Liar Paradox Puns

During a solid session, I came across a documentary on YouTube about paradoxes and one in particular has not left me. The paradox as named above is essentially this:

“This sentence is false.” Is it true or false? Well, if it’s true, then it’s false. But then if it’s false, it’s true. And so on.

This is the simplest example of the paradox but you get my drift. While I'm locked in my couch, my mind just loops as above.

What if you were spending your time telling the truth and weren’t lying, but then someone asks you if you are lying about something even though you hadn’t lied before you tell them you were lying. Are you lying?

If you weren’t lying about lying then you were telling the truth as you weren’t lying about lying.

If you were tell the truth then you were lying.

TLDR: What can you ask someone who you believe is a pathological liar to determine if they are a pathological liar or not?

Background: Years ago, I knew someone who my friends and I determined was a pathological liar. While our certainty wasn't based on some clinical diagnosis, we were no less sure of this condition. He would lie about outrageous things, like having a Ferarri he wouldn't show us for an endlessly growing list of reasons. He would lie when lies weren't needed. Occasionally, he would speak the truth, which made detecting the lies difficult at best. So, a pathological liar doesn't always tell lies. Therefore, catching someone telling the truth doesn't automatically classify that person as "not a pathological liar."

I also realized over time that being a "liar" is an emergent property, like how many grains of sand does it take to make a pile of sand? How many lies does one need to tell to become a liar? I don't think we'd call someone a liar if they told one lie in their life, or even two or three. That's just part of the learning curve of discovering who they are going to be - and they test lies to see how they fit. Eventually, if a person tells enough lies beyond some learning phase or a rare lie, we'd identify that person as a liar. Go well beyond that point to where the person doesn't know they are lying or just does it as part of their nature, and we might say that person is a pathological liar.

Current Situation: I know someone else now who reminds me a lot about the guy I knew previously. Heck, since we've only talked over the internet, I even suspect there is some remote possibility he's the same guy. Not ironically, the pathological liar I knew from years ago has crossed my path out of the blue before, so I don't think the possibility is a stretch of the imagination. However, that's not the information I am after.

The Paradoxical Question: I've been half-thinking along the lines of just asking this guy if he's a pathological liar, and I am starting to realize even if it wouldn't be taken as a complete insult, there is no useful answer.

"By the way - and I don't mean any insult here - I just get this impression: Are you by any chance a pathological liar?

Possible Answers:

• "No."
• "Yes."
• "I don't know"
• "WTF dude?! Are you on crack?!"

Obvious Interpretations of the Answers:

"No" is the expected answer. If the person isn't a pathological liar, they would be telling the truth to deny it. However, if th

What would happen if you went to the police to confess to making a false confession (this one)? Since you made the false confession, you're telling the truth. But if you're telling the truth, then it's a not a false confession, which means you lied. But if you lied... [ad infinitum].

Also curious if there are any examples of paradoxes as legal defenses?

If the song isn’t about you, you’re vain because you think it is, which means the song is about you, which means you’re correctly assessing the content of the song and are not vain, which means the song isn’t about you, ad infinitum

Could one solution to the liar's paradox be simply to accept the limitations of our logic. To accept that, while the laws of logic do apply to mind-independent reality, they dont always apply to our linguistic concepts, which are mind-dependent?

So all the paradox is showing us is how our language and our logic isnt perfectly coherent, but just like all of our tools, language and logic are prone to glitches, flaws and errors. Its just showing us the limit of our language and thought process to be 100% coherent, and thus we should simply abandon this concept of 100% coherency and treat logic as a sort of "good-enough" tool, rather than completely throwing it out the window because of this one apparent flaw.

Ive been reading about different solutions to the problem but all of them seem to be focused on redefining truth or redefining language to mean something that it normally doesnt as an attempt to patch up this glitch. It seems we arent really discovering any solutions, but just inventing solutions to resolve this inconsistency. It seems to be completely ad hoc.

The Liar's Paradox: "This statement is false."

I have heard it argued that, since this statement is neither true nor false, it demonstrates an exception to the axiom that a proposition must be either true or false.

But why shouldn't it rather be categorized as a meaningless statement, since "it ascribes properties to particulars which admit of no such properties"? In this case, the particular would be the sentence in question and the property would be falseness. After all, if it is neither true nor false, then it is not false.

Just looking at some of the posts here, I'm in way over my head, as I know basically zero formal logic or higher math (finished AP Calc BC and haven't yet started uni). That being said, I'm still curious about the answer.

