Talk:Liar paradox/Archive 2

A way to solve the paradox?

I had a thought witle reading the article that you could use the following argument to solve the paradox.

Short belives that every thing Squat says is true

Squat tells Short that whatever he says is false.

Short believes that Squat is right, so what Squat says is true

If Squat is wrong, then Squat is right

Short only believes that Squat is always right. Squat is really sometimes right.

The reader of the liar pardox belives that the sentance is true. The sentance is really sometimes true.

              What do other Wikipedians think?   Alex Wahl

As a software developer, this common expression of the liar's paradox given as "This statement is false" does not instill any sort of logical dilemma to me. Quite simply it is a very subjective paradox depending on how one interprets the semantics of the language-- in this case, English. If one were to substitute the word "is" with the words "evaluates to" then the semantic dilemma of the word is, in my opinion is lifted.

This statement is false.

is semantically equivalent to:

This statement evaluates to false.

is semantically equivalent to:

class foo {
    boolean statement = false;

    public void print() {
        System.out.println("This statement is " + this.statement); // this.statement is false
    }
}

Since Java 1.4 we can even do this:

    assert this.statement == false; // if this.statement is false, then the assertion is true!

So, like I said: semantics. Clinton was right: "It depends on what the meaning of the word "is" is" --Dpcavanaugh (talk) 16:10, 23 March 2010 (UTC)

• Um, thanks for your input, but this has to be considered WP:OR. It is also not appropriate here per WP:TPG. Please note that it is not our job to solve problems in here (see also WP:GREATWRONGS), we merely report what the literature has to say on the topic. If you have questions, please feel free to ask them. Happy editing, Paradoctor (talk) 19:22, 23 March 2010 (UTC)

Chris Langan

The section on Chris Langan should probably be removed. He's completely unknown in the literature on the liar, and the quote doesn't even indicate a solution to the liar (it's a closer to an informal explanation of Gödel's first incompleteness theorem.) --NoizHed (talk) 15:55, 20 April 2010 (UTC)

I found one reference to Langan's paper by one Anthony Judge. I'll remove the section per WP:DUE. Paradoctor (talk) 16:39, 20 April 2010 (UTC)

Irrational Statements

What appears to be the problem with trying to assign truth values to such self negating propositions as, “This statement is not true.”, is that such propositions violate the Law of Contradiction, and so are irrational. What makes them irrational is the fact that it is implicit in every declarative statement that the statement itself is ‘true’, and so by explicitly declaring itself to be not true, it violates the First Principle of Reason; the Law of Contradiction being a correlate of the Law of Identity. RGGehue (talk) 13:30, 31 October 2010 (UTC)

Calvinball is not a paradox

I have removed the following: In Calvin and Hobbes, one rule of Calvinball is that you can't play it the same way twice. However, by following that rule, you are using that same rule twice.

Since it is not a liar's paradox, because the rule refers to the game as a whole, not to just a single rule.

what if instead of just limiting this to truth and false you put it in terms of correct incorrect then it would be incorrect and saying that the person is mistaken and not lying or telling the truth — Preceding unsigned comment added by Timmyone (talk • contribs) 20:32, 2 March 2012 (UTC)

Arthur Prior

The article says:

"But the claim that every statement is really a conjunction in which the first conjunct says this statement is true seems to run afoul of standard rules of propositional logic, especially the rule, sometimes called Conjunction Elimination, that from a conjunction any of the conjuncts can be derived. Thus, from This statement is true and this statement is false it follows that this statement is false and so we have, once again, a paradoxical (and non-conjunctive) statement. It seems then that Prior's attempt at resolution requires either a whole new propositional logic or else the postulation that the "and" in This statement is true and this statement is false is a special type of conjunctive for which Conjunction Elimination does not apply. But then we need, at least, an expansion of standard propositional logic to account for this new kind of "and".[4]"

