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.
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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?
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!
Terrapin Station wrote: ↑January 12th, 2022, 8:55 pm What's true or false is a proposition.Best thing I've read in a week. Kudos to you.
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.
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