Graham Priest: The Liar Paradox

[@evilpandakillabzonattkoccu4879]

One issue I never see mentioned is the following: the sentence "This very thing I'm telling you now is false." .... is a declarative statement. It's a statement and not an argument. An argument would have a premise and a conclusion, with the premise supporting the conclusion. The statement in question, however, isn't making an argument but stating a claim as if it were facr. The person making the statement isn't saying "What I'm telling you now is false because of the following reasons".... instead, it just makes a declaration. This declaration can't be given a truth-value without making assumptions (which would mean guessing without any evidence). In this case, we would have to make the assumption that "The truth-value of a statement that lacks a premise must be based on the components of the statement". If we look at it this way, we would say that 'we must conclude that the subject of the sentence (what you were telling us at that moment or "What I am telling you now") is in a state of being (is being the verb) false and our evidence for this is predicated on the assumption that the predicate of the sentence *says so and is true.* *[Restated without the annotations]* If we look at it this way, than we would say: 'We must conclude that the subject of the sentence is in a state of being false and our evidence for this is predicated on the assumption that the predicate of the sentence *says so.* The issue with this logic is that it (incorrectly, imho) it imposes assumptions and rules that force a contradiction when none exists and it suggests that a statement like this can be accurately defined as true or false merely by the words and components of the sentence. It doesn't consider how the truth-value of a declaration relates to reality. A declaration is a claim made without evidence. "My hair is blonde" is a declaration. There is no component of that sentence that is a contradiction to another. This is a statement, however, isn't true. My hair isn't blonde. Thus, we know that when I make the declaration "My hair is blonde", that the statement has a truth-value of false, in reality. All the words I said in my declaration were false. It's fair to assume I have hair and to presume it could be blonde...but there is no reason for the assumption that because I declared it to be so, then it must be true. So, when I made the delegation that "my hair is blonde", the reality is "the words I'm saying now are false" is as true as the declaration itself. The truth of a declaration is relative to the context of the claim being declared. "The words I'm saying now are false", if considered an argument... would be an invalid argument and wouldn't have a truth-value. The truth-value of a sentence cannot be based on assumption and the sentence in question is invalid as an argument as it lacks a premise to support a conclusion.

[@rocio8851]

I think dialetheism is false but my neighbour says Graham and I are both right. Now I am at peace.

[@paulaustinmurphy]

Upshot: i) Arguments to support the law of non-contradiction have failed (have they?). ii) Therefore let's accept the conclusion of the Liar Paradox. Now is this advice to accept the *arguments* which say accept the conclusion of the Liar Paradox? Or is it a statement (not an argument) that we should simply accept the conclusion? Full stop. Graham Priest seems to take the later position - at least in this video. Priest may be correct to say that the Humean "evidence" shows us that logical defences of the law of excluded have not worked . However, how does that *alone* show us that we should accept contradictions? This is similar to the well-known *pessimistic meta-induction* which states: i) All/most previous scientific theories have been shown to be wanting. ii) Therefore that must also be true of contemporary scientific theories. Surely, if all attempts to defend the law of non-contradiction have failed. Then accept the Liar Paradox's contradiction. But this doesn't work as it stands. Let's take an extreme equivalent: i) All previous attempts to cure cancer have failed. ii) So let's stop attempting to cure cancer. So is Priest's *dialetheic logic* about the world (i.e., an ontological position) or is it about what we can - or even *should* - say about it? If it's the former, then Priest can literally be *both* in New York and *not* in New York? If it's the latter, then it's simply a logic that can helpfully capture and formulate such things as the inconsistencies in scientific theories. Or it can advance the pragmatic option of seeing two contradictory positions as true - at least for the time being.

[@tylerantony7399]

I don't think the argument in this video is as strong as the one he gives in his book. Namely, if English satisfies a set of conditions (called Tarski conditions) then a contradiction similar to the heterological paradox must be concluded to be true. He argues pretty forcefully that not only are attempts to prove that language doesn't satisfy the Tarski conditions flawed, but that it is more difficult, *in general* than was originally thought to even conceive of an argument in favor of regarding English as not satisying these conditions, namely because, no matter what structural accomodations are made to the language to accomodate a paradox by presuming one of the conditions false (including any structural accomodations that have a notion of some sort of higher level "Truth predicate" and "Non-Truth (either False or Vacuous) Predicate", we can always extend the "Liar's Paradox" to the structural accomodation. This video seemed to be an attempt at giving an overarching summary in 5 minutes. At any rate, his books "In Contradiction" is, even if we "hold out" on the existence of dialetheisms, a really good summary of the flaws in attempts to avoid paradoxes in languages and formal systems. As a student of mathematics, things like ZFC and Category Theory, while interesting in their own right and sometimes even useful or beautiful, always seemed like they were patching the analogous issues (like Russell's paradox) that would appear in set theory, and he does a really good job of explicating some bothersome features of these theories (large parts of which were quite literally concocted to patch Russell's paradox).

