Paradox of the Liar

9 Jun

This is a well known paradox by Eubulides of semantic meaningless.  Eubulides presents the riddle by saying the following:

“The declaration that I lie will be either true or false. But if this declaration is true, then I lie, and my declaration will be false. But if that declaration is false, then what it says-namely that I lie- is not the case and I must be speaking the truth. Thus either way the truth status being assigned is inappropriate.”

When you read Eubulides’ riddle, how do you think the word ‘liar’ is defined? If a person is a liar, here he is defined as one who cannot tell the truth. When the liar says ‘ I am lying’ there is way too much complexity there to fully know for sure if that person is telling the truth.

Think about it. If a liar says, I’m lying, how can you be sure that he is telling the truth? All truth statements would be wrong in some way. Every form of logic that is formulated is immediately denied because the statement is self contradictory and largely false. Lets try a truth table on this while classifying the statement ‘I lie’ as A

A                          Truth Value of the Statement

T                                       F

Why? If a congenital liar says ‘I lie’, and it is true that he is lying (A), then the truth value of the statement is false. If he says ‘I lie’, and its true that he is lying, then the truth of ‘I lie’ is zero.

F                                     T

Why?  If it is false  as a statement ‘I lie’, then he is not lying making the truth value of the statement true.

I believe that this paradox causes immediate negation when the statement is analyzed for its truth. When Nicolas Rescher explains this paradox in his book Paradoxes, he explains Ruestow’s  4 possibilities of explanation of this paradox.

First, Ruestow states the possibility of  the use of a fallacy in the foundation of the lie statement. My thoughts are that fallacy is not committed when this paradox is laid out. If this were so, you could just go to the beginning of the argument and change some things allowing for the whole paradox to eliminate itself, and I think this paradox to be more complicated than that.

Second, Ruestow’s solutions considered that the argument self destructs due to self negation. I think this is a big possibility, because like mentioned above, when statement A is true, its truth value is false. This denotes some self negation to some extent. However, I do not think the argument self destructs due to this self negation.

Third, Ruestow stated that there is semantic meaningless in the argument because it fails to remain true or false. Also, fourth, that the argument has referential failure. I think that this lie argument has semantic meaningless because when there is meaning, it just goes back to where it started.

My opinion is that there is a mix of the second and third issues in the lie paradox. I think that there is semantic meaninglessness because of how one has to think so hard about the words and how they connect to meaning to even understand the paradox itself. I also think there is self negation, but the argument does not self destruct due to this self negation.

Rescher states in his book the possibility of having a U as a truth value in a truth table because of the semantic meaninglessness and the self negation for these kind of paradoxes. He states this because, it is not fully known if the liar is lying (in case he can possibly tell the truth at times). He also states that this undecided truth value accurately solves the liar paradox because it is often undecided whether or not this person is lying.

So lets recap about the truth values of the statement A (‘I lie’). If statement A is true, then the truth value is false because of the truth in the fact that he is lying. If statement A is false, then the truth value is true because, if it is false that the man is lying, then the truth value of the statement is true. If statement A is undecided, then the truth value is true because it is not stated that he is lying, therefore what he is saying is true.

I think this argument is understood and solved because of how it is known that the argument self negates itself and is semantically meaningless. The argument is never fully solved, but the use of a U truth value makes it easier to grasp. This paradox is well known because of its difficulty of understanding. I have been having a hard time understanding my argument as I explain its properties.

Info was found from Paradoxes by Nicolas Rescher.

Comment below how you think the ‘I lie’ statement is paradoxical and how it is possibly solved.

See you tomorrow at 8pm central time for another dose of philosophical thought.


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