This is an incorrect criticism since, if I'm not mistaken, conjunction elimination can only be used on a conjunction that is true. In this case the conjunction "This statement is true and this statement is false" would be false because one of the conjuncts would have to be false. Therefore, conjunction elimination cannot be used. —Preceding unsigned comment added by 70.171.20.157 (talk) 04:30, 14 December 2010 (UTC)

I place this under same heading because its in the same section that I fail to follow a deduction:

Thus, from, "This statement is true and this statement is false", it follows that "this statement is false" and so we have, once again, a paradoxical (and non-conjunctive) statement.

according to me and the expansion that was used above this results in

S^(S^ not S)=S^(false)=false

so I cant see the problem — Preceding unsigned comment added by 83.134.157.9 (talk) 04:37, 24 January 2012 (UTC)

Technical tag

This article gets technical at points and loses clarity. Some clearer language would be helpful. —Ute in DC (talk) 22:54, 11 January 2011 (UTC)

Clarity is always helpful, but at this reading I do not see anything that is too technical. --Trovatore (talk) 19:16, 16 November 2012 (UTC)

Not a paradox

"Every man is a liar!" is similar to the "I always lie" statement they can't be true but they can be false, like in the statement "I don't always lie" could be true since in lying that he always lies it would not contradict the statement therefore the non-negative, (doesn't contain the "don't") true statement would be written as "I sometimes lie" the statement "Every man is a liar" must be false since it can't be true but wouldn't contradict itself it was false so the non-negative, true statement would be "At least the speaker (but not every man) is a liar "Props888 (talk) 01:38, 26 April 2011 (UTC)

Statements of the form "I always lie" or "This sentence is a lie" are always self-contradictory--that's true. However, indicting one (or everyone, in this case) as a liar says that the individual tells falsehoods, but doesn't comment on whether everything the individual says (much less any specific statement made by said individual) is a falsehood. Given David's statement, "Every man is a liar," could be either true or false, we're left in a situation where the statement can be judged solely on the listener's subjective evaluation, but we can comment on it in objective terms. If true, the individual in question could have been speaking truthfully or falsely (which, as I understand it, is widely regarded as the default listening position of every individual that will ever have existed for every statement that will have ever been made, save some hypothetical time or place where/when individual humans were/will be/are incapable of lying), and the individual is therefore capable of making the statement in question truthfully or falsely. If false, the speaker in question could be a member of basically any size group of possible liars, including a group that includes only the speaker. There is no paradox present in this particular statement, though the fact that such a statement could be regarded as true or false (and that the speaker could somehow know such a universal truth) is an epistemological nightmare in itself. Bondolon (talk) 07:09, 20 August 2012

who on this earth, either in the present or past had the authority to define "what is an opposite?". Is not a "-" the same as "1". A line is a line, whether two or one. What if the word "not" was meant to be the word "knot". Meaning tied together as one, instead of seperated as two. "+". Science and religion, or the science of religion. Together they are one, apart they are two. Things come in two when we place more importance on one instead of the other. Like a first child jealous of the second. Knot = not. The further we get away from that, the further man gets away from himself. Is not the opposite of Knot, instead of "is". "not a Knot", would that mean is a "Knot". What is truth? Who defines what is true. There is no over or under, "line". A line is a line.12.177.242.131 (talk) 00:38, 14 September 2011 (UTC)

what are you talking about??? — Preceding unsigned comment added by 24.145.48.230 (talk) 18:06, 18 November 2011 (UTC)

Portal 2

Video proof that the paradox is referred to in Portal 2: http://www.youtube.com/watch?v=jVinP2Y0iLQ 78.62.184.165 (talk) 17:45, 9 November 2011 (UTC)

Not a sentence

The "sentence" in question, "this sentence is false" (or equally "I am a liar"), is just not a meaningful utterance. It only looks and sounds as though it were, but it isn't. It is just a meaningless sequence of words. Each word has a certain meaning under certain conditions and suppositions when used in certain situations; but together they just don't belong to one world-picture. It's like an Escher drawing of stairs going ever up. Each step makes sense, but not them all together.