> The king of Germany's name is Bill Weld.

Now, this statement isn't true obviously, but I don't believe it's false either -- as there isn't a king of Germany with a name other than Bill Weld, the question is invalid. Similarly:

> The length of each of a circle's sides is equal to πr/7.

A circle has no sides, and therefore there's nothing with the characteristic of length to be described.

And then what brought me originally to this:

> If your parents didn't have any children, chances are you won't either.

I commented here at /r/technicallythetruth asserting that the statement was neither true nor false (as I had semi-recently seen a comment about a similar statement making a similar assertion), and I realized I'm talking out of my ass, so I've come here to find out -- am I correct? And if so, does this have a name, and how would statements like these be formally expressed?

I apologize for being a complete newb, and hopefully I don't have a complete misunderstanding of what formal logic is.

Example:
Is the statement "These letters are black." true or false?

If the letters are black, then the statement is true.
If the letters are not black, then the statement is false.

In this example we have a subject (These letters) and a proposed description of that subject (black). In the same way, we have the Liar Paradox:

Is the statement "This sentence is false." true or false?

If the sentence is true, then the statement is false.
If the sentence is false, then the statement is true.

Here we have a subject (This sentence) and a proposed description of that subject (false).

The questions is, how do we determine if the description is correct?

To start, we have to realize that in this context the statement itself cannot tell us that the sentence is false as it might appear to. This is because when asking "Is the statement 'This sentence is false.' true or false?" we are implying that the description of the subject may be either true or false. This means that the description (false) of the subject (This Sentence) is solely a proposed description as stated above.

Therefore, the word "false" is not defining the truth value of the sentence as it might first appear, but only proposing a truth value for it. It is our job to determine whether this proposed truth value is correct or incorrect.

To do that, we need to understand what the proposed description (false) is actually proposing. What does it mean to describe something as "false"?

True and false are names for relationships between a subject and some proposed description of that subject. If the proposed description matches the subject, then the relationship is named true. If the proposed description does not match the subject, then the relationship is named false.

If true and false are only names given to relationships between a subject and a proposed description of that subject, then you need both a subject and a proposed description of that subject before you can determine which relationship exists.

In the statement 'This sentence is false,' we have a subject (This sentence) and a proposed relationship that subject has with some proposed description of it (false). The proposed description of it is not stated, therefore it is impossible to determine whether or not the proposed relationship is correct or incorrect.

This means that the statement "This sentence is false" cannot hold a truth value because there is nothing to attach one to; in the same way that you cannot attach a

If we presuppose mathematical fictionalism, is it possible that the statement S, “This statement is unprovable”, can be “true” relative to the fiction but otherwise false?

I was thinking that if this is the case, then it seems that we can say that S is both true (according to our fiction) and provable (because we can show that it is unprovable according to our fiction).

Introduction

The problem being addressed is the problem of the liar paradox. The thesis of this post is: The expression that constitutes the liar paradox betrays a syntactical error in an attempt to construct a proposition. The thesis contributes to the problem by denying the existence of a proposition within the liar paradox, thereby by extension asserting that there is no proposition to evaluate the truth value of in the liar paradox, thereby positing that the whole purported problem of the liar paradox, namely, the purported discovery of a contradiction found by investigating the truth value of a proposition within the paradox, does not present itself, because there is no proposition within the paradox.

Proof of Thesis

The liar paradox is the statement "This proposition is false." People think that it is a paradox because it appears that if it is true, it is false, and if it is false, it is true. But this expression is simply making a syntactical error in defining the proposition it is trying to define.

First, let's clarify a law of Aristotelian logic, that, even if you don't buy into the entirety of that school of logic, I'm pretty sure most people agree with. This law is the conjecture A=A. This means any proposition equals itself, or any proposition is itself. In this post, I will accept this law of logic, as to do otherwise is self-contradictory. Accepting this law of logic, any "definition" of a term that disagrees with it is not in fact a definition of a term, but the result of a failed attempt to define a term. This is because if this law of logic governs anything, what it governs is how to define a term. Therefore, if it is broken in the defining of a term, then the definer of the term simply failed in defining it. To say otherwise is to say that the definer of the term succeeded in defining it, which means that a term exists which contradicts a law of logic, which would mean that the law of logic is invalid, which it is obviously not.

