Philosophy Now Forum

http://en.wikipedia.org/wiki/Eubulides#Paradoxes_of_Eubulides wrote:A man says: "What I am saying now is a lie." If the statement is true, then he is lying, even though the statement is true. If the statement is a lie, then he is not actually lying, even though the statement is a lie. Thus, if the speaker is lying, he tells the truth, and vice versa.

If we define a lie, L, as any false claim contrary to the claimant's belief then:

∀x: L := ¬x ∧ C(x) ∧ B(¬x)

If the claim, x, is "what I am saying now is a lie" then the application of the above definition is:

L := ¬L ∧ C(L) ∧ B(¬L)

A lie is being partly defined as not a lie: this is incoherent. Therefore, if the claim, x, is "what I am saying now is a lie" then it cannot be a lie, and if it is not a lie then it is false. This then shows that a lie cannot be defined as any false claim contrary to the claimant's belief as there is at least one false claim that, even if contrary to the claimant's belief, necessarily is not a lie:

∃x: ¬(L := ¬x ∧ C(x) ∧ B(¬x))

Not every falsehood is a lie.

A possible counter-claim is that a lie need not be false; that a lie is simply defined as any claim contrary the claimant's belief (if I believe that there is another beer but tell you that there isn't then I am lying even if I am wrong and there is another beer):

∀x: L := C(x) ∧ B(¬x)

If the claim, x, is "what I am saying now is a lie" then the application of the above definition is:

L := C(L) ∧ B(¬L)

If the claimant believes that what he is saying now is not a lie then the above definition is satisfied. Therefore, if the claim, x, is "what I am saying now is a lie", then it can be a lie, and if it is a lie then it is true.

Not every lie is a falsehood.

A similar line of reasoning can be used to solve the Pinocchio paradox:

Premise 1. Pinocchio's nose grows if and only if he claims any falsehood
Premise 2. Pinocchio claims "my nose grows now"

If his claim is true then his nose will not grow as it only grows if he claims any falsehood; but his claim is that his nose will grow and so if true his nose will grow. This is a contradiction. If his claim is false then his nose will grow as it grows if he claims any falsehood; but his claim is that his nose will grow and so if false his nose will not grow. This is a contradiction.

If Pinocchio's nose grows, G, if and only if he claims any falsehood then:

∀x: C(x) ∧ ¬x ↔ G

If Pinocchio's claim, x, is "my nose grows now" then the application of the above premise is:

C(G) ∧ ¬G ↔ G

Pinocchio's nose grows if and only if his nose doesn't grow: this is a contradiction. Therefore, if Pinocchio's claim, x, is "my nose grows now", then his nose doesn't grow, and if his nose doesn't grow then it is false. This then shows that Pinocchio's nose does not grow if and only if he claims any falsehood as there is at least one falsehood that, even if claimed, necessarily will not cause his nose to grow:

∃x: C(x) ∧ ¬x → ¬G

The first premise is shown to be false; proof by contradiction.

Hello Yahadreas.
In saying the sentence, "What I am saying now is a lie". The man was telling the truth up to the word now - because he is going to say something. But after the word now, it becomes a lie; because
If he is going to tell a lie, then he is telling the truth about telling a lie. AND so he is going to tell a lie.
If he is going to tell the truth, then he is telling a lie about telling a lie. AND so he is going to tell a (hidden) lie.
In both cases, he is lying.

Also, because the man first told the truth, then he lied, the sentence no longer is a paradox but a half-truth. However, because of the lie attached to the truth, this half-truth becomes a deception - not a truth. The whole sentence is both deceptive and tells a lie.

Skip all of the formal logic.

"What I am saying now is a lie." -> is not a matter or true or false, it's nonsense, a particular answer between true or false.

Being confused by it is silly, like feeling that something is neither cold nor warm but only being able to express it in terms of cold or warm, when it's in fact "lukewarm" (or in Norwegian "lunkent").

Hello The Voice of Time.
Yes, I can see your point.
To explain myself a bit more. Much of my philosophy comes from the branch of psychology. I tend to use that approach to search for 'what is true'. I guess it all depends on how far we want to go down the rabbit hole. The deeper we go the more fearful (to the ego) it gets. In the deep, where among all the confusion lies the truth, like a diamond in the rough.

I support the resolve of the Liar's Paradox that regards the paradox as Austin speech act.

This view has no room for contradictions inside logics per se.

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

This is all just a meaningless game of words.

But it does point out that it is possible to conceive meaningless word phrases that are impossible to meet.

Words don't always have meaning.

Words are sometimes pure nonsense.