory than I am comradered, have you not come accross supposed paradoxes there? I think there were a few in the link that Rosa posted towards me (I think), and explanations.

[ComradeRed]

You are far more familiar with set theory than I am comradered, have you not come accross supposed paradoxes there? I think there were a few in the link that Rosa posted towards me (I think), and explanations. It depends what you use the set theory for; I've seen it used mostly for physics, rarely for philosophy (except, of course, Russell's Principles of Mathematics).

I really haven't looked at it too much from the philosophical perspective ;)

[Rosa Lichtenstein]

Well, I was taking this as a statement in ordinary language; if the paradox occurs in set theory, that is too bad -- but not philsophically interesting.

It's a sort of mathematical parlour game, in that case. :)

[Iroquois Xavier]

I was lying when i said that i lie... :blink:

[Hegemonicretribution]

Originally posted by Iroquois [email protected] 4 2006, 01:54 PM
I was lying when i said that i lie... :blink:
I assume you are trying a variation on it?

Well the statement refers to a lie previously told, and by definition this lie must have been untrue. So it follows that you must have been lying.

I don't get it? What you said wasn't a paradox, it made perfect sense...well it does refer to a lie that I have no way of knowing about, or may not have existed (in which case it would be a meaningless statement).

[Rosa Lichtenstein]

IX:


I was lying when i said that i lie.

Since the personal pronoun in this context lacks a referent this sentence lacks a truth-value, and hence can neither be true nor false, and so cannot feature in a lie.

[Recall, that words cannot refer, only human beings can, even if they have to use words to do it.]

[TC]

Originally posted by Fist of [email protected] 15 2006, 01:59 AM

For those of you unaware of the idea I will give you a typical example of it for you.

"A person who always lies, says that he always lies."
or
"I am lying right now"

The statements seem to present truths that contradict themselves. This isn't like some paradoxes that can be solved mathmatically or others that rely on the presence of a supernatural being.

The statement, "I am lying right now." cannot be true, yet it can't be false. It lies within that other "zone". It isn't really a middle ground, but more like an entirely different plane.

It's nuts, this is what I think about all day and night.

Any comments?
or
Am I full of bullshit?
This isn't a true paradox though its simply an absurd statement.

A real paradox is two or several deductively sound (a logically valid argument with true premises) but with mutually exclusive conclusions.

The liar paradox only appeared to be a paradox when it was proposed thousands of years ago i don't think its really a contemporary philosophical problem.

[Body Count]

The problem that I have with the arguments in this thread (And with philosophy in general really) is that often, linguinstic arguments are translated to logical/truthfulness problems.

In the real world, one is either lying, or she isn't, these little riddles are just really problems of our ways to communicate imho.

[Rosa Lichtenstein]

Body count, I think your distinction between real life and language is a little suspect: you can't lie if you do not have a language.

Tragic, well it's not an important 'problem' (in fact it is not even a problem, but a bogus use of language), but it is still alive and kicking. Countless books and articles in the philosophical literature are published every year on this and other 'paradoxes'.

http://en.wikipedia.org/wiki/Liar_paradox

http://www.iep.utm.edu/p/par-liar.htm

http://ucsu.colorado.edu/~brindell/soc-epi.../Truth/liar.htm (http://ucsu.colorado.edu/~brindell/soc-epistemology/Bibliographies/Truth/liar.htm)

http://www.hku.hk/philodep/dept/lg/artipara.html

And I reckon this book will be worth reading when it comes out:

http://www.hku.hk/philodep/dept/lg/wip.html

[TC]

Yah but they're all published with the presumption that they're false paradoxes...its the linguistic structure thats being evaluated not a the logical structure.

additionally...a lot of philosophical articles are quite lame...:-p

[Vageli]

How about this, "I. Vageli, claim that this statement I typed that you are reading right this moment is false". Does that negate the whole thing that you were talking about Rosa?

[Rosa Lichtenstein]

Well, now you have an unassigned demonstrative: 'this statement'.


"I. Vageli, claim that this statement I typed that you are reading right this moment is false". Does that negate the whole thing that you were talking about Rosa?

Which one am I now reading?

You can try all you like; whatever you do, I will be able to point to an unresolved ambiguity in what you post.

[Rosa Lichtenstein]

Tragic, I beg to differ; many of the ones I linked to actually argue that the paradoxes are neither true nor false, since they all contain unresolved ambiguities (of alleged self-reference), as I point out to Vageli.

[Iroquois Xavier]

Originally posted by Hegemonicretribution+May 4 2006, 05:46 PM--> (Hegemonicretribution @ May 4 2006, 05:46 PM)
Iroquois [email protected] 4 2006, 01:54 PM
I was lying when i said that i lie... :blink:
I assume you are trying a variation on it?

