What is a good example of a paradox?

[Edwardo Piet]

That wasn't the point of my question. The point is that "I always tell lies" is not a paradox, because the definition of a lie is not "a false statement", for starters.

Hmm, the Oxford dictionary offers:

lie2



NOUN

• 1An intentionally false statement.
  ‘they hint rather than tell outright lies’
  
  ‘the whole thing is a pack of lies’
  

Unless "intentional" is the only thing that is different, missing, then your statement seems to vie with the above.

Um.... so you recognize my point and then you ignore it? Intention is extremely relevant.

In fact it's all that's relevant because, more accurately, it's not "an intentionally false statement", it's a statement with false intentions . . . the statement itself doesn't have to be false. That particular dictionary definition is very much not a very good one. A lie is actually a statement that one makes that one believes to be false, regardless of how true or false that statement actually is. A lie is something someone says that they don't actually believe. Whether something is objectively true or false or not is irrelevant. If someone says "2+2=4" but they actually believe that 2+2=5, then they are lying. If someone says "2+2=5", but they genuinely are deluded and believe that 2+2 really is 5, then they are telling the truth. The fact that the first belief is objectively true and the latter belief is objectively false is irrelevant.

Of course, this particular solution to the so-called Liar's Paradox would only work on versions like "I always lie", but it wouldn't work on versions of the Liar's Paradox such as "Everything I say is false" or "This sentence is false."

IMO, Arthur Prior, the creator of temporal logic, offered the correct solution to all versions of the so-called Liar's Paradox.