Wikipedia is claiming that when St. Jermone was saying that when David said in the book of Psalm that every man is a liar, it is a form of the Liar’s paradox. Can’t it be said that only some men are liars “in this case, he would be one of them”, ending the paradox?
How is this a paradox? Even liars can tell the truth some times.
Well, if this is some variant on a Cretan saying “all Cretans are liars”, I never understood the so-called paradox. It can be resolved by reasoning that the speaker is a liar and there is at least one truth-telling Cretan.
I think it would only be a paradox if men always lied. Saying that all men are liars, to me, does not mean that men always lie. They can tell the truth sometimes.
I think it is true without doubt that all men (which includes females) lie to some extent (some more than others).
Even then, the OP’s point is that it’s not a paradox: if a liar is someone who always lies, and some guy tells you that all men are liars, and he’s a Liar Who Always Lies, then (a) he’s lying, such that (b) plenty of other men don’t happen to be liars. Which ain’t a paradox.
Well, no, it isn’t. Whether he was a liar, St. Jermome was apparently a fool. The liar’s paradox requires, you know, a paradox. There’s nothing paradoxical about “All men are liars”.
All men *are *liars, we know that to be true from experience and introspection without needing to be told. Yet we still believe almost everything that we are told by men. The relevant point is that nobody, including David, takes a position that all men are liars all the time. We all accept that most men are honest most of the time. Since we accept that most men are honest most of the time we can accept the truth of David’s statement that “All men are liars” because the probability is high that David was telling the truth at the time he made that statement.
Looking at the Wikipedia article, it’s clear that St. Jerome is utilising a logical fallacy. He supposedly said “If it is true that every man is a liar, and David’s statement, ‘Every man is a liar’ is true, then David also is lying.” This is a textbook example of the Undistributed Middle fallacy. Jerome’s argument runs:
All men, including David, are liars.
Liars sometimes tell untruths.
Therefore all statements David makes must be untruths.
If Jerome was really too dense to see the flaw in that reasoning then he was truly a fool. While David may have always been a man, and all men may lie some of the time, there’s no justification for Jerome’s claim that David has to either always lie or else cease to be a liar. And that is entirely what the argument hinges, the idea that if a man tells the truth even once in his life he ceases to be a liar. But there’ no basis for such a claim. A liar is a man who lies at least some of the time,nothing more. David’s statement, ‘Every man is a liar’ can be true, and David can still be liar because he speaks untruths at other times.
No, it wouldn’t end Jerome’s paradox, because the paradox is based on a logical fallacy. In stepwise fashion, Jerome’s argument runs:
- David is a man
- David says “*All *men are liars”.
- Liars *sometimes *do not tell the truth.
- Therefore David says “No man can *ever *tell the truth.”
- If David was speaking the truth at (4) then (4) is false.
- If (4) is false then Davis was speaking the truth at (4).
- Goto 6.
Stipulating that only some men, including David, are liars won’t solve the “paradox”, because Jerome’s argument relies on the undistributed middle, that all men are liars all the time. So long as *any *of David’s statements can be proven true then, obviously, David can’t be a man.
But as I’ve said, it’s not a real paradox anyway. It’s just the result of a rather blatant logical fallacy. Once you remove the fallacy the argument becomes:
- David is a man
- David says “All men are liars”.
- Liars *sometimes *do not tell the truth.
- Therefore David says “No man has *always *told the truth”
- If David was speaking the truth at (4) then he still would have told lies in the past, and doubtless told more in future.
- Therefore what David said at (4) is perfectly true.
- End
(But we’re all agreed, right, that there’s a genuine puzzle to be solved concerning sentences like “This sentence is false”, right?)
Sure. But there’s no such genuine puzzle for “All sentences are false”.
Right. Just making sure.
That doesn’t resolve the paradox though. You are using information that “Some Guy” didn’t provide you with in order to ascertain the veracity of his statement. You can’t do that and produce a valid conclusion. What you are trying to do is to insert intuitive information for which you have no basis. If some guy is a liar, then there may be other men out there who don’t happen to be liars, but since you have absolutely no evidence for the existence of such men so you can’t conclude anything from their putative existence. The point of logical reasoning is to state all your premises and facts quite clearly at the outset. You can’t just introduce information from the outside willy-nilly and expect to reach a logical conclusion.
It might help if you imagined a more fanciful scenario. The Martians send a single delegate to Earth. It tells us that every sentence that every Martian delegate speaks is a lie. It then tells us that they will invade the Earth, killing us all if we don’t brutally torture him to death. What do you do, what do you do?
Obviously this is pretty fanciful, but it serves to illustrate the point of the exercise. The paradox really does exist. Sure, you can solve it or at least optimise your actions by bringing in other information, but that’s not the point. You are supposed to see if it can be resolved using the information from just a single source. The point of the fanciful scenario is to show what happens when you can’t bring in any outside information, including your intuitive knowledge of how the human mind works.
Yeah, there is. This time it’s the Venusians. They send us the following letter"
Care to solve this non-genuine puzzle, without introducing any outside information? What is your course of action, using only the information contained in this letter?
No, I’m saying there’s nothing paradoxical about the statement unless we add in extra information we’re not given by “Some Guy”.
To borrow an example from Raymond Smullyan, there’s nothing paradoxical about the following statement: “Al is taller than Bill.” It would, I suppose, become paradoxical if we go on to add another statement: “Bill is taller than Al.” But that first statement creates no paradoxes until and unless we insert extra information.