Well the statement refers to a lie previously told, and by definition this lie must have been untrue. So it follows that you must have been lying.

I don't get it? What you said wasn't a paradox, it made perfect sense...well it does refer to a lie that I have no way of knowing about, or may not have existed (in which case it would be a meaningless statement). [/b]
You won't get it because you are not supposed to. It's supposed to make you try and figure out what the statement means but you cannot, nobody can. either way i am lying.

[Hegemonicretribution]

Originally posted by Iroquois [email protected] 5 2006, 01:02 PM
You won't get it because you are not supposed to. It's supposed to make you try and figure out what the statement means but you cannot, nobody can. either way i am lying.
A small child could get it, because what you said made sense. For sure you were lying when you told a lie, if you weren'y it would not be a lie.

For that to even approach a paradox you would have to make reference to the statement that you make a truth claim about in a way that makes it appear as a lie.

Again, think it through, you can't not be lying when you tell a lie and therefore what you said made sense. Perhaps it should have read, "I am lying as I say this lie" but that doesn't really make reference to anything, and exists only as an absurd statement.

I know I am not supposed to be able to get it, but I am claiming that I do. If what you posted was necessarily a "paradox" I would still have a go at it, but what you posted were different from all other variations because it made perfect sense. The statement was akin to, "This blue pen is blue" or "I was running when I ran that race."

Vageli; the conclusion could well be that you are lying, but only about the fact that you are lying. The claim that the statement is false could itself be a lie, and thus solve the "paradox."

[Iroquois Xavier]

Originally posted by Hegemonicretribution+May 5 2006, 01:27 PM--> (Hegemonicretribution @ May 5 2006, 01:27 PM)
Iroquois [email protected] 5 2006, 01:02 PM
You won't get it because you are not supposed to. It's supposed to make you try and figure out what the statement means but you cannot, nobody can. either way i am lying.
A small child could get it, because what you said made sense. For sure you were lying when you told a lie, if you weren'y it would not be a lie.

For that to even approach a paradox you would have to make reference to the statement that you make a truth claim about in a way that makes it appear as a lie.

Again, think it through, you can't not be lying when you tell a lie and therefore what you said made sense. Perhaps it should have read, "I am lying as I say this lie" but that doesn't really make reference to anything, and exists only as an absurd statement.

I know I am not supposed to be able to get it, but I am claiming that I do. If what you posted was necessarily a "paradox" I would still have a go at it, but what you posted were different from all other variations because it made perfect sense. The statement was akin to, "This blue pen is blue" or "I was running when I ran that race."

Vageli; the conclusion could well be that you are lying, but only about the fact that you are lying. The claim that the statement is false could itself be a lie, and thus solve the "paradox." [/b]
Believe me i have tryed it on a child...they stood there and said "fuck off weirdo!" :lol:

You claim to understand it but you are lying, you think you do but you know you dont. "I am lying when i say this lie" is just the same as the last one but it is in the present tense where the last one was in the past tense.

I didn't post it to be a paradox, i posted it to fuck with your heads. :P

[Hegemonicretribution]

Originally posted by Iroquois [email protected] 5 2006, 01:34 PM
You claim to understand it but you are lying, you think you do but you know you dont. "I am lying when i say this lie" is just the same as the last one but it is in the present tense where the last one was in the past tense.

I didn't post it to be a paradox, i posted it to fuck with your heads. :P
No, you assume I don't. If that is your view, and despite my best efforts and explanations you refuse to see this as you have taken the incomprehensibility of your statement as an a-priori truth, then I can really add little more to the debate than I could to one with the most dogmatic religious believer.

In the past tense the statement is entirely different. Again, I was lying when I lied, I was running when I ran. They are pointless statements, and unnecessary, but they make sense.

In the present tense it is more confusing, but when you break it down in terms of what is being claimed, and what it actually means, you can understand it as much as it can be understood.

The reason it is more confusing is because it references itself, whereas the previous statemt referenced a seperate lie, and was therefore easily verifiable.

What is the lie that you claim to be telling? If you don't know then you can't be lying and the statement makes no sense. If the claim is that you are telling a lie, and that is wha why you are lying then it is self-referential, and pointless because it the statemnt "I am lying" would suffice. If you are claiming that you are not telling the truth as you make this statemnt of untruth, then you have still to establish what the untruth actually is.

I could go on, but my main point is merely showing the absurdity of the statement. I agree that it is fun, and could be difficult to work out (the secret is you can't because it doesn't make sense) and is an excellent trick to keep a child entertained with perhaps, but as you said is not a paradox and doesn't pose a real problem for us.

There are lots of tricks you can create like this in language, doing it with numbers is more entertaining though ;)

[mikelepore]

When I was in graduate school, we were asked the following as a bonus question on the final exam. (I don't know why, since it was a class in semiconductor fabrication processes.) The instructor later said that I was the only student who gave a correct answer.