[@frankt9156]

I think the liar paradox is like self application in computer science which results in an infinite loop. So with infinite loop the function never return the answer. Same with the liar paradox, so essentially the same in liar paradox sentence which also an infinite loop because of self referencing. A premise cannot also be a solution.

[@GeorgWilde]

It is not a conclusion of an argument, it is a hypothetical position which he tries to take. "i) All previous attempts to cure cancer have failed. ii) So let's stop attempting to cure cancer." - You mean ii) All future atempts will also fail. To not mix is and ought.

[@crawlFace]

That was cool- definitely feels like an introduction regarding a situation that will take more than 5 minutes to explore. I think innovative ideas on such logic and reasoning are becoming more accepted or understood as we learn more about behavior/nature on the quantum scale.

[@eidolor]

I hate that in a quantum context this wouldn’t even get the bat of an eye, not that it would make any more sense to me

[@emanuelbenicio3501]

The proper solution is not to deny that it is a contradiction, rather it is to deny that it even means anything. If we are going by intuition, dialetheias and claiming that it is not a contradiction are two equally unintuitive answers. The intuitive answer is this: this is absolute nonsense. Meaningless. Basically, there is no proposition which is true and false, there is just a mix of words which hopefully emanates meaning, but upon the analysis of its parts individually, the sentence as a whole simply cannot be given meaning.

[@Leif-yv5ql]

The phrase "I am lying" is a meaningless statement. The phrase "I am telling the truth" is equally meaningless.

[@chicken29843]

The principle of not being able to have contradictions does seem to be contradicted in and of itself by our discoveries in physics though that may be a generous interpretation of superpositions and things of the like

[@evilpandakillabzonattkoccu4879]

You're absolutely right. The logic used that makes this appear to be a paradox is based on Aristotle's logical calculus, which there are only two possible values for any proposition: "True" and "False" There are many forms of propositional calculus that allow for more than just two possible outcomes. This type of calculus is called many-valued logic. While there are some forms that allow for infinite values, the most popular form is the three-valued logic calculus. With this form of propositional calculus, the value possibilities are: "true", "false" and "unknown". This logic is used to find truth values of propositions that bivalent logic isn't able to. Aristotle suggested that bivalent logic isn't applicable to future contingents. For example, the statement "There will be a sea battle tomorrow" cannot be said to be true or false using classical bivalent logic. Using three-valued logic, we can address the issue. Three-valued logic would say that the statement "There will be a sea battle tomorrow" can have three possible values. Since we ruled out true and false, the statement would be given a value of "unknown". ....so, there really is no paradox in the "liars paradox" unless one limits their logical calculus to create a paradox. This type of "paradox" has a different name: a 'falsidical’ paradox "A ‘falsidical’ paradox is one whose ‘proposition’ or conclusion is indeed obviously false or self-contradictory, but which contains a fallacy that is detectably responsible for delivering the absurd conclusion" Considering the definition above: the liars paradox is clearly self-contradictory (it says its false, making it true and false at the same time) ....but there is a fallacy that creates this contradiction. In this case, it's the idea the truth-value of a declaration can be determined by assigning truth-values to the declaration's components and determining if the opposite statement can negate the statement. This would require the assumption that "if the statement is made, then it can only be true or false." When we limit ourselves to two outcomes.... paradox created. When we accept that 'unknown' is also a possible solution, there is no paradox. "My hair is blonde right now." There is no way to know if that declaration is true or false. 1) people have hair.... but the declaration isn't an argument, so there is no premise. it's just a conclusion. That is to say: the statement doesn't say "My hair is a light golden color right now, thus, my hair is blonde right now" ...instead it makes a conclusion based on nothing. 2) people have blonde hair and can dye their hair, so "my hair is blonde right now" is still feasible 3) the negation, "my hair is not blonde right now" isn't in any contradiction with the proposal. ....still: we can't honestly say that the statement is true. We can say it's "unknown" if we wish to put a truth-value on it... otherwise, the best we can conclude is a probability and not a fact. If we are given context or added information, then we can do more with the statement. "My hair is actually brown and I was lying when I said it was blonde" ....that, incidently, is true in reality. That fact, however, is unknowable to a person who just has access to my first statement. Using logical calculus and reasoning to find the truth of my first claim.... will only result in a probability value (uncertainty) or a value of unknown (a certainty). Nothing about this form of propositional calculus is unreasonable. The truth of a satements being 'unknown' isn't an illogical or irrational. 🤷‍♂️ instead, when this paradox is presented: its omitted as an option completely. The assumption, then, us that "every single statement is either true or false. there is nothing else it could be." .....which, itself, isn't an invalid argument as the premise doesn't actually provide evidence to support the conclusion in anyway. "it's can't be both" doesn't answer "why can it not be both? why does it have to be one or the other?". 🤷‍♂️ ...so, I find it odd that "The liars paradox" is still thought of as a real paradox when it clearly isn't. There are many more values a statement can have: valid, flawed... Yet, when it's stated that the only possible values are true and false...and a statement can't be both at the same time, then yep: paradox created. It's, basically, "schrodinger's statement" but instead or being both "true and false until measured", the statement is neither true or false but 'unknown', unless further information is presented or collected (kind of like measuring somehting) and constructed into a premise or set of premises that claim to support the conclusion (the proposal made in the declaration). At that point, we can tell if it's true or false because it's has stopped being a declarative statement and has become an actual argument. (jokinly, it could be said: it's 'wave function' ostensibly 'collapsed' and it went from a 'superposition' of unknown many values to one known value 😂) Turns out: once you measure, the cat is either dead or alive.... before then, it's unknown to you. Same with the liars paradox.