It's not that this utterance isn't true or false or both or neither; it just has no meaning whatever. The speaker can not speak of the final outcome of judgement of veracity of his utterance which will be performed by an objective observer/judge (say, me). What he's actually saying is "you will deem my words false" but he's not in a position to make any such determination, is he.

Moreover, which are the words he's referring to? He's actually saying "you will deem these my words false" but what is he talking about? Is he talking about anything I can pass an objective judgment over? Or is he trying to influence my decision making process - about my decision making process??? (the process of me making a decision whether he spoke the words of truth or not, when he spoke about me making a decision... ). He is in fact trying to induce a bad loop in my thought process. This is not just some bad loop; it's a bad loop squared.

As for self-reference, to forbid any and all self-reference is an enormous overkill here. It's not to self that a sentence can't refer to be still meaningful, but to its own veracity. On a related note, can you possibly have an ability to say in the morning, on which leg you'll stand first? Obviously not, because if you could, you'd just stand on the other one and cause a contradiction. Right? Isn't that what the halting problem argument amounts to?

Short version of the above: left recursion BAD. Right recursion - nothing wrong with it.

To define X in terms of its parts, somehow otherwise constrained/specified, - OK. To define X as X, is not to define it at all. When you say X is X, what are you saying? You just aren't saying anything at all. When all you say is AAAAAAAAAA..., you could just as well kept quiet.

Now, where did I read this? Hmm. I don't recall. WillNess (talk) 15:46, 10 November 2011 (UTC)

Chris Langan

The section on Langan should be removed as he unknown in the literature, the quote is not obviously on the liar paradox (it sounds more like an informal explanation of Gödel's incompleteness theorem), and it's not published. The "theory of theories" seems to be something Langan has written on his website. Incidentally, the section was removed in April 2010 on similar grounds and has reappeared since. — Preceding unsigned comment added by 188.222.226.167 (talk) 15:21, 6 January 2012 (UTC)

Another Solution

In my eyes this paradox exists only because of simple minds, who think there are always only two opposites. Like: who is not a man is a woman. True? Think again. Of course this person could also be a boy, a hermaphrodite, asexual, an animal and countless other possible things. For all of the paradoxical statements here there is also not only one other possibility which would make the paradox complete. The opposite of "I always lie" is not just "I always say the truth", but also "I sometimes lie". So the statement "I always lie" can be false (meaning I lied) without creating the paradox. Same applies to "All cretins always lie". (First of all because you can doubt he is a cretin at all. If he always lies, then maybe also about his heritage. And if he is not a cretin, then he is not bound to the spell and can lie or tell the truth whenever he wants.) One opposite is of course "all cretins always tell the truth". Others are "Some cretins always lie" "Some cretins sometimes lie", "All cretins sometimes lie" and so on. So when he lied with saying "All cretins always lie" and is a cretin himself doesn't create a paradox. Because nobody ever said he cannot lie anymore if his statement is false. The only paradox is that "there are no absolutes". And - paradox or not - it is true.--TeakHoken213.150.232.3 (talk) 11:29, 14 May 2012 (UTC)

Cretan is a person from the island of Crete; cretin is a mentally-deficient person, originally due to lack of Iodine as a result of living in the Alps, resulting in thyroid disease. If you were attempting to paradoxically exemplify your argument, score it as a miss. If you weren't, score it as a hit. Was that a paradox? Steve8394 (talk) 20:20, 14 April 2013 (UTC)

Thanks about the very interesting (honestly) explanation of the word cretin. I originally used it to give my explanations a little humor. Because my point is, that this paradox is just a paradox for people who see everything too seriously and too black/white yes/no true/false funny/serious good/bad cretin/cretan. I don't understand the last part of your post, but I consider my post always as a hit. And always is as often as I lie, except when I tell the truth or the half-truth.--TeakHoken91.47.72.119 (talk) 17:41, 16 March 2014 (UTC)