Now, back to the liar paradox. Let's assume this is a proposition and abstract it. Let the proposition be A. As we know, the content of the proposition is denying itself; in other words, the content is ¬A (this means not-A in the symbolic language of logic, which is much like the symbolic language of math). So, the liar paradox can be put into logic language like so:

A=¬A

This definition is clearly in contradiction with the law of logic discussed above. As we have discussed, this means that either t

For anyone who doesn’t know what the Liar Paradox is, I’ve put a description below. Found out about this after reading, “This Story Is A Lie”, by Tom Pollock. I do recommend reading that by the way, it has its flaws but is generally a good read. It’s just the ending makes me want to kill the universe. But hey, that’s fine...Right?

(The text below is copied and pasted)

Liar Paradox

If "this sentence is false" is true, then the sentence is false, but if the sentence states that it is false, and it is false, then it must be true, and so on.

The simplest version of the paradox is the sentence: A: This statement (A) is false. If (A) is true, then "This statement is false" is true. Therefore, (A) must be false. The hypothesis that (A) is true leads to the conclusion that (A) is false, a contradiction. If (A) is false, then "This statement is false" is false. Therefore, (A) must be true. The hypothesis that (A) is false leads to the conclusion that (A) is true, another contradiction. Either way, (A) is both true and false, which is a paradox. However, that the liar sentence can be shown to be true if it is false and false if it is true has led some to conclude that it is "neither true nor false".[8] This response to the paradox is, in effect, the rejection of the claim that every statement has to be either true or false, also known as the principle of bivalence, a concept related to the law of the excluded middle. The proposal that the statement is neither true nor false has given rise to the following, strengthened version of the paradox: This statement is not true. (B) If (B) is neither true nor false, then it must be not true. Since this is what (B) itself states, it means that (B) must be true. Since initially (B) was not true and is now true, another paradox arises. Another reaction to the paradox of (A) is to posit, as Graham Priest has, that the statement is both true and false. Nevertheless, even Priest's analysis is susceptible to the following version of the liar: This statement is only false. (C) If (C) is both true and false, then (C) is only false. But then, it is not true. Since initially (C) was true and is now not true, it is a paradox. However, it has been argued that by adopting a two-valued relational semantics (as opposed to functional semantics), the dialetheic approach can overcome this version of the Liar.[9] There are also multi-sentence versions of the liar paradox. The following is the two-sentence version: The following statement i

I don’t know. I’ve never understood it.

The Liars Paradox is commonly expressed as "This sentence is false." We are asked to evaluate if this proposition is true or false. My thesis is that if evaluated carefully and explicitly, the proposition can be shown to be trivially self-contradictory, equivalent to a proposition such as "A is true and false." or "I am a married bachelor." Trivially self-contradictory sentences are sentences that break the law of identity. These types of sentences are generally not considered paradoxical. Therefore, if the "The Liars Paradox" is trivially breaking the law of identity, it isn't a paradox at all.

All propositions have what I will call a truth property, denoted with (A). (A) is either true or false, and depends on the content of the proposition, (B). (A) is our unknown variable that we solve for using (B). This is just standard logic and proposition evaluation:

a.) If B then A. (a.k.a. If B is true, then A is true.)

Let’s look at some propositions.

b.) Bears are animals.

Is (A) true? To determine (A), we will evaluate the content of this proposition, (B). In this case, you could go in different levels of detail, but I think we all agree (B) is true, hence (A) is true.

Formally:
c.) If B is true then A is true
d.) B = true
e.) Therefore: A = true

2.) This sentence has five words.

Is (A) true? To determine (A), we will evaluate the content of this proposition, (B). In this case, the referenced sentence (itself) does have 5 words, which matches (B), so (B) is true, hence (A) is true.

Again:
f.) If B is true then A is true
g.) B = true
h.) Therefore: A = true

Moving on.

3.) This sentence is true.

In this case, the content of the proposition, (B), is regarding its own property (A). (B) is simply claiming "(A) is true."

Formally:
i.) If B is true then A is true
j.) B = A is True
k.) Therefore: If A is True then A is true.

That didn't get us anywhere, we already knew that. Sadly, we will never know if A is true. To explain this with an analogy: imagine we are trying to solve an unknown value, how much a house is worth (A), and the only way to calculate the value of a house, is by knowing the value of the house (B). In this case, you cannot ever find or calculate (A). In other words, if we have an unknown, that is dependent on its own value, it will forever be unknown.

Proposition (3) is of that type. But, to be clear, the sentence doesn't entail a logical contradiction, it's just unsolvable. No