No, I’m trying to say that inserting extra information is the only way to turn a sentence that’s not necessarily paradoxical into one that is – be it All Men Are Liars or Al Is Taller Than Bill.
Well, yeah, in that it’s not a paradox.
I’m not sure I understand what you’re asking. Until we get to that last bit, any given sentence in the letter might be true or false; that last sentence is false, but that (a) gives us no insight whatsoever into the truth or falsehood of any other sentence in the letter, sure as it (b) introduces no paradox. There are puzzles that can be solved without additional information; this ain’t one of 'em.
“Lie” has a definition, it means telling an untruth. Therefore a self-referential inclusion of the word “lie” has a bearing on the truth value of the statement.
Can you please tell us how “Tall” gives you any ability at all to determine the truth value of a statement that includes the word?
If it is not a paradox then you will be able to lay out the argument that allowed you to determine the truth value of the statement. Please do so.
Please lay out the the argument that allowed you to determine the truth value of the statement.
I have already laid out the arguments that show that you logically cannot determine the truth value. At this stage, rather than simply asserting that you can determine such truth values you really need to show us how you reached that determination.
If you can’t do that then you really have nothing but an argument from assertion.
Exactly. The truth value can not be determined using the information to hand, despite the truth value being stated blatantly in the statement itself.
This is why it is called a paradox.
The sentence contained in the p.s. must be false. If it were true, it would be false, so it can’t be true. And there is no contradiction in saying that it is false–for it to be false, it simply has to be that Venusians sometimes say things that are true.
ETA: A simpler example.
Dear Earthlings:
Cats typically have fur. Also, everything we say is false.
Love, the Venusians
In that letter, the sentence “everything we say is false” is false.
No, that’s not what a paradox is. Look, imagine I’m on trial for murder – and upon telling everyone in court that I didn’t kill her, I emphatically add that “I’m telling the truth!” Or, if you prefer: “I never lie!” Or: “Everything I’ve told you is true!” Or compound it for clunkiness: “I’m not lying when I say I didn’t kill her!” Or whatever.
Despite the truth value being stated blatantly in the statement itself, you can’t determine the truth value from the information at hand: maybe I’m lying, maybe I’m telling the truth. That’s not a paradox.
“The sentence following this one will be false. The previous sentence was true.” That’s a paradox. Assume for the sake of argument the first sentence is true; the second would have to be false, which means the first would have to be false. Assume for the sake of argument the first sentence is false; the second would have to be true, which means the first would have to be – true. That’s a built-in contradiction. Does Not Compute.
It’s one thing when you can’t determine the truth value from the info given, but the statement could be true or false – be it “I’m taller than my brother” or “I never lie”. You need something more for a paradox.
Well, in the statement “I’m taller than my brother”, it can be true or false – which is a vast improvement over “The sentence following this one will be false. The previous sentence was true.” Likewise, with regard to the lone Martian:
Sure. Either he was lying or telling the truth when he said that every sentence that every Martian delegate speaks is a lie. Assume for the sake of argument he was telling the truth: such Martians always lie in such circumstances. The sentence must then have been a lie – which means he was lying. Assume for the sake of argument he was lying; such Martians don’t always lie in such circumstances – which means he was lying, just like we assumed. That’s not yet a paradox; it’s entirely possible that he sometimes lies and sometimes tells the truth, and lied in his statement about how Every Sentence That Every Martian Delegate Speaks Is A Lie, and he then sometimes lies and sometimes tells the truth in later statements.
We need more for a paradox. As for the Venusians:
If you’re a Venusian, and you write that, for cultural and biological reasons, all sentences written by a Venusian are false – well, look, that’s either true or false. If we assume it’s true, then the sentence is false, which means it’s false. If we assume it’s false – again, we can have it play out false quite uncomplicatedly.
I guess it depends on how you define “liar”.
I disagree; as far as I can tell, there’s no paradox whether we define “liar” to mean “one who sometimes lies” or “one who always lies”, since no necessary contradiction follows either way.
Let’s say “liar” means “one who sometimes lies”. Imagine a man tells you that all men are liars; assume, for the sake of argument, that his statement was true; if so, then he’d be a liar (by dint of being a man), which means he sometimes lies, which means his statement may have been a lie or may have been true (and we were assuming it was true). If, on the other hand, we assume for the sake of argument that his statement was a lie – well, then, he’s a liar (since we’re assuming he lied) sure as not all men are liars (since we’re assuming he lied about whether all men are liars). So maybe it’s true, and maybe it’s a lie; that’s not a paradox.
Let’s say “liar” means “one who always lies”. Imagine a man tells you that all men are liars; assume, for the sake of argument, that his statement was true; if so, then he’d be a liar (by dint of being a man), which means he’d always lie – which means his statement must have been a lie, so we can’t assume it was true. So don’t assume it was true; instead assume for the sake of argument that his statement was a lie, which means that not all men are liars – in which case it’s possible that he always lies, but so what? We can assume it was a lie; that’s not a paradox.
Again, if you want a paradox: “The next statement is false. The previous statement is true.” If we assume the first statement is true, then the second would be false, which means the first would be false; that’s a no-no. So don’t assume it was true; instead assume the first statement is false, which means the second is true, which means the first would be true; that’s a no-no. So we can’t assume it’s true, and we can’t assume it’s false; it’s false if it’s true, and it’s true if it’s false; that’s a paradox.