Chris Langan

The arguments for removing the part on Chris Langan, made earlier, are not very good. The fact that he is unknown in the literature doesn`t mean that he can`t have important insights. In fact, one could argue that the part on Langan shows that he should be known in the literature! Also, in a similar manner, the argument that the article "Theory of theories" is not published, does not invalidate Chris Langans ideas. In fact, one could argue that it supports Langans claims that academia automatically exludes anybody without a degree, without regard to the content of what they have to contribute. It could also be checked if Langan is relevant with regard to the Liar Paradox or not, as it is argued that it is not obvious that Langan is relevant. — Preceding unsigned comment added by 89.9.210.128 (talk) 12:46, 8 August 2012 (UTC)

Resolution of Epimenides' Paradox

Author wrote: "Epimenides' statement that all Cretans are liars can be resolved as false, given that he knows of at least one other Cretan who does not lie."

Suggested re-wording: Epimenides' statement that all Cretans are always liars can be resolved as false, given that assuming othewise leads to contradiction. For, if his claim was true, then, being a Cretan, his claim would be false -- a contradiction. No such contradiction arises from his statement being false. In that case, not all Cretans would be always liars, and at least one Cretan would have told the truth at least once. --Danchristensen (talk) 05:01, 11 September 2012 (UTC)

Criticism of Arthur Prior

I've removed an uncited criticism of Arthur Prior's explanation that smacks of OR. I've pasted it here for reference. If someone can find a reliable source that asserts this, feel free to add it back in, but it stuck out very clearly as OR as I was reading through the article.

It must be recognized that this reasoning is not correct.

1. This statement is false.

is equivalent to

2. It is true that this statement is false.

but not equivalent to

3. This statement is true and this statement is false.

Version 2 contains a single self-reference, but in version 3 we have two self-references, thus 2. and 3. are essentially different.

Arathald (talk) 09:12, 26 September 2012 (UTC)

. .

• Here’s a two-part true/false quiz:

Part 1. A. The following word is an instance of fallacy. Fallacy.

True or False?

Part 2. B. A is partly true.

True or False?

What is truth? Or, what is the act of true reference? Is the word ‘fallacy’ a true reference to the idea of fallacy? Yes, it is. So, there is truth in A, despite that A is false. The fact is that, in order to lie at all, some true reference must be made. For example, in the normal usage of the statement ‘Abraham Lincoln was a little green Martian‘, both the man Abraham Lincoln and the idea of ‘little green Martian-ness’ is made reference to. PatternOfPersona (talk) —Preceding undated comment added 21:16, 14 November 2012 (UTC)

History

The cited historical (Biblical) use of the paradox is a straw-man flaw, which only serves to distract from the actual understanding of the paradox. The statement "all men are liars" is not an example of the liar paradox since it makes no claim to its own veracity. A man can be a liar, and still tell the truth occasionally, which is the essence of being a liar. If "liar" were defined as "one who always lies", it would lose meaning since the truth would be the only logical result of every one of the "liar's" statements. Therefore, "liar" must be defined as one "one who unpredictably lies", leaving the statement "all men are liars" patently true and non-pardoxical in any way. As such, it should be removed from the paradox page. Steve8394 (talk) 20:08, 14 April 2013 (UTC)

Logical structure of the liar paradox

I'd like to edit the final paragraph of the section as below, but don't want to run afoul of OR rules. I personally don't believe this to be OR since I'm using widely accepted boolean methods.

---

A = (A = false)

This is an equation from which the truth value of A = "this statement is false" could hopefully be obtained. This equation would be simplified according to boolean rules as such:

A = (~A = true)
A = (~A)
A = ~A
false

... indicating that our original statement is contradictory. Note that the final value is not equated to A, but is the reduced value of the proposition that A exists. Bukzor (talk) 06:14, 23 September 2013 (UTC)

False dilemma

This "Paradox" assumes that all statements are either true or false. They can also be neither, as the paradox clearly shows. JedG

Statements can also be both true and false; such as 'This statement is true' which if it is true, is true and if it is false, is false. Helixmooncalf (talk) 04:43, 26 November 2011 (UTC)

