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The liar's paradox may be made visible by uttering the following statement, which I shall call the "liar statement":
"This statement is false."
There are many alternative versions of the liar's paradox. I provide a solution to the paradox in this essay, and it applies to all of the different versions.
The meaning of the statement is quite easy for anyone to understand. It means that the statement itself, is a false one. The statement is well-defined.
We can assign a truth-value of "true" to the statement simply by uttering it. After this assignment, we can use the statement's meaning and truth-value together with simple logic to assign the truth-value of "false" to the statement. Therefore, assigning a truth-value of "true" to the liar statement leads to a contradiction.
We can start-over, and assign a truth-value of "false" to the statement instead. After this assignment, using the same argument as above, we can then assign a truth-value of "true" to the statement. Therefore, assigning a truth-value of "false" to the liar statement leads to a contradiction.
We have proven that we cannot successfully assign a truth-value of either "true" or "false" to the liar statement.
Most people believe throughout their lives that every well-defined english statement has to be either true, or false, and cannot be both true and false at the same time, nor can it be neither true nor false. This is the source of the paradox.
So either the life-long held belief is false, or the argument presented above is flawed.
Most people will have so much trouble abandoning their life-long held belief, that the liar's paradox will remain in their head as an unsolved paradox for a very very long time.
In section 3 above, I have proven that we cannot successfully assign either "true" or "false" to the liar statement. The liar statement is a well-defined english statement, as explained in section 2 above. This proves that the life-long held belief is false. And it also proves the following statement:
Not every well-defined english statement is either true or false.
I hope I have helped to show you that even your life-long held beliefs may be wrong.
You need to stop blindly believing in everything you've believed in so far, and start testing every statement you have believed in for years. You should only fully believe in the statements that you have logically proven to be true. This is the only way to avoid living in a world of lies.
Liar's Paradox, by The Humanoid