If the sentence is true, then it is a lie as it says. But if it is a lie, it cannot be true. A lie cannot also be a truth. So the sentence being true makes it a lie.
On the other hand, if the sentence is a lie, then it is not as it says: it is true. But that is just what the sentence says, which makes the content of the sentence true. So the sentence being a lie makes it true.
Another example is the statement that "there is no cabal". Only a cabal can know if there is no cabal, so this is either a guess, or, it is a cabal trying to pretend it does not exist.
Not all paradoxes are true logical paradoxes, since they can also be common-sense-defying statements that appear true. Some famous examples of this kind of paradox include:
Informal uses of "paradox"Edit
A paradox can also arise in ethics. Assuming power over others may sometimes be required to protect them while diminishing their right to autonomy. This is an ethical dilemma but not a logical paradox.
- "The Definitive Glossary of Higher Mathematical Jargon". Math Vault. 2019-08-01. Retrieved 2020-10-08.
- "Definition of PARADOX". www.merriam-webster.com. Retrieved 2020-10-08.