[@chicken29843]

@@evilpandakillabzonattkoccu4879 since you wrote all that out I'm going to put some time together tomorrow to read through it properly

[@evilpandakillabzonattkoccu4879]

@@chicken29843 my apologies if it ends up being a waste of your time (for example: a clearly flawed post).

[@jimporfit]

I wonder to what extent this equates to the suspiciously 'self evident' axioms of mathematics

[@IndustrialMilitia]

A major problem with accepting the Liar’s Paradox "this statement is false" as a true contradiction - or both true and false - is that it's negation "this statement isn't false" is not also both true and false. The negation of a dialetheia should be a dialetheia. But that is not the case for the Liar’s Paradox. It is the case however for Russell's Paradox.

[@wagfinpis]

I like your bow and bow next to the bow. True/ False can be logical or narrative. If someone is lying or has a different perception then it is narrative, if it is logical we are trying to reduce an immediate interpretation, not devine the ultimate truth. Is true and Is false logic rule: "is true or "is false" logic can only be applied outside of/after/beyond a complete statement. "This sentence" is not a statement. "This sentence is false" is like "9÷0="; it is like saying there is a hole in nothing. "This sentence is true" is like "0÷9=0"; it is like making nothing disappear. These sentences are intuitively not logical, so you make a correlated rule or method to categorize them in a way that tags them as logically invalid or to lack any communicated logic value. *They subjectively make grammar, but they lack any objective logic, so you correlate their logic against the grammar via a rule that represents practical observation. It's just nomenclature like particle "spin" in physics; it's based on what we can know.

[@Ber9200]

(1) ‘This sentence’ is not the statement the liar is negating. (2) ‘0/9=0’ is just an arithmetic truth. ‘This sentence is true’ is not a truth, it seems semantically underdetermined . (3) I didn’t understand the rest. What does it mean for neither the liar nor the truth teller to be ‘logical’? The proof of a contradiction in the liar reasoning is prima facie valid. That’s why it’s called a paradox. Did you mean illformed? What gives rise to a contradiction here is semantic closure. That is, the fact that natural language can express its own semantic concepts.

[@tobiasyoder]

What if the law of non contradiction is both true and false ?

[@dy8576]

Correct me please but to consider a false statement; and then comment if that it being false is true are not related at all, as it just commenting that a the consideration is infact false, that truth cannot change the fact that the initial statement withing itself is false, its its status quo of being false that is true. Consider an example, "i am hungry" = false (ie i am not hungry). Now, once i have assigned this, verifying if it is true that this statement is infact false does not change the fact that i am not hungry but state again that it is false that i am hungry, you see i do not understand how this will change the value of the statement to be true because for that i would have to assign that i am hungry = true and not say that "i am hungry = false" is true.

[@robertcooper1952]

Perhaps there is simply no solution to the liar paradox.