But more importantly, not every utterance is a statement. It may be a meaningless sequence of words masquerading as a sentence. I think so too is your sentence (in English), not a sentence (in any formal logic language). Like not every picture of a sequence of steps is a picture of a ladder. Cf. Escher drawings. See my comment at the bottom of the page. But I don't have sources for that. WillNess (talk) 23:38, 27 November 2011 (UTC)

No. The "assumption" of only true/false actually has no bearing on the paradox at all and is a complete red herring. The easiest way to see this is to rephrase the paradox in a way that entirely eliminates the apparent assumption. It can be replaced by the following "This statement implies (__ fill in the blank __)" -- from which you can conclude whatever you filled in the blank with. What this shows is that truth and falsehood are entirely irrelevant to the essence of the paradox, but rather it is (a) the notion of self-reference (i.e. unrestrained second order logic), combined with (b) the ability to both use modus ponens and the "deduction theorem" that lies at the root of the paradox. To drive the point home: both classical and intuitionist logic (which does not have the exclusive true/false assumption) have property (b), so the above revised version of the liar's paradox entails anything and everything in both forms of logic. In quantum logic, on the other hand, one cannot define an implication operator that has both the modus ponens and deduction theorem property (otherwise the quantum logic reduces to a boolean logic). So, the paradox is avoided in that setting. But then, I don't know if you can do any kind of second order logic on a quantum logic foundation, so you probably also lose the ability to do (a). — Preceding unsigned comment added by 64.136.26.17 (talk) 12:46, 30 May 2012 (UTC)

Trying it out here: (There is a statement such that it implies fill-in-the-blank (F))

A = ( A -> F )

A = ( F + ~A )

( A * (F + ~A) ) + ( ~A * ~(F + ~A) )

( AF + 0 ) + ( ~A * (~FA) )

( AF ) + ( 0 )

AF

This doesn't look like the liar's paradox, unless fill-in-the-blank is false. Bukzor (talk) 06:37, 23 September 2013 (UTC)

Lying David not a paradox

David said, "Every man is a liar". The remaining conclusion is not accurate. A liar does not always lie. Therefore, if "Every man is a liar" is the only true statement David ever makes, then it is not a paradox. If David is lying by saying "Every man is a liar", then someone is not a liar, and only David need be a liar, which is still not a paradox. The paradox only exists if David would have said, "Every man always lies." 198.202.137.29 (talk) 18:07, 7 August 2014 (UTC)

Deltora Quest

I am sure that the riddle mentioned in the paragraph about Deltora Quest has its origins. What's the name of that paradox? IllidanS4 (talk) 21:57, 2 July 2015 (UTC)

The Assertion of Nothing

I would submit that the 'liar paradox' is not a paradox at all, but merely an non-nonsensical utterance. The reason that we do not readily see that it is nonsense, is that we do not recognize the fact that it is tacitly implicit in every assertion that the assertion itself is true. If this were not the case, then we would have no good reason to believe the speaker's assertion and would require an explicit declaration of it truth. However, if the truth of this declaration (assertion) were not implicit, then we should require another declaration to make explicit the the truth of the first; and so on, ad infinitum. Further, if there were no tacit implication of truth in an assertion, then we would have no reason to hold in low esteem those (liars) who deliberately mislead us by making false assertions.

Once we recognize this tacit implication, and render it explicit, it is readily apparent that any assertion that declares itself to be false is in violation of the law of non-contradiction, and so communicates nothing:

Implicit – This assertion is true. Explicit – This assertion is not true. Combined – This assertion is – at the same time and in the same sense – both true and not true.

Since true and false (not true|) are mutually exclusive concepts, the two simply cancel out and the assertion becomes unintelligible. It would be as if one were to have uttered “This sentence is.”; an assertion that assert nothing more than that it 'is an assertion' – the truth of which is undeniable. — Preceding unsigned comment added by RGGehue (talk • contribs) 16:49, 31 December 2015 (UTC)