You come to a fork in the road. There are two people there. You know that one of them will lie, and the other will tell the truth, but you don't know which is which. You are allowed to ask only one question, and both people will answer it. What question can you ask to determine which road goes to the town?

[Hegemonicretribution]

Originally posted by [email protected] 11 2006, 08:09 PM
When I was in graduate school, we were asked the following as a bonus question on the final exam. (I don't know why, since it was a class in semiconductor fabrication processes.) The instructor later said that I was the only student who gave a correct answer.

You come to a fork in the road. There are two people there. You know that one of them will lie, and the other will tell the truth, but you don't know which is which. You are allowed to ask only one question, and both people will answer it. What question can you ask to determine which road goes to the town?
I feel a little guilty for answering this so soon but here goes ;) "If I were to ask the other person the question what would they say?"

If you get the lier then they will lie about what the other says and you assume the opposite. If you get the truthful one they will tell you the truth (which will be a lie as they are answering for the other) and again you do the opposite.

Really you need to specify what you want to ascertain from the question, but whatever it is (assuming there are only two answers) a variation on the question I posed above is correct.

[Rosa Lichtenstein]

Mickel:


You come to a fork in the road. There are two people there. You know that one of them will lie, and the other will tell the truth, but you don't know which is which. You are allowed to ask only one question, and both people will answer it. What question can you ask to determine which road goes to the town?

Ask: If I were to ask you which way to go, what would you say?

The truth-teller tells you truthfully, the liar lies about what he/she would tell you if you asked, and ends up telling you the truth.

Well, that is the standard response, but if a liar wishes to deceive you he/she will say "Go on ask me and I will tell you".

[mikelepore]

I never thought of Hegemonicretribution's answer before. The solution I came up with was the one that Rosa said.

[Hegemonicretribution]

Originally posted by [email protected] 11 2006, 10:06 PM
I never thought of Hegemonicretribution's answer before. The solution I came up with was the one that Rosa said.
To be fair Rosa's fits better here...mine is a general version of a specific answer to a variation on this.

The one I am familiar with is when I persona arrives in heaven, but it is left up to them to choose a door to either heaven or hell. There are two angels (one that always lies and one that always tells the truth) guarding the doors, and the person standing there is allowed one question before chosing. The question would be "If I were to ask the other angel which door were to lead me to heaven which would they say?" Then you choose the other.

I could have phrased it better if I knew the question was relating to which fork in the road to take...essentially very similar.

[mikelepore]

Rosa said, 'but if a liar wishes to deceive you he/she will say "Go on ask me and I will tell you".'

Perhaps the answer has to be constrained to a binary range: either "take the left road" or "take the right road."

*

My dog apparently knows trigonometry. I asked her, "If the sine of pi over six radians equals 0.5, then bark." Then she barked.

[Hegemonicretribution]

Originally posted by [email protected] 11 2006, 10:18 PM
Perhaps the answer has to be constrained to a binary range: either "take the left road" or "take the right road."
That is what I thought was being implied...


My dog apparently knows trigonometry. I asked her, "If the sine of pi over six radians equals 0.5, then bark." Then she barked.
:lol:

[Rosa Lichtenstein]

Mikel, well if the liar really wants to screw with you, he/she will answer falsely, so that you think it is true (on the basis of taking Heg or my advice), and thus take the wrong route.

You see, a liar only has to be a deceiver, and he/she can do that by falsely getting you to think that they are telling the truth.

Knowing of the smart answer logicians have come up with to this problem, and knowing you expect the truth from the liar, he/she just tells you the wrong route. You think it is the right one, and you are deceived.

Now, there is no way around that smart liar.

[peaccenicked]

Paradox really lies mostly in maths, if you think of computer bugs, these are a result of command conflicts at the basic level.
Look at Eschers drawings for visual paradox resulting from representing 3D in 2D.
It is pointless being pedantic about exact paradoxes, it will only end up in paradoxes about technical terms.
Another display of paradox is in godels theorem which says in any large scale number theory, not all of the propositions can be proven.

Paradox, can be real or apparrent.
Dialectics is concerned with the dynamic paradox ; the negation of the negation.ie movement. Formal logic is inadequate to the process of becoming, being and decaying.
The goal of dialectics is the clarification and resolution of lifes tensions by studying a process in development in the real world from as many sides, shades or angles as possible.
To day it is still the best way to size up any situation as scientifically as possible. It is really merely leaving as little out as possible from any analysis and it merely states universal laws of development, are good framework or prism to see the world through, and they are not meant to be rigid at all.

[Hegemonicretribution]

Lets not make this into another thread about dialectics....there are plenty around and active, but it is good to see you back peaccenicked. :)