The Liar Paradox. "Truth" for English sentences is not
definable in English.
Proof. Suppose it is. Then so is its complement
"False".
Let s be the sentence "This sentence is false" .
Since the phrase "This sentence" refers to s, we
have
s iff "This sentence is false" iff "s is
false" iff not s.
A contradiction.


This concept, presented as a formal logical
presentation of the traditional liar's paradox "if the
liar says he is a liar, then he is telling the truth,"
can be applied directly to counselling psychology and
conflict resolution.

One of the biggest "relationship breakers" is the
statement "I know I'm right!". There is no effective
response, it cuts off all argument or discussion. An
informal presentation of the liar's paradox
effectively proves that there is no absolute truth:

"So, you know you're right?"
"Certaintly."
"Then, you know when you're wrong?"
"Of course."
"Then, when you're wrong, you're wrong about it?
"What? No, when I'm wrong I'm right!"
"That doesn't make any sense."