The Liar Paradox

WanderingGaze22 · Post by **WanderingGaze22** » January 12th, 2022, 3:36 am

This is similar to my past post, except it debates whether or not this is a lie: Suppose someone tells you “I am lying.” If what they tell you is true, then that person is lying, in which case what they tell you is false. On the other hand, if what is told is false, then they are not lying, in which case what is told is true. In short: if “I am lying” is true then it is false, and if it is false then it is true. The paradox arises for any sentence that says or implies of itself that it is false (the simplest example being “This sentence is false”). It is attributed to the ancient Greek seer Epimenides (fl. c. 6th century BCE), an inhabitant of Crete.

The paradox is important in part because it creates severe difficulties for logically rigorous theories of truth; it was not adequately addressed (which is not to say solved) until the 20th century.

Michael McMahon · Post by **Michael McMahon** » January 12th, 2022, 6:17 pm

Would it make any difference if they said they were lying in the introduction or the conclusion of their piece? So if it was written at the end of a piece then everything before it would be suspect. When it's stated right at the start then everything that comes after it will be uncertain. So the time-frame of the statement is important. The validity of other statements can be used to infer whether the deceit applied antecedently or subsequently.

Michael McMahon · Post by **Michael McMahon** » January 12th, 2022, 6:19 pm

You'd need to ask them for clarification; I "was" lying or I "will" be lying!

Michael McMahon · Post by **Michael McMahon** » January 12th, 2022, 6:23 pm

This is a cool thread. I'm lying. It's a terrible thread.
vs.
This a terrible thread. I'm lying. It's a cool thread.

Michael McMahon · Post by **Michael McMahon** » January 12th, 2022, 6:31 pm

Some anti-humour might be appropriate!
https://www.youtube.com/watch?v=fhIdbRp6xeg
Borat - Not Joke (full scene)

Michael McMahon · Post by **Michael McMahon** » January 12th, 2022, 6:38 pm

I'm lying that I'm lying means it's true seeing as a minus times a minus is a positive.

Michael McMahon · Post by **Michael McMahon** » January 12th, 2022, 6:41 pm

I'm lying that I'm telling the truth means that I'm ultimately lying since a negative times a positive is a negative.

Michael McMahon · Post by **Michael McMahon** » January 12th, 2022, 6:49 pm

I'm not lying is another way to say I'm lying that I'm lying.

Terrapin Station · Post by **Terrapin Station** » January 12th, 2022, 8:55 pm

What's true or false is a proposition.

We have to predicate something of a subject, and then that claim will be true or false.

For example, we can predicate whiteness for a particular cat--"Fluffy is white." And a proposition such as that is what's true or false. If we add "true" or "false" to the sentence, it looks like this: "Fluffy is white is true." Or "Fluffy is white is false."

So, in other words, what comes before "is true" or "is false" has to be a proposition. It has to claim something. "True" and "false" tells you whether what was claimed obtains. "P is true"--that only makes sense if P is a proposition. And then "is true" tells us that (supposedly), the proposition P, what was claimed, what was predicated of a subject, is the case/it obtains.

"Lying" functions similarly to "false." If we're lying, it has to be with respect to something we claimed. And then "is (or was) lying" tells us that what was claimed wasn't what the person believes to be the case.

So if we ONLY say, "I am lying," we have a problem. "Am lying" is supposed to be about a proposition. But "I" isn't a proposition. It doesn't claim anything. So although "I am lying" in isolation may appear to be substantive, it might appear to be saying something, it really isn't. It's equivalent to saying something like "This is false" in isolation. "This" isn't claiming anything. It's not predicating something of a subject. It's not a proposition. So it can't be true or false. Only propositions can be true or false. The same would go for "This sentence is false." "This sentence" isn't a proposition.

Likewise "am lying" can only be about propositions. And "I" isn't a proposition.

So the solution is that "I am lying," said in isolation, and not about some particular proposition, is basically an "illegal formation," like dividing by zero.

RJG · Post by **RJG** » January 13th, 2022, 8:58 am

WanderingGaze22 wrote:...if “I am lying” is true then it is false, and if it is false then it is true.

There is no real paradox here. The answer depends on what is being referred to. Does "it" refer to the statement itself, or to the person uttering the statement?

It is one or the other. Falsely equivocating the TWO different reference points as ONE in the same reference point is the "trick" behind this so-called paradox.

WanderingGaze22 wrote:The paradox is important in part because it creates severe difficulties for logically rigorous theories of truth; it was not adequately addressed (which is not to say solved) until the 20th century.

Not so. Paradoxes are not real (much like "magic" is not real). Paradoxes are just tricks/puzzles yet to be solved, nothing more significant than that!

Post by **LuckyR** » January 14th, 2022, 2:53 am

Terrapin Station wrote: ↑January 12th, 2022, 8:55 pm What's true or false is a proposition.

We have to predicate something of a subject, and then that claim will be true or false.

For example, we can predicate whiteness for a particular cat--"Fluffy is white." And a proposition such as that is what's true or false. If we add "true" or "false" to the sentence, it looks like this: "Fluffy is white is true." Or "Fluffy is white is false."

So, in other words, what comes before "is true" or "is false" has to be a proposition. It has to claim something. "True" and "false" tells you whether what was claimed obtains. "P is true"--that only makes sense if P is a proposition. And then "is true" tells us that (supposedly), the proposition P, what was claimed, what was predicated of a subject, is the case/it obtains.

"Lying" functions similarly to "false." If we're lying, it has to be with respect to something we claimed. And then "is (or was) lying" tells us that what was claimed wasn't what the person believes to be the case.

So if we ONLY say, "I am lying," we have a problem. "Am lying" is supposed to be about a proposition. But "I" isn't a proposition. It doesn't claim anything. So although "I am lying" in isolation may appear to be substantive, it might appear to be saying something, it really isn't. It's equivalent to saying something like "This is false" in isolation. "This" isn't claiming anything. It's not predicating something of a subject. It's not a proposition. So it can't be true or false. Only propositions can be true or false. The same would go for "This sentence is false." "This sentence" isn't a proposition.

Likewise "am lying" can only be about propositions. And "I" isn't a proposition.

So the solution is that "I am lying," said in isolation, and not about some particular proposition, is basically an "illegal formation," like dividing by zero.

Best thing I've read in a week. Kudos to you.