[@ABC-yt1nq]

"This sentence is false" Classic Liar's Paradox. Which isn't a paradox at all. It's simply an incomplete utterance - a piece of linguistic fuckery. This purported paradox proceeds on the false premise that the evaluation of something can be contained within that thing being evaluated. It appears impossible for the evaluation of something - let's call it X - to also be contained in that X. The evaluation of X changes the value of X from X to X + [Evaluation of X]. Prima facie these values are not and can never be equal. Imagine X can only be either True or False. We know some things about X, but not whether or not it is T or F. To learn that will add information to and expand our definition of X, changing it from X to either X+T or X+F. This appears to be similar to the observer effect, which alters the results of the double slit experiment by the act of observation of sub-atomic particles, which previously were waves, by collapsing the wave function. Thus, in order to evaluate X, and not X + [Evaluation of X] , the evaluator of X must be completely separate from and independent of X and must not affect the value of X by the act of evaluation. This is impossible when observing sub-atomic particles because of the workings of quantum mechanics, but it is possible in larger, grosser information systems. Symbology - specifically written language - is such a system. This appears similar to asking someone to calculate the square root of ... and then not telling them the number you want them to calculate the square root of. Without the separate sentence to be evaluated being set out, the word combination "This sentence is false" is gibberish with zero information value. The sentence "This sentence is false" must by necessity be an evaluation of a separate and independent sentence which was communicated, in full, at some point in time prior to the evaluation. The only proper answer to the Liar's Paradox of "Is this sentence false?" is, "Which sentence are you asking me to evaluate the Truth or Falsity of?"

[@Leif-yv5ql]

It isn't a paradox. It is a poorly phrased puzzle.

[@ryansobol8991]

Liar Paradox best relegated to reductio ad absurdum. Good fit for youtube

[@julianmorrisette6642]

He’s ignoring the notion of Absolute Truth, such as Truth independent of mind and language. If he did that, The Law of Non Contraction wouldn’t be moved

[@2tehnik]

> logic is true and mind-independent but only when it doesn't question the LNC

[@Zenithguy]

He’s not negating “Absolute Truth” but rather just stating how the LNC is a lot more difficult to perceive than it already is from an objective standpoint. You certainly can’t have for an example two cloned persons accounted as the “same” because they’re two full complex beings. But what does that mean? What does it even mean to be the “same” while having two objects apart from each other? The difficulty lies within the source of evidential properties when accounting for absolutes. Hence there’s no negation of truth- otherwise we just fall into nihilism (which is still another absolute view another can see).

[@marcotuliao2140]

Amazing.

[@theochasid8996]

Meaningless statement. This sentence is sad. This sentence is blue. This sentence is 1. The sentence is 0. You are giving a sentence qualities which is does not possess. Thus the law of non-contradiction reigns Supreme, and you cannot escape.

[@badsocks756]

The extended Liar demonstrates your argument to be nonsense. Eg "This sentence is either false or incoherent"

[@jamesppesch]

Corey Herrick this sentence is either misbehaving or it is grue. *Grue being green until a time (T) at which point it will be blue. The extended liars paradox is an attempt to salvage that which was demonstrated by this sentence is 0 or it is blue by defining a paradox into existence.

[@mothernature1755]

1)This statement is not true 2)Meaningless statements arent true 3) proposition 1 is meaningless 4) therefore proposition 1 is not true

[@tylerantony7399]

Lel but this is just the value gap argument, which is again brought down by an extended liars paradox that you would be compelled to accept even given your reclassification of sentences as possibly being meaningless in addition to true or false. The basic gist of your examples is that truth values can be trinary: True, False, or "Meaningless". But if you take the sentence "This sentence is not true", then you get the same result and you still have to acknowledge it. If "This sentence is not true" is true, you get a contradiction, but if it is either false or meaningless, then it is also true, which just gives you the paradox again, because if you are claiming that the sentence is meaningless then it is necessarily not true.

[@josejrtuti]

he talked and didn't say anything

[@abelperalta9393]

Actually, he says something as: "30 years ago I've been questioning the principle of non-contradiction, and the establishment considers me a bit heretical, but not a complete fruitcake." He's right: something went wrong in the academy.

[@MontyCantsin5]

I think you need to start listening a bit more.

[@rocio8851]

You're right

[@JaKommenterar]

Yes he did, probably you what lack the ability to understand

[@ericray7173]

I'm sorry but people who waste their time on this shit need better things to do lol

[@joshuaboulton36]

I'm sorry but the machine you're using wouldn't be here if it weren't for Alan Turing "wasting" his time on topics like this.

[@MontyCantsin5]

@ericray7